Abstracts

A mosquito behavioural dynamics-based Mathematical modelling approach for studying malaria transmission dynamics between growing human and mosquito populations will be presented. The methods of mathematical model development and analysis will be explained. The modelling framework uses nonlinear deterministic ordinary differential equations based on a direct interpretation of the behaviour and life style of the female Anopheles species mosquito by explicitly counting the gonotrophic cycles that each female mosquito must complete during its entire adult reproductive life. The advantages and disadvantages of considering the mosquito's gonotrophic cycle count will be identified and discussed. The simple fact that the female Anopheles species mosquito has a human biting habit is shown to be crucial in the model development phase.

Multiple probing by adult female mosquitoes, as they quest for blood within the human population, is examined in view of establishing measurable indices linked to invasion, mosquito population persistence, and extinction. The equations for the multiple probing model are derived based on the idea that the reproductive cycle of the mosquito can be viewed as a set of alternating egg laying and blood feeding outcomes realised on a directed path called the gonotrophic cycle pathway. There exists a threshold parameter, the basic offspring number for mosquitoes, whose nature is affected by the way we interpret the transitions involving the different classes on the gonotrophic cycle path. The (mosquito only population) model predicts that the non-trivial steady state, when it exists, is stable for a range of values of the threshold parameter but can also be driven to instability via a Hopf bifurcation, and the center manifold theory can be used to compute the amplitude and phase of the oscillating solutions. We see mosquito population fluctuations arising naturally as an important outcome of the modelling process. Our model's paradigm therefore captures oscillations, known to exist in population densities of mosquitoes, without recourse to external seasonal forcing.

The epidemiological model is built on a system of equations representing a demographic model for mosquito population growth dynamics. Some measurable outcomes of the study include a formula for the basic offspring number for mosquitoes as well as the malaria disease transmissibility potential captured by the basic reproduction number for malaria.

We demonstrate the explicit dependence of the sizes of the essential quantities, including the malaria disease reproduction number and the endemic equilibrium, on the sizes of the basic offspring number and the number of gonotrophic cycles that each adult mosquito vector can complete in its entire reproductive life.

The net outcome of this paper is the introduction of an alternate paradigm for Mathematical models for indirectly transmitted diseases that uses malaria as a base case.

The Fokker-Planck equation is a partial differential equation which is a key ingredient in many models in physics. Given that relevant models relate to the description of large systems, quantization of the Fokker-Planck equation should be done in a manner that respects this fact. With this in mind we develop a quantum counterpart of Fokker-Planck dynamics suited to non-commutative analysis within the context of von Neumann algebras. We achieve this by first quantizing the generalized Laplace operator, and by also identifying a potential term conditioned to noncommutative analysis. We next obtain conditions under which the composite term generates Markov dynamics, before in closing examining the asymptotic behaviour of the Markov semigroup thus obtained. We also present a noncommutative Csiszar-Kullback inequality formulated in terms of a notion of relative entropy, and show that for more general systems, good behaviour with respect to this notion of entropy similarly ensures good asymptotic behaviour of the dynamics.

It is well known that in multiple linear regression the least squares estimates of the regression coefficients are not unique when p (the number of variables) is larger than n (the number of units) and even when, for p slightly smaller than n, a unique solution to the least squares problem exists, the estimates can be really unstable making inference completely unreliable.
In this talk we will review different solutions that have been proposed in the statistical literature to tackle these issues and propose some new ones. We will discuss approaches based on the regularization of the predictor covariance matrix and introduce a proposal based on its decomposition into the sum of a low rank and a sparse matrix. We will also address the problem for the completely different perspective of variable screening putting forward a new method based on random projection ensembles.

We discuss dynamic risk assessment and critically consider its commonly assumed features. Then we discuss the different time horizons appearing in some applied context such as pensions. There both short and very long term horizons appear. In this respect we identify horizon risk as the possibility to make a mistake in using a risk measure that is not adequate to the actual time horizon. We shall introduce horizon longevity as an evaluation of such horizon risk. We give examples of dynamic risk measures able to capture horizon risk and constructed via backward stochastic differential equations. In addition we plunge the problem of long horizon into the framework of interest rate uncertainty and see how we can design risk measure that are able to take care of this uncertainty as well. Examples are provided.

A ring is called a V-ring if all simple modules over the ring are injective. The name honours the Argentine mathematician Villamayor who, in the 1970s, was the first to subject rings with this property to a systematic study.
The first known result on V-rings is much older, however. In the 1950s Kaplansky showed, in an unpublished work, that for commutative rings, the V-ring property is equivalent to the ring being Von Neumann Regular (VNR). This equivalence does not hold for noncommutative rings.
VNR rings are, of course, replete with zero divisors (unless they are division rings) a fact which prompted Carl Faith to ask whether there existed V-domains (V-rings with no zero divisors) that were not division rings.
His question was answered in the affirmative in the early 1970s by John Cozzens (a graduate student of Faith) who produced a differential polynomial ring over a differential field that was a V-domain. Cozzens’ example was followed soon thereafter by a further example, the creation of another of Faith’s students, Barbara Osofsky. Hers was a twisted Laurent polynomial ring over a carefully chosen field of nonzero characteristic.
In both cases, stringent conditions needed to be imposed on the ground field in question in order that the corresponding overring be a V-domain. In the case of the differential polynomial ring, the differential field had to be ‘universal’ in the sense that it admits a solution to every linear differential equation. Although motivated by quite different needs, such universal fields had already been constructed much earlier by Kolchin in his pioneering work in differential algebra. These were put to use by Cozzens to produce the first example of a V-domain.
For Osofsky’s twisted Laurent polynomial ring, the analogue of a Kolchin universal field is a field equipped with an automorphism and which possesses a type of ‘algebraic closedness’ in respect of certain linear equations in the ground field that involve the automorphism.
In this paper a systematic method is developed in the spirit of Kolchin's construction of the universal field, which shows that each field equipped with a fixed automorphism may be extended to one which is ‘algebraically closed’ in the (rather loose) sense described above.
The consequence is a rich supply of new examples of V-domains. In particular, we obtain the first known examples of twisted Laurent polynomial rings in characteristic zero that are V-domains.

The COVID-19 Pandemic represented a unique period in our recent history, where many stages of a pandemic occurred with various dynamics, control measures, and forms of data collection. In a retrospective, various models for the COVID-19 pandemic and the associated conclusions will be discussed. The lessons learned in modeling and epidemiology from the COVID-19 pandemic can be extended to other outbreaks, in terms of model dynamics, management strategies, and numerical analyses.

Conjugate gradient method (CGM) is widely acclaimed to be efficient for solving large-scale unconstrained optimization problems. In this paper, new families of Dai-Liao (DL)-type CG methods are proposed using proper combination of the update parameters of DL and Bamigbola-Alli-Nwaeze (BAN) methods. Under some certain assumptions, descent and convergence properties were established for general functions. Preliminary results illustrate that the new schemes can outperform some existing ones.

Keywords: unconstrained optimization, strong Wolfe line search, descent property, global convergence.
AMS subject classification. 49J52, 49J53, 90C30

Weather prediction and climate change studies are crucial for understanding and mitigating the impacts of weather and climate on society and the environment. Deep learning techniques and explainable artificial intelligence (XAI) have emerged as powerful tools for addressing these issues. This study focuses on applying Convolutional Neural Network (CNN) deep learning techniques for weather prediction and climate change studies, incorporating explainable artificial intelligence (XAI). Traditional weather prediction models rely on complex physical equations that are computationally intensive and challenging to interpret. CNN models have demonstrated impressive performance in various weather prediction tasks, such as temperature forecasting, precipitation estimation, and storm tracking. In addition, CNN models have been used to model the complex interactions involved in climate change and predict future climate scenarios. The use of XAI techniques provides insight into the inner workings of these models, allowing researchers to identify which variables have the most significant impact on weather patterns and climate change. The integration of CNN models with XAI can help achieve a more sustainable future by providing interpretable explanations for the model's decisions, building trust in the models, and leading to better-informed policy decisions.

We shall consider the second order non-autonomous nonlinear ordi-
nary differential equations. In the work, different forms of integral
inequalities and two forms of mean value theorem for integrals will be
used to investigate the boundedness of all solutions and their derivatives.

A suitable decision plan is followed as an effective financial management to achieve optimality while investing in a competing stock portfolio. This study altered a Dynamic Programming (DP) model of Bellman. The modified model was used to solve a business problem. The problems of choosing a stock portfolio for optimal return among investors in financial markets have resulted in a financial crisis. Most financial analysts provide investors with incorrect and non-validated investment information. The consequences were minimal optimum, no return, and an investment problem. The goals are to ensure optimality in investor returns, validate the results using two validity tests, and select the test that best validated the model. The silhouette and Dunn tests were used to validate the outcome result. The results of using Silhouette reduced computational complexity and produced a more robust and validated return. The k-means clustering (an aspect of unsupervised machine learning) provides better statistical evaluation, the best fit, and investment patterns. In comparison to previous work, the introduction of variables allowed for the best return at stage one. Finally, a validated investment report can help to avoid mistakes made by market analysts and investors when making decisions on investment.

Molecular Study on the DKP Equation in (1+3) Dimensions with Isotropic Oscillator plus Inverse Quadratic Potential in Non-Commutative Space

O. J. Oluwadare1*, T. O. Abiola1, E. A.Odo1, O. Olubosede1 and K. J. Oyewumi2

1 Department of Physics, Federal University Oye-Ekiti, PMB. 373, Ekiti State, Nigeria
2, Department of Physics, University of Ilorin, PMB 1515 Ilorin, Kwara State, Nigeria

Email Addresses: [email protected]; [email protected], [email protected]; [email protected]; [email protected]
*Corresponding author email: [email protected]

Corresponding author Email: [email protected]
Phone number: +2348032378284

Abstract
Recently, some authors revealed that the study of space non-commutative effect of quantum mechanical systems could provide explanation about deformed structures. The noncommutativity of the space modifies the potential part of the Hamiltonian of the system in such a way that the potential function models under consideration would be perturbed. Using relativistic and/or nonrelativistic equations, few potentials of interest have been considered, which include: hydrogen atom, Coulomb potential, Kratzer potential, modified Kratzer potential among others. With respect to our review, the results obtained under this discourse have not been applied to examine the behaviour of diatomic molecules (H_2,ScH,CuLi,ScN,ScF,I_2), which warrant the study of this type. In this work, the non-commutative spin-one Duffin-Kermer Petiau (DKP) equation in (1+3) dimension with isotropic oscillator plus inverse quadratic potential is solved within the Nikiforov-Uvarov method to obtain eigenvalues and the associated eigenfunctions. The energy shift arises as a result of space non-commutativity is evaluated within the ambit of perturbation theory. Using the molecular constants for some molecules (H_2,ScH,CuLi,ScN,ScF,I_2), the effect of non-commutative space on the behaviour of some molecules are studied. The results revealed that the space non-commutativity modify the bound state energy levels significantly for all the molecules as it was seen that the energy shifts increases for any increase in perturbation parameter θ (which is having the dimension of area).

Keywords: DKP equation; Isotropic oscillator plus inverse quadratic potential; parametric Nikiforov-Uvarov method; Non-commutative space; Perturbation theory; Diatomic molecules.

In this paper, we first propose a relaxed regularization projection method involving only
a single projection for solving monotone bilevel variational inequality problem in Hilbert
spaces and secondly we give an alternated inertial version of the first algorithm. The two
proposed algorithms involve self adaptive step-sizes and the algorithms can easily be implemented without the prior knowledge of Lipschitz and strongly monotone constants of
operators. Under some mild standard assumptions, we obtain the strong convergence of
the two algorithms to the unique solution of the bilevel variational iniequality problem. Moreover, some interesting numerical experiments are given to demonstrate the applicability of the results and also to compare with existing algorithms.

By the inclusion of the two end points of the integration interval as collocation points in addition to the Gaussian interior collocation points, we construct methods which are stable, with fewer function evaluations per step and hence the rate of convergence of the methods is very high. The advantage of these methods as compared, for example, with methods of the conventional type (Gauss, Radau and Lobatto Runge-Kutta methods) consists of the fact that they provide uniform approximations of the solution of stiff systems in ordinary differential equations (ODEs), over the entire integration interval. This is in contrast to the conventional Runge-Kutta methods for which the continuous approximation to the exact solution of ODEs is obtained at the mesh points only. Although the computational cost of these methods is little more than the explicit methods, the advantages gained such as high orders and stage orders, improved region of absolute stability and lower error constants, make the methods suitable for solving stable stiff systems. We demonstrate two potential techniques of applying the collocation methods in order to accomplish the goal of the derivation (To achieve the desired goal of the derivation, we show two possible ways of implementing the collocation methods). Pertinent results are presented in Tables, while efficiency curves are shown in Figures to illustrate the accuracy and efficiency of these methods.


Keywords: Block hybrid scheme, Continuous scheme, Two-Step Runge-Kutta method, Stiff system

Phishing is a very common type of cybercrime attack in which the personally identifiable information of the targets are used for financial gains. The classification of phishing websites from their legitimate counterparts using machine learning architectures has been researched in some of the previous studies, but further study is required in this area as a result of the persistent prevailing attack on websites.
In this research paper, the performance of five machine learning techniques is experimentally compared with one another for the detection of phishing websites. Two publicly available datasets from Mendeley are used. The datasets are divided into two different variations making it a total of four. Each dataset is split into the training set (which is 80% of the dataset) and testing set (20% of the dataset).
StandardScaler and Principal Component Analysis (PCA) are used as data preprocessing techniques on the datasets before they are fed into the machine learning models. The single model that gives the best performance is the Random Forest (RF) in all the variations of the two datasets. In the ensemble models, the combination of Random Forest with Extremely Randomized Tree outperformed others. A key result of this research is that the two models having the same base learner (Decision Tree) outperformed other traditional machine learning models used.

This paper deals with the stability for a Waves Coupled System with a domain control condition of fractional derivative type. We study the existence and uniqueness of solutions and the strong stabilization using semigroups theory and LaSalle’s principle theorem..

Introduction: Regression analysis is conceptually the simplest method used for investigating the functional relationship between dependent and independent variables. Sometimes, however, there might be outliers contained in the dependent variables that is the Y’s values, the independent variables that is the X’s values, or in both Y’s and X’s values. In that situation, many procedures of estimation in either linear or multiple regression models may hardly be precise. An outlier is a data point that is significantly different from the remaining data.
Material and Methods: This study reviews methods of outlier detection in multiple linear regressions using Deffits, Cooks distance, Dfbetas, R-students, and Mahalanobis distance. A set of replication of data sets was generated from the multiple linear regression models with three independent variables. The R-statistic simulation has been used to show the best method for detecting the absence of outliers among the five methods under study.
Result: These five methods have been evaluated and compared. The results obtain from R- simulation yielded that Dfbetas is better than the other procedures for the entire sample sizes and percentage of outliers. Mahalanobis distance was found to be the next best specifically for small sample size and 10% of outliers. The result indicates that the Cook distance and Deffits are more liberal than all other outlier procedures.
Conclusion and Recommendation: It was seen from the result analyzed that the methods of outliers detection are following the same trend irrespective of which of the independent variable contained the outlier. The R-code simulation shows the performance of five outliers detection methods in multiple linear regression, from the five techniques compared Dfbetas, performed better than all the methods for all the sample sizes and all the percentages of outliers.

Keywords: outliers, multiple linear regression, Regressor, R- simulation.

A mortality table, also known as an actuarial life table, provides information about the likelihood or rate of death within a specific population at different ages during a given time frame. These tables are essential for analyzing mortality patterns, projecting population growth, estimating life expectancy, and identifying key factors contributing to high mortality rates within a population. In the context of the insurance industry in Malawi, a notable challenge faced by insurance companies is the absence of mortality tables. Therefore, the objective of this study is to construct ordinary life tables specifically for Malawi, covering the period from 2016 to 2022. The Whittaker-Henderson method is employed in this study to smooth the raw mortality rates, which are then forecast for a five-year period using the logistic regression model. The Malawian ordinary life table constructed has effectively demonstrated that as individuals age advances, the likelihood of mortality also escalates. In addition, it is observed that males exhibit a higher mortality rate comparing to females and further analysis show that pandemics affects the mortality by increasing the rate.

In this work, the problem of non-Newtonian fractional Maxwell fluid in an oscillating pipeline was considered. An analytical solution of fluid velocity was derived using Bessel transform and solution was simulated with the use of Mathcad software and graphical results for different flow was analyzed. Results show that the flow performance of fractional Maxwell fluid has distinct behavior with corresponding ordinary Maxell model in pipeline. The retardation waveform of oscillating motion can result in a higher flow performance.

Abstract: In this paper, we examine the 8 by 8 S8 S-boxes used in popular block ciphers. The analysis can be extended to S-boxes of other sizes without losing generality. An S-box is statistically assessed to determine whether it is appropriate for use in image encryption applications. By analyzing various parameters generated by numerous statistical analyses, an encryption based on the S-box can be evaluated for strength. In order to make informed decisions, it is imperative that one is aware of the significance of results from different types of analyses, as well as the relationships between them. As a result, we developed a criterion based on majority logic assessment that carefully examines and scrutinizes the available parameters. In the first step, a correlation analysis is performed. Using correlation information, this method determines the similarity between the pixel patterns in a given image and its encrypted version. Due to its importance and acceptability in comparing and determining similarities between images, this analysis has been widely used to evaluate various image encryption algorithms. There are instances when correlation analysis does not provide sufficient information to determine the strength of encryption; therefore, in order to enhance the reliability of the decision, we employ additional techniques, including entropy analysis, contrast analysis, homogeneity analysis, energy analysis, and mean absolute deviation analysis.

This paper investigates the flow of heat transfer of the non-Newtonian behaviour of fluids, oscillating motion of fluid flow in a capillary tube resulting in an increase of heat transfer coefficient. In the current investigation, an oscillating motion of fluid flow in a round tube was investigated to determine a sinusoidal waveform effect on the heat transfer coefficient. The analytical solutions of both velocity and temperature distributions were obtained using Bessel transform and solution was simulated with the use of Mathcad software and graphical results for different flow was analysed. Results show that the heat transfer coefficient of the oscillating flow depends on the fluid properties and oscillating waveform. The retardation waveform of oscillating motion can result in a higher heat transfer.

Many physical problems in real life can be modeled as nonlinear problems involving different types of mappings. Finding exact solutions of such nonlinear problems analytically is difficult. Thus, introducing different algorithms for approximating solutions of nonlinear problems has become of much interest once the existence of solutions to such problems is known. One of the methods is to transform the nonlinear problems into Hammerstein integral equations. Several nonlinear problems that arise from differential equations, for instance, elliptic boundary value problems whose linear parts possess Green’s functions can be transformed into Hammerstein type equation problems.

In this study, we introduced and studied a more general problem called Split Equality Hammerstein Type Equation Problem. This problem combines two Hammerstein type equation problems which are defined in two different Banach spaces.

An inertial iterative algorithm is introduced to approximate a solution of the split equality Hammerstein type equation problem in general reflexive real Banach spaces. Strong convergence results are established under the assumption that the associated mappings are monotone and uniformly continuous. Finally, we have provided a numerical example to validate our theoretical findings.

The results in this paper generalize and improve many of the existing results in the literature in the sense that the underlying mappings are relaxed from Lipschitz continuous to uniformly continuous and the spaces under consideration are extended from Hilbert spaces to reflexive real Banach spaces with a more general problem which includes the Hammerstein type equation problems.

Women are frequently considered as a vulnerable gender group in most third-world nations; yet, the catastrophic and humiliating repercussions of ill health, such as VVF, make them even more vulnerable in these societies, revealing their emotional fragility.
The vesico vaginal fistula (VVF) problems in Jahun General Hospital occur in the presence of lack of knowledge and early marriage of teenage girls and some disease, and the most common system of vesico vaginal fistula VVF is urinary incontinence urine leakage from the vagina, which is often exacerbated by physical activities. Additionally, the patient may develop vulva discomfort, itching, and recurring urinary tract infections.
Information about VVF community awareness will alert health professionals and support groups to the need for primary prevention by raising awareness of the condition in rural communities. VVF prevention necessitates strategies to educate the community on cultural, social, and psychological factors that raise the incidence of fistula. Lack of knowledge, awareness level on contributing factors and Early age of the mother obstetric complication are the most common cause of VVF, which include not only early pregnancy, but also delayed and obstructed labor.
This study employed cross-sectional research design to investigate the relationship between level of knowledge on VVF and awareness level on risk factors contributing to VVF. In this study, the cross sectional study design was used because the purpose of the study was to determine the relationship between level of knowledge on VVF and level of awareness on the risk factors contributing to VVF at the Jahun General Hospital.
The findings of this study revealed that there is a lack of knowledge of VVF in the Jahun and the communities around. This could be due to a lack of awareness efforts aimed at raising women's understanding contributing factors, and prevention of VVF. According to the findings, the respondents had inadequate knowledge of VVF. As a result, they lacked the necessary understanding about the occurrence of VVF. Health of women in Jigawa State and Nigeria as a whole is a major concern. The government must be fully prepared for girl child education because the majority of women who are victims of this threat lack formal education, and the majority of cases occur during the first pregnancy. Jigawa state government should put more serious on issues of women and maternal health which put woman health in jeopardy.
Keywords: Vesico-vaginal fistula, Awareness, pregnancy, cross-sectional research, Data

The impact of the increased Lassa fever infection can better be understood when considering the various possible transmission routes. In recent times, multiscale models have also been used to describe infectious disease systems in terms of the complete pathogen life cycle which represents multiple targets for control. We designed a mathematical model for the epidemiology of Lassa Fever to determine the effect of transmission pathways toward the infection progression in humans and rodents including those usually neglected such as the environmental surface and aerosol routes. We also investigated the disease dynamics incorporating the collection of individual pathogen loads. We analyzed the model and carried out numerical simulations to determine the effect of each transmission routes, control of the viral loads in the different population with their cost effectiveness. Our results show that it is important to consider multiple transmission routes as a better estimate of the Lassa fever burden and equipped us with useful recommendations from the control interventions.

Ebola virus disease (EVD) is one of the most highly stigmatised diseases in any affected
country because of the disease’s high infectivity and case fatality rate. Infected individuals and most especially survivors are often stigmatised by their communities for fear of contagion. We propose and analyse a mathematical model to examine the impact of stigmatisation of Ebola survivors on the disease dynamics. The model captures both the internal stigmatisation experienced by infected individuals after witnessing survivors being stigmatised and the external stigmatisation imposed on survivors by their communities. The results obtained from our analysis and simulations show that both internal and external stigma may lead to an increase in the burden of Ebola virus disease by sustaining the number of infected individuals who hide their infection and the number of unsafe burials of deceased Ebola victims. Strategies that seek to put an end to both forms of stigmatisation and promote safe burials will therefore go a long way in averting the EVD burden.

How do terrestrial female mosquitoes that fail in their attempt to draw blood from humans impact mosquito populations and vector-borne disease dynamics? When female mosquitoes interact with humans, they may succeed to obtain blood or fail in their attempt. For those waiting mosquitoes that failed but lived to try again and succeed, what impact do their second or later successful attempts have on mosquito populations and disease, and how can the results be exploited for control? We use a system of nonlinear differential equations derived based on the idea that the reproductive cycle of mosquitoes can be viewed as a set of alternating egg laying and blood feeding outcomes realized on a directed path called the gonotrophic cycle pathway, to investigate the aforementioned questions. Results from the model analyses reveal that waiting class mosquitoes contribute positively in sustaining mosquito populations as well as increase their interactions with humans via increased frequency and initial amplitude of oscillations. We identified a threshold parameter, the basic offspring number for mosquitoes, whose nature is affected by how we interpret the transitions involving the different classes on the gonotrophic cycle path. The trivial steady state for the system, which always exists, can be globally asymptomatically stable when the threshold parameter is less than unity. The non-trivial steady state, when it exists, is stable for a range of threshold values but can also be driven to instability via a Hopf bifurcation.

This research focuses on investigating the synergistic effects of combining two oncolytic viruses for cancer treatment. Oncolytic virotherapy involves the use of genetically engineered viruses that infect, multiply and directly lyse tumor cells with less-severe side effects compared to the traditional cancer treatments, for example chemotherapy. The main aim of this paper is to develop and analyse mathematical models that describe the synergistic effects of combining two oncolytic viruses. A combined analytical-numerical approach has been used to characterize the transient and qualitative dynamics of the models.

Modelling noisy data in a network context remains an unavoidable obstacle. More so, random matrix theory comprehensively describes network environments effectively. Thus it necessitates the probabilistic characterisation of these networks (and accompanying noisy data) using matrix variate models. Denoising network data using a Bayes approach is not common in surveyed literature. Thus we briefly introduce a new matrix-variate t model in a prior sense for the noise process following the Gaussian graphical network, for the cases when the assumption of Gaussianity is violated in the model and cases when normality is no longer sufficient to explain variation in the data. We investigate the performance of this matrix-variate t distribution applied to a network setting within a Bayesian context. Calculation and approximation of the resulting posterior are of interest to assess the considered model’s
network centrality measures, which we illustrate using real-life stock price data.
Keywords: Adjacency matrix; Bayesian estimation; Gaussian graphical model; Matrix-variate t; Network; Precision matrix; Stock price data.

For many years, experts have recognized the complex nature of rainfall, considering it as one of the prime examples of highly non-linear and intricate systems. In recent times, rainfall patterns have become increasingly inconsistent. This paper focuses on a state space approach that utilizes dynamic linear models (DLM) to effectively model annual rainfall in Katsina metropolis from 1949 to 2019. By hybridizing trend, seasonal, and regressive components, this method allows for a natural interpretation of the data. The DLM model's parameters are estimated, and its validity is assessed through residual analysis, which reveals that the residual auto-correlation function (ACF) is uncorrelated and follows a normal distribution. The validated DLM model is then employed for one-step-ahead forecasts of annual rainfall. Comparing the predicted values with the observed annual rainfall series demonstrates a close match, indicating that the model accurately replicates the actual data. Consequently, the model is considered suitable for representing annual rainfall of Katsina allied.

Characterization of an antenna’s far-field radiation profile is very important in antenna design. It describes the radiated power of the antenna in different spatial directions. The advent of 5G and other devices with increasing power, controllability, and potential for secondary lobes to damage other devices when in high power regimes makes the characterization highly necessary. It is well known that the phase is oftentimes more crucial than the amplitude in reconstructing a signal's far field profile from its spherical mode coefficients (SMC). However, in many real-life measurement systems, only the square of the amplitude of the SMC of the underlying signal is available. This may be due to the fact that the phase is lost or expensive/impractical to measure. The problem of reconstructing a signal from its phaseless measurement is known as phase retrieval problem. In this research, we extend the recent convex optimization technique for phase recovery from Fourier measurements with random mask to the case of antenna measurement. Our numerical results confirm the success of this approach to the new case study.

COVID-19 infection caused a lot of damage in many countries. In South Africa, the burden was exacerbated by a number of factors, and among them, social factors such as stigma and the presence of defaulting self-isolating individuals were confounding in their contribution to the COVID-19 burden. We investigate the effects of COVID-19-related stigma on the dynamics of COVID-19 infection when self-isolating infectious individuals default on isolation regulations. A deterministic model will capture the COVID-19 dynamics and be calibrated with COVID-19 wave data from South Africa. The associated continuous-time Markov chain model will be used to determine the important thresholds using the multitype branching process. The results obtained in this paper showed that stigmatized and defaulting self-isolated individuals have an impact on spreading COVID-19 disease. We discovered that the probability of disease extinction increased with each successive wave, but the presence of stigmatized and defaulting self-isolating infectious individuals in combination with other infectious individuals slowed the rate of improvement over time.

In this work, we explore the application of multi-domain based spectral method for solving singular nonlinear hyperbolic partial differential equations (PDEs) over large computational domains. In the solution algorithm, the nonlinear PDEs are first re-worked into a linearized form of an iterative scheme, using quasilinearization method. The space domain is divided into overlapping sub-intervals of equal length, whereas the time domain is decomposed into equal non-overlapping sub-intervals. Bivariate Lagrange interpolating polynomials constructed using Chebyshev-Gauss-Lobatto points, are used to approximate the solutions to nonlinear PDEs. In the time domain, numerical solutions are computed independently in each sub-interval, and the continuity condition is used to get initial conditions for the subsequent sub-intervals. On the other hand, PDEs are solved simultaneously across the overlapping sub-intervals in space. The efficacy, stability and accuracy of the method are demonstrated by presenting error analysis, condition numbers and computational time for the solution of some examples of singular nonlinear hyperbolic PDEs arising in fluid mechanics. The accuracy of the scheme is also validated by comparing approximate solutions with existing exact solutions. The adoption of domain-decomposition technique is effective in minimizing numerical challenges that are associated with large matrices and ill-conditioned nature of the resultant coefficient matrix. The obtained results confirm that the method is highly accurate, stable, computationally cheaper, and converges rapidly when solving singular nonlinear hyperbolic PDEs using fewer grid points.

We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance, insurance, epidemiology, seismology and other fields.

We show that the model is arbitrage-free and incomplete by proving a general result on the existence of a family of equivalent (local) martingale measures. In addition, we derive Thiele's PIDE for unit-linked life insurance policies in this stochastic volatility model. The established and practical method to compute reserves in life insurance is by solving Thiele’s equation, which is crucial to guarantee the solvency of the insurance company.

Solving Mixed Integer Nonlinear Chance Constrained
Optimization and Applications
Agegnehu Tesfaye 1;∗,Dr.D.Sc Abebe Geletu, AIMS,Rwanda2;∗ and Dr.Birhanu Guta, AAU2
Abstract
Mixed Integer Nonlinear Chance Constrained Programming Problem (CCMINLP) has many
application in engineering areas.However because of the structural nature CCMINLP, it is
very difficult to solve this types of problem by existing solvers. The main difficulty comes
from NP nature of MINLP and evaluation of the probabilistic constraint by usual method.
Therefore, in our work we propose two new approximating approach, namely inner and outer
approximation approach. We approximate the probabilistic constraint by continuously and
differentiable function and then the optimization problem approximated by sequence of parametric nonlinear programming problems(NLPs) which can be solved by NLP solver. In our
work, we also discussed the feasibility and convergence nature of optimal solution of approximated problem to the original CCMINLP. We also showed the solution of both inner and outer
problems, respectively converge to the solution of CCMINLP problem. The expected value of
the objective function at each iteration is evaluated by sample average approximation method.
In our study, the algorithm continues to solve the sequence of inner and outer approximated
problems until the pre-specified tolerance is satisfied. Then the obtained optimal solution of
approximated problem at this stage become an optimal solution of the ordinal problem.

Keywords: Mixed integer nonlinear chance constrained optimization , inner approximation ,outer approximation,sample average approximation

This research investigates the application of Generative Artificial Intelligence (AI) technologies, specifically exemplified by ChatGPT, in the conceptualization, analysis, and implementation of block hybrid methods for solving initial and boundary value problems (IVP/BVPs). The study establishes the efficacy of these AI tools in systematically generating pseudo-code, which can be easily translated into multiple programming languages, including Matlab, Mathematica, and Python, for the purpose of solving numerical schemes. Beginning with elementary single-equation systems, the AI technologies are utilized to scale the algorithms to accommodate complex systems of equations. Additionally, the study integrates accuracy-enhancing techniques such as adaptive step-size adjustment. This work underscores the substantial benefits that Generative AI offers in advancing the field of numerical analysis, particularly in developing sophisticated algorithms to solve intricate mathematical models framed as initial or boundary value problems.

This study considers the optimal investment and reinsurance strategies under the Geometric Mean Reversion (GMR) model when the insurer pays federal income tax on the dividends. A Brownian motion with drift is used for modeling the insurer's surplus process. The financial market consists of one risk-free asset and one risky asset whose price process satisfies the Geometric Mean Reversion (GMR) model. The objective of the insurer is to maximize the utility of terminal wealth. In the framework of stochastic control, explicit expressions for optimal strategies are derived. Additionally, a number of intriguing results are obtained, and numerical simulations are presented to demonstrate our findings.

This study is concerned with a theory of two-step nucleation and growth of crystals in a metastable liquid. This mechanism is that the crystalline nuclei formation occurs in dense liquid clusters suspended in the solution. These clusters contain the higher solution concentration and viscosity, leading to lower surface free energy barrier and faster phase transition route. The theory is based on varies growth laws of crystals during the two-step bulk phase transformation. At the first initial stage, the crystals evolve in a diffusion limited environment with almost unchanged supersaturation. At the second stage, they become larger, move beyond these clusters and evolve in accordance with the hyperbolic tangent law. A generalized particle growth law joining the first and second stages is obtained by stitching the diffusion limited and hyperbolic tangent laws. On this basis, an integrodifferential model of the evolution of a polydisperse ensemble of crystals was formulated and solved. The crystal-size distribution function increases and the solution supersaturation remains practically unchanged until the particle size corresponds to a switch in the particle growth rate from a diffusion-limited branch to a hyperbolic tangent branch. This is followed by an increase in the crystal growth rate, a decrease in the distribution function and solution supersaturation. Then the distribution function increases up to the maximum size of crystals grown in the solution. A sufficiently long time interval of almost constant supersaturation and the N-shaped behaviour of the distribution function are the consequences of a two-step nucleation mechanism of crystals with switching of their growth rates.

This work was financially supported by the Russian Science Foundation (project no. 23-19-00337).

This study extends a post-Keynesian methodology for measuring cyclical economic growth, initially proposed by Goodwin in 1967. We consider the perpetual class conflict between capitalists and the labor force as endogenous factors whose manipulation and interpretation yield a measure of economic growth. The study focuses on the competitive dynamics between growth in real wages, and its effect on consumption, profitability, and employment. The main aim of this study is to consider the effect of a baseline net income, given a labor force population with a bounded growth rate. The study uses coupled ordinary differential equations of the Lotka-Volterra type with a focus on the existence and nature of endemic steady-states, limit cycles, and bifurcations. The results provide further evidence of the symbiotic contradictions of capitalism and correspond to those that exist in literature. This work also contributes to the question of optimality as far as the timing of economic booms and recessions is concerned. The model affirms the need for baseline net income as a necessary condition, albeit insufficient, for the perpetual stability of the endemic steady-states, to maintain a sustainable relationship between employment and profitability, inherent factors of natural economic growth.

In this talk, we study some properties of a Bishop - Phelps (BP) cone. The existence of a non - solid BP cone in a non - reflexive Banach space is investigated. We present the partial result of I Polyrakis et.al to the question posed by Qui for separable non - reflexive spaces with different proof using geometric properties of BP cone. Finally, the extension of I. Polyrakis' result to non-separable spaces has been considered.

The movement of individuals during the COVID-19 pandemic has played a significant role in increasing the spread of COVID-19 variants from one region to another. A deterministic mathematical modelling is proposed to study the contribution of open border in the spread of COVID-19 pandemic in a country. The potential roles played by cross-border movements on the number of detected cases in a developing country are studied. More precisely, we consider cases where persons cross borders through either designated controlled border points with proper facilitation for screening and detection of potentially infected cases, as well as border crossings through uncontrolled points. The persons crossing borders are considered to be either susceptible, exposed or infected with no or mild symptom. These statuses of individuals are incorporated in the model formulation. The basic reproduction number of the model is calculated and the model analysis is given by using the basic reproduction number.
Moreover, a dynamically consistent nonstandard finite difference scheme is proposed to replicate the properties of the continuous model. Finally, Numerical simulations are presented to support the theoretical analysis of the model.

Cervical cancer is the leading cause of cancer deaths among women in Botswana. This burden is mainly due to limited screening uptake and a high HIV prevalence. In this systematic review and meta-analysis, we explored the barriers, facilitators, and cervical cancer screening uptake among women in the country. We identified relevant publications through PubMed/Medline, Scopus, Web of Science, and Google Scholar for a ten year period, using predefined inclusion and exclusion criteria. The selection, assessment, and data extraction process was conducted in duplicate by two researchers. For the analysis, a fixed effects model was adopted to pool evidence on the screening uptake. All selected studies reported on the facilitators while some studies reported barriers to cervical cancer screening uptake on four levels (individual, institutional, community, and policy levels). The most frequently reported barriers were the low level of knowledge and awareness, misconceptions about screening, and delays in receipt of screening results (in some cases no delivery of results). Reported facilitators included high socio-economic status, having health care insurance, and having a personal health care provider. This work will inform interventions for specific groups of women, which will ultimately reduce the burden of cervical cancer in Botswana.

Keywords: barriers; Botswana; cervical cancer; facilitators; screening; meta-analysis; systematic review

Quantification of Spatio-Temporal Variability of Solar Energy Availability in a Short Measurement Scale

1 Fernando Mucomole; 2 Carlos Silva & 3 Lourenço Magaia

1 Eduardo Mondlane University, Faculty of Sciences, Department of Physics, Mozambique (Mz),
2 University of Lisbon, Instituto Superior Técnico, Department of Mechanical Eng., Portugal, Lisbon;
3 Eduardo Mondlane University, Faculty of Science, Department of Mathematics and Informatics, Mz.
Corresponding author’s email: [email protected]

The optimal performance of solar systems has been affected by instability in the operation of solar panels. Motivated by the need to minimize the effects of the increase in solar energy variability that affects solar panels, the objective of analyzing the spatio-temporal variability of solar energy availability on a short measurement scale emerged. The theoretical method was used, which consists of determining the clear sky index to generate random values based on clear sky radiation that uses local atmospheric variables and characteristics, using as materials: the sample of solar radiation data from the southern region of Mozambique, measured in the years 2012, 2013 and 2014. Statistical analysis shows that of the total of around 18 years processed (212 months), distributed across all seasons of the year, Mozambique has mostly clear sky days, to the detriment of intermediate days. From the statistical analysis of frequency density variability, it is shown that the variation in the clear sky index has a central maximum, and gradually decreases as they increase in value. Intermediate sky days show similar behavior to the previous ones, but there is a slight decrease, as the variation in the clear sky index in the interval [-1,1] is greater. It can be concluded from the spatial autocorrelation structures that the values of the clear sky index have a minimum observed in July and a maximum in December and the variations during the daily course of the clear sky index determined according to their standard deviation show a lot of adequacy to the adopted model.

Keywords: Variability; clear sky index; radiation; irradiance; intermediate sky; cloudy sky.

Bibliography: Mucomole, F. V. et al. (2023). Temporal Variability of Solar Energy Availability in the Conditions of the Southern Region of Mozambique; Duffie, A. John & Beckman, A. William (1991), Solar Engineering of Thermal Processes; Lohmann, Gerald M. (2018), Irradiance Variability Quantification and Small-Scale Averaging in Space and Time: A Short Review.

There has been significant interest in the study of flexible and asymmetric probabilistic models during recent decades; with some emphasis on the mode as a more "natural" measure of location than the mean or the median. The practical interpretation of the parameters when they are mode-parameterised is of succinct value when considering finite mixtures in a clustering framework. This work introduces and studies a mode-parameterized inverted Dirichlet model (also known as a Dirichlet type II/multivariate inverted beta distribution) as candidate to model multivariate data in the positive real p-dimensional space, and we demonstrate how the parameterization simplifies its use in various fields of statistics, particularly in nonparameteric and robust statistics. The interpretability and impact of this model is illustrated using real data within a clustering framework, to emphasise the value of the mode viewpoint.

Co-infections of infectious diseases pose significant challenges to public health, particularly in regions where multiple pathogens are endemic. This study presents a mathematical model aimed at understanding the dynamics of the co-infection of Malaria and COVID-19, two of the most prevalent and potentially lethal infectious diseases worldwide. The proposed model integrates epidemiological factors to assess the interactions between these diseases, offering insights into the potential synergistic or antagonistic effects they may have on each other within a population.
Our mathematical framework incorporates parameters related to disease transmission, host immunity, and vector dynamics, allowing us to simulate various scenarios of co-infection dynamics. By analyzing the model's outputs, we explore the impacts of factors such as seasonality, vaccination, treatment availability, and population mobility on the prevalence and spread of both diseases when they coexist in a community.
Furthermore, sensitivity analyses are conducted to identify key parameters that drive the co-infection dynamics and to assess the effectiveness of control strategies, including vector control, vaccination campaigns, and treatment interventions. Our findings highlight the importance of tailored public health interventions and surveillance strategies to address the unique challenges posed by the co-infection of Malaria and COVID-19, especially in regions where both diseases are endemic.
In conclusion, this mathematical model provides a valuable tool for understanding the complex interactions between Malaria and COVID-19 when they co-occur in a population. The insights gained from this study have the potential to inform evidence-based strategies for disease control and resource allocation, ultimately contributing to more effective public health responses in regions facing the dual burden of these infectious diseases.

Geostatistical data is observed from a continuous spatial process. A variogram quantifies the spatial variability of such data. Spatial lattice data, however, is observed from a discrete spatial process. Herein, we extend the variogram to spatial lattice data. In order to increase the number of data points from the centroids of each spatial unit (representative points), multiple points are simulated to more closely represent the continuous nature of the true underlying event occurrences. We thus represent spatial lattice data by a continuous spatial process in order to capture the spatial variability using a variogram. Different simulated representations are explored, compared and evaluated using a simulation study. The method proposed provides a new technique for variogram estimation on discrete lattice data.

Despite the fact that it is well known that vectors do not visit hosts randomly, many epidemiological models of vector-borne diseases do not take into account this biological fact. Indeed, vectors may be differentially attracted toward infected and uninfected hosts depending on whether they carry the pathogen or not. We would like to know what would be the implication for the long-term dynamics of our system. This talk is based on publication [1].

We consider a system of partial differential equations with vector diffusion. For the non-spatial model, we show that conditional vector preferences may induce bistability between the disease-free equilibrium and an endemic equilibrium. Backward bifurcation may also occur. For the model with diffusion, we show that bistable travelling waves may exists with positive or negative spreading speeds such that the disease either invades or retreats into space. When a monostable travelling wave occurs, we show that the disease spreading speed depends on conditional vectorial preferences. We illustrate the theoretical results with several simulations. We also discuss the implication of our findings in terms of control strategies.

Reference:

[1] Frédéric M. Hamelin, Frank M. Hilker, Yves Dumont. Spatial spread of infectious diseases with conditional vector preferences. Journal of Mathematical Biology, 2023, 87 (2), pp.38.

Objective: Cardiovascular disease is increasing in many low and middle-income countries, including those in Africa. To inform strategies for the prevention of cardiovascular disease in South Africa, we sought to determine the broad heritability of phenotypic markers of cardiovascular risk across three generations.
Methods: A cross-sectional study was conducted in a longitudinal family cohort. Setting was in a research unit within a tertiary hospital in a historically disadvantaged, large urban township of South Africa. Participants were 195 individuals from 65 biological families with all three generations including third-generation children aged 4–10 years being recruited from the longest running intergenerational cohort study in Africa, the Birth to Twenty Plus cohort. All adults (grandparents and parents) were female while children were male or female. Primary and secondary outcome measures were heritability of blood pressure (BP; brachial and central pressures) and heritability of arterial stiffness (pulse wave velocity), carotid intima media thickness (cIMT) and left ventricular mass indexed to body surface area (LVMI) respectively. Random family methods were used to screen for candidate health measures that promised potential heritability in families and Hierarchical models
were applied to estimate heritability using Restricted Maximum Likelihood (ReLM), MCMC and HMC frameworks.
Results: While no significant intergenerational relationships of BP or arterial stiffness were found, there were significant relationships in LVMI across all three generations (p < 0.04), and in cIMT between grandparents and parents (p=0.0166). Heritability, the proportion of phenotypic trait variation attributable to genetics, was estimated from three common statistical methods and ranged from 23% to 44% for cIMT and from 21% to 39% for LVMI.
Conclusions: Structural indicators of vascular health, which are strong markers of future clinical cardiovascular outcomes, transmit between generations within African families. Identification of these markers in parents may be useful to trigger assessments of preventable risk factors for cardiovascular disease in offspring.

The role of police in controlling crime and rehabilitation of criminals are difficult to quantify. The relationship between the police and criminals is analogously modelled like an ecological model in which predators and prey interact. In this paper, we formulate and analyze a mathematical model of the spread of crime in the presence of police, rehabilitation and recidivism. The model equilibria and threshold quantity that determines the dynamics of crime is determined. Numerical simulations are done to determine the impact of various parameters on the long term dynamics of crime.

We develop an approach for a two player constraint nonzero-sum stochastic differential game, which is modelled by a Markov regime-switching jump-diffusion process. We provide the relations between a usual stochastic optimal control setting and a Lagrangian method. In this context,we prove corresponding theorems for two different type of constraints, which lead us to find the real valued and the stochastic Lagrange multipliers, respectively. Then, we illustrate our results for an example of cooperation between a bank and an insurance company, which is a popular, well-known business agreement type, called Bancassurance. We find a Nash equilibrium for this game and solve the adjoint equations explicitly for each state by using Stochastic Maximum Principle.

Reference: Savku E., A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes. Mathematics (2023), 11, 3043. DOI:10.3390/math11143043

Hard-clustering methods such as k-means and hierarchical clustering have been used to identify nutritionally similar food items. However, hard clustering could be inefficient because a food item is assigned to only one cluster and is unable to detect two highly overlapping clusters. In recent times, finite mixture models are being used to cluster unlabelled data in much the same way while accounting for the uncertainty between cluster boundary thresholds. This is the case with the South African Food Composition Database (SAFCDB) where separation between the food items in terms of nutritional content is not well-defined. In addition, while applying univariate model-based clustering methods to food items is useful for ranking food items to inform therapeutic diets, this does not consider that food items contain several nutrients. From the SAFCDB, we extracted a data matrix consisting of 971 food items and 28 nutrients and applied multivariate Gaussian mixture models to cluster food items based on their nutrient composition. A 5-component Gaussian mixture model best described the distribution of the food items. The identified mixtures corresponded with food items high in fatty acid, cholesterol and sodium content, food items low in overall nutrient content and food items high in moisture, total fibre and vitamin C content. The 18-component, 13-component and 16-component Gaussian mixture models best described all the food items based on their macronutrient, mineral and vitamin content, respectively. Our study has shown that the food groups obtained through model-based clustering provides more detailed nutrient content information than that of traditionally known food groups and can make food composition data more accessible and user-friendly.

An important challenge with regards to directional statistics is the fact that many models neglect to address the curvature of underlying sample spaces. Hauberg addressed this practical problem by introducing the spherical normal model, as a spherical extension of the usual (real) Gaussian case. We introduce here a model that further allows for skewness in the spherical domain, inspired by the real case where accounting for skewness enriches the possibilities for accurate representation and inference for real-life data. The developed model is governed by the squared geodesic distance in the spirit of the intrinsic framework. This implies to substitute the standard Euclidean norm with the great-circle distance, which is the length of the shortest path joining two points on the unit sphere. Theoretical results on maximum likelihood estimation as well as a sampling scheme is presented and discussed. An application of model-based clustering is worth investigating within the finite mixture model framework.

Abstract

Environmental pollutant continues to pose a great threat to public health, leading to development of chronic diseases. In this study, a nonlinear mathematical model is formulated and analysed to study the effect of genetic risk, environmental pollutant, public health education/awareness on asthma development. Conditions for the existence of the unique positive steady state and permanence of the system are assessed. Using Lyapunov function analysis, the unique positive steady state is locally and globally asymptotically stable. Results reveal that genetic risk, pollutant emission rate, effective exposure rate of population to polluted environment and recurrence rate contribute to asthma prevalence. However, sufficiently effective pollutant reduction strategies, improvement in compliance to public health education/awareness together with human dependent environmental pollutant depletion lead to a marked reduction in disease prevalence.

The purpose of this research is to analyse the possible definitions and existence of local times (according to the different definitions) of model-free deterministic price paths. The analysis is carried out using two continuous but nowhere differentiable functions. The results show consistent local time estimates for the function constructed from a component of the Peano curve whereas those of the other function are divergent, perhaps suggesting the need for another normalising factor.

We show that the problem of counting the number of flats of size k for a cycle matroid of a complete graph is equivalent to the problem of counting the number of partitions of an integer k into triangular numbers. In addition, we give some values of k such that there is no
flat of size k in a cycle matroid of a complete graph of order n: Finally, we give a minimum bound for the number of values, k, for which there are no flats of size k in the given cycle matroid.

In this study, we compare the performance of three variable selection methods in a high-dimensional data setting from cancer genomics, namely, the linear models for microarrays (LIMMA), the principal component analysis (PCA), and the significant analysis of microarrays (SAM). We employ the methods in class comparison on three microarray data with binary groups from the gene expression omnibus (GEO) to obtain gene signatures, and assess the performance of the gene signatures in class prediction via cross-validation. Finally, we recommend the best method for gene selection after external validation with three independent cancer datasets from the cancer genome atlas (TCGA).

Key Words: Cancer genomics; linear models for microarrays; principal component analysis; significance analysis of microarrays; TCGA.

Child death rates are often regarded as reliable indicators for overall welfare of a country since they give insight of health accessibility and development. For planning and controlling purposes, it is important to understand which ages are at higher risks of experiencing child death as well as determinants thereof.
We used the Sierra Leone DHS 2019 data which was collected using two stage sampling methods. Data collection involved interviewing women aged from 15–49 to obtain information about children they had in the past up to 2019. Age at death of child was modelled using discrete-time survival analysis with a logit link at the same time applying survey weights. The analysis also sought to estimate the determinants of child death (under-five mortality). The baseline hazard was modelled with a polynomial function.
Results showed that children from rural areas had significantly lower odds of dying compared with those from urban areas (odds ratio (OR) = 0.861, p-value = 0.0003). Children of mothers who were currently using contraceptives, and those whose mothers had been using since their last birth were at higher odds of child death compared to children whose mothers had never used contraceptives before (currently using: OR = 1.118, p-value =  < .0001; used since last birth: OR = 1.372, p-value =  < .0001). Children with no health insurance had significantly higher odds of death than those with health insurance (OR = 1.036, p-value =  < .0001). Children of women who were married, and of women who were formerly married were at significantly higher odds of experiencing child death than children of women who had never been in union (married: OR = 1.207, p-value = 0.0003; formerly married: OR = 1.308, p-value = 0.0009 compared to those that have never been married). Increase in the age group of mothers increases the odds of their children experiencing child death compared to mothers in their teenage years (20-29: OR = 1.943, p-value =  < .0001, 30-39: OR = 2.397, p-value =  < .0001 and >  = 40: OR = 2.895, p-value =  < .0001 compared to mothers in their 15-19 years).
The study provides evidence that residing in urban areas, marital union of the mother, children having no health insurance, use of contraceptives by mother, older ages of the mother and no health insurance significantly increase the odds of child death. This points out to a possible need for improved health infrastructure to be made available in all places of delivery and more awareness on pregnancy related complications.

Intervention analysis plays a pivotal role in understanding how black swan events, such as the Covid-19 pandemic, influence time series data, enabling informed decision-making regarding policy adjustments and actions. Given the significant economic importance of the South African manufacturing sector, conducting an intervention analysis on the manufacturing sales data offers valuable insights for policymakers and industry stakeholders. Despite the impact of the Covid-19 pandemic on South Africa's manufacturing industry, there is a notable gap in the literature, with no prior studies addressing the industry's recovery trajectory. The study aims to apply a time series intervention model to evaluate the impact and recovery of South Africa's manufacturing sales from the COVID-19 pandemic. The total manufacturing monthly sales data for South Africa (SA) spanning from January 2009 to July 2023 is used in the analysis and the intervention point is identified as April 2020. The SARIMA (0,1,1)(0,1,1)12 model plus the Covid-19 pandemic intervention with one innovative outlier provided a good fit for total manufacturing sales. In April 2020, there was an immediate 49.32% reduction in total manufacturing sales attributed to the COVID-19 pandemic. The intervention's impact can be characterised as sudden but was short-lived, as the recovery took only 9 months to recover the COVID-19 pandemic initial shock. The results highlight the significance of employing robust time series analysis, including intervention models, for assessing and managing economic disruptions. The short-lived nature of the intervention impact highlights the resilience of the manufacturing industry but also stresses the need for continued vigilance and adaptability in the face of ongoing pandemic challenges. There is a need for industry leaders to maintain contingency plans and agile production processes and to swiftly adjust to changing circumstances, ensuring a more rapid recovery in future disruptions, while safeguarding against potential long-term impacts.

A new extension of the Topp-Leone Marshall-Olkin-G (TL-MO-G) family of distributions, by Chipepa et al. (2020), was developed in this paper via the combination of the TL-MO-G with the generalized Gompertz distribution by El-Gohary et al. (2013). Derivation of the desired statistical properties was carried out. Estimation of the model's parameters was done using the Maximum Likelihood Estimation (MLE), least squares (LS), weighted least squares (WLS), Anderson Darling (AD) and Cramer-von Mises methods with the MLE reigning its supremacy. To ascertain the model's flexibility and applicability, three real life data sets in the medical field were considered with one being a censored data set. The newly suggested model performed exceptionally well in comparison to six other existing non-nested models despite their past dominance.

In this talk, we begin by introducing the nearest integer continued fraction with complex partial quotients. Instead of finding rational complex approximations for a complex irrational by truncating its nearest integer continued fraction, we use geometry in three-dimensional hyperbolic space to illustrate the process underlying the generation of these approximations.

Flow instability is a major challenge experienced in medical, engineering and industrial
settings globally. For instance, flow instability linked with irregular cardiac output of the heart leads to organ malfunctioning in the medical field, it also encourages mechanical vibrations in the case of fluctuating flow rate, and several other applications. In this study, linear stability analysis is conducted to monitor the behavior of a small disturbance that is imposed on hydromagnetic Casson fluid that flows steadily through a saturated porous medium. A new variant of the Orr-Sommerfield equation is obtained and solved numerically by using spectral point collocation weighted residual approach with eigenfunction expansion of the Chebyshev polynomial as the admissible trial function. Based on the QZ algorithm, numerical results are obtained for wave and Reynold’s numbers, wave velocity as functions of Magnetic field intensity and porosity shape parameters. Results are validated against previously released data. The biophysics of the heart, particularly in cardiac rhythm analysis, as well as several other medicinal and technical applications, is among the areas where the current work has applicability.

The abundancy index of a positive integer n is obtained by dividing the sum of the factors of n by n. Two different positive integers are called friends if they have the same abundancy index. The number 10 is the smallest positive integer n such that it is not known whether a friend of n exists.

It is also currently unknown whether an odd perfect number -- that is, an odd friend of 6 -- exists. Nielsen showed that every odd perfect number has at least nine different prime factors in a 2007 paper, and then at least 10 different prime factors in a more involved 2015 paper that included a months-long computer program run.

It appears that the question of the existence of friends of 10 could be more amenable to investigation by computer search than the question of the existence of odd perfect numbers. This paper adapts techniques used in the first of the two papers by Nielsen to prove that every friend of 10 has at least 10 different prime factors.

References:
Nielsen, P. P. 2007. Odd perfect numbers have at least nine distinct prime factors. Math. Comp. 76(260): 2109--2126.
Nielsen, P. P. 2015. Odd perfect numbers, Diophantine equations, and upper bounds. Math. Comp. 84(295): 2549--2567.

In this study, we extend the hybrid block method with equally spaced intra-step points to solve both linear and nonlinear third-order initial value problems. The proposed hybrid block method employs a simple iteration scheme to linearize the nonlinear equations. Numerical experimentation results demonstrate that equally spaced grid points in the block hybrid method enhance its speed and effectiveness compared to other conventional block methods found in the literature. This improvement can be attributed to the implementation of the linearization process, which avoids the use of derivatives. Furthermore, the newly introduced hybrid block method has proven to be consistent, stable, and capable of rapid convergence to approximate solutions. We show that the simple iteration method, when combined with the hybrid block method, exhibits impressive convergence characteristics while preserving computational efficiency.

Despite the success of the existing malaria control strategies, reported malaria cases are still quite high. In 2021, the WHO reported about 247 million malaria cases; 95% of which occurred in the WHO African Region. In this presentation, a mathematical model for the in-host Plasmodium falciparum malaria subject to malaria vaccines is formulated and analyzed. An efficacious preerythrocytic vaccine is shown to grately reduce the severity of clinical malaria. Based on the normalized forward sensitivity index technique, the average number of merozoites released per bursting blood schizont is shown to be the most sensitive parameter in the model. Numerical simulation results further suggest that an efficacious blood stage vaccine has the potential to reduce the burst size of the blood schizonts and maximize the rate of activation of CD8+T-cells during malaria infection. Moreover, vaccine combinations that are efficacious might help in achieving a malaria free population by the year 2030. These results provide useful insights in within-host malaria control and a unique opportunity to intensify support and funding for malaria vaccine development.

Extensive literature delves into the adoption of sustainable agricultural practices, yet scant consideration has been given to their long-term sustainability on the landscape following initial adoption. One such agricultural practice is cover cropping, which serves to reduce erosion, prevent fertilizer runoff from polluting waterways, offer resources for pollinators, and enhance soil health. Persistent use of cover cropping over time is deemed crucial for maximizing cumulative environmental benefits. However, we know little about what factors affect persistence of cover cropping, and these factors are likely to be different from those that affect initial adoption of the practice.

We use ensemble models and interpretable machine learning techniques to identify features of natural and human systems that are associated with the field-level persistence of cover cropping in Indiana, USA from 2014-2019. Random forests and gradient-boosted decision trees classifier algorithms were utilized to derive models that best predict field-level persistence of cover cropping using several hundred environmental and socio-economic variables. To identify the most important features associated with field-level persistence of cover-cropping, we performed recursive feature elimination with cross-validation (RFECV) to select a parsimonious model with high prediction accuracy. We described how individual features in the final selected model influence the prediction of cover crop persistence using accumulated local effects (ALE) plots, since many of the features are correlated. Global Shapley additive explanations (SHAP), averaged per feature across the entire data, were calculated, and we used SHAP dependence plots to describe average effects of selected features across the range of persistence of cover cropping. We found features such as soil properties, localized weather patterns, long-term climate trends, and agricultural decisions to be important for predicting persistence of cover cropping at the field level. These findings generate new insights into what induces the persistence of sustainable agricultural practices and provide a more informed foundation for researchers to formulate testable hypotheses about behavioral and environmental causes of persistence.


Keywords: interpretable machine learning, Shapley values, causal inference, causal machine learning, cover crop, conservation, agriculture

Category: Statistics

References
[1] Apley, D. W. and Zhu, J. (2020). Visualizing the effects of predictor variables in
black box supervised learning models. Journal of the Royal Statistical Society Series
B: Statistical Methodology, 82(4),1059–1086.
[2] Basche, A. D., Archontoulis, S. V., Kaspar, T. C., Jaynes, D. B., Parkin, T. B., and
Miguez, F. E. (2016). Simulating long-term impacts of cover crops and climate change
on crop production and environmental outcomes in the Midwestern United States.
Agriculture, Ecosystems, and Environment, 218:95–106.
[3] Covert, I. and Lee, S.-I. (2021). Improving KernelSHAP: Practical Shapley Value Estimation
Using Linear Regression. Proceedings of The 24th International Conference
on Artificial Intelligence and Statistics, PMLR. 130:3457–3465.
[4] Guyon, I., Weston, J., Barnhill, S. and Vapnik, V. (2002). Gene Selection for Cancer
Classification using Support Vector Machines. Machine Learning, 46:389–422.
[5] Lundberg, S. M. and Lee, S.-I. A unified approach to interpreting model predictions.
Proceedings of the 31st International Conference on Neural Information Processing
Systems, 2017.
[6] Prokopy, L. S., Floress, K., Arbuckle, J. G., Church, S. P., Eanes, F. R., Gao, Y.,
Gramig, B. M., Ranjan, P. and Singh, A. S. (2019). Adoption of agricultural conservation
practices in the United States: Evidence from 35 years of quantitative literature.
Journal of Soil and Water Conservation, 74(5):520–534.
[7] Tran, D. Q. and Kurkalova, L. A. (2019). Persistence in tillage decisions: Aggregate
data analysis. International Soil and Water Conservation Research, 7(2):109–118.

Ease of accessibility to essential facilities is an important component of any society. This is important for several reasons including equality in provision of resources and services. Spatial accessibility can be defined by the ease at which a facility, or any point of interest (POI) is arrived at from a demand location. POIs are facilities which provide services and/or products and are usually grouped by sub-industry level (laboratories, pharmacies, clinics, schools, universities, etc.) or industry level (health care, education etc.). Spatial accessibility is dependent on the spatial impedance (drive-time or Euclidean distance) between the POI and demand location and on the capacity of the POI in question. Catchment areas formed around POIs can be classified into one of the following three categories: in potential spatial accessible areas it can either be i) overlapping or ii) non-overlapping and beyond spatial accessible areas, iii) spatially inaccessible. We propose a method to structure fuzzy lattice data that will represent the potential spatially accessible areas. Spatially inaccessible areas (which otherwise would have been omitted) will also be identified and structured using spatial and community detection techniques.

The success of Bitcoin has spurred emergence of countless alternative coins with some
of them shutting down only few weeks after their inception, thus disappearing with millions of dollars collected from enthusiast investors through initial coin offering (ICO) process. This has led investors from the general population to the institutional ones, to become skeptical in venturing in the cryptocurrency market, adding to its highly volatile characteristic. It is then of vital interest to investigate the life span of available coins and tokens, and to evaluate their level of survivability. This will make investors more knowledgeable and hence build their confidence in hazarding in the cryptocurrency market. Survival analysis approach is well suited to provide the needed information. In this study, we discuss the survival outcomes of coins and tokens from the first release of a cryptocurrency in 2009. Non-parametric methods of time-to-event analysis namely Aalen Additive Hazards Model (AAHM) trough counting and martingale processes, Cox Proportional Hazard Model (CPHM) are based on six covariates of interest. Proportional hazards assumption (PHA) is checked by
assessing the Kaplan-Meier estimates of survival functions at the levels of each covariate. The results in different regression models display significant and non-significant covariates, relative risks and standard errors. Among the results, it was found that cryptocurrencies under standalone blockchain were at a relatively higher risk of collapsing. It was also found that the 2013–2017 cryptocurrencies release was at a high risk as compared to 2009–2013 release and that cryptocurrencies for which headquarters are known had the relatively better survival outcomes. This provides clear indicators to watch out for while selecting the coins or tokens in which to invest.

Livestock farming is an essential part of our food system and economy, which provides us with meat, dairy, and other animal products. However, changing climatic conditions are putting this industry at risk. Over the past few years, we have experienced extremely high and extremely low temperatures. This has resulted in extremely high rainfall, leading to floods and extremely low rainfall leading to droughts, all with devastating effects on livestock farming, leading to reduced productivity, increased mortality rates, and higher costs for farmers. Therefore, there is a need to develop effective strategies to adapt to these changes. Climate change has been identified as one of the biggest threats to livestock in recent times. As temperatures rise and rainfall patterns become more erratic, livestock farmers are facing unprecedented challenges that threaten their livelihoods. There is a need to investigate the impact of climate change on livestock using statistical modelling techniques. It is important to understand the relationship between climate variables and key livestock performance indicators such as growth rates, reproduction, and mortality. By doing so, we can identify the most vulnerable areas and develop effective adaptation strategies to mitigate the impact of climate change on livestock around the country and the Southern region of Africa.
The climate impacts anticipated for developing countries are similar to those being experienced around the world: general warming (day and night temperatures all year round); changes in rainfall timing and quantities; changes in seasons (longer summers); increased climate variability (e.g. floods, droughts and heat waves); higher sea-levels; and increasing frequency and intensity of extreme weather events. Such impacts were recently experienced in most Southern African countries of late, Mozambique, Zimbabwe and Malawi.
Livestock production has also been considerably affected by lack of pasture and water. Significant livestock deaths have been recorded in Lesotho, South Africa, Swaziland and Zimbabwe. Furthermore, outbreaks of diseases such as anthrax have been reported in Zimbabwe and Lesotho; and incidences of animal diseases such as foot-and-mouth disease have been reported in northern Namibia and southern Angola as a result of increased movement of livestock in search of pasture and water.
Measuring livestock systems is still a great challenge due to a lack of high-quality, nationally representative data. Due to this challenge, livestock is often neglected in many national statistical operations and as a result, decision-makers and policymakers are unable to design evidence-based livestock sector policies and investments.
Many rural households in low- and middle-income countries depend on livestock for their livelihoods. Sustainable livestock systems can contribute to reducing poverty, ending hunger, and improving health, and are of great importance in addressing environmental degradation and climate change and preserving biodiversity.
Machine learning algorithms were used to provide valuable insights into the relationships between climate change and livestock, aiding in better understanding and prediction of potential impacts. Of particular interest was the Random Forest Regression model, which was used to handle non-linear relationships between climate variables and livestock data. It captured the complex interactions and produced robust predictions. The K-Nearest Neighbors (KNN) algorithm was used for classification and spatial analysis, identifying regions with similar climate and livestock indicators. This approach helped the researchers to understand geographical variations in climate impacts on livestock. The data used for this project including historical records of rainfall and temperature, was collected from Eswatini Meteorological Office located in Mbabane, Eswatini. Additionally, data on key livestock performance indicators such as growth rate, reproductive efficiency, and mortality rates were obtained from the Eswatini Veterinary Office located in Manzini, Eswatini.

Malaria transmission dynamics are complex due to variations in space, time, heterogeneity, stochasticity, and other exogenous forces like the weather. These variations affect mosquito ecology and malaria transmission dynamics through blood feeding. From the Ross-Macdonald model, several individual-based models have been developed and analyzed but with little emphasis on spatial dynamics and uncertainty. Modeling and analyzing real systems can become computationally overwhelming with parametric challenges and increasing factors from dimension, interactions, and system processes. This always leads to the development of simple but unrealistic models that give limited room for robustness. This study aims at providing a modular framework as an alternative approach to dealing with complexity that is analytically tractable. It also provides algorithms to understand mosquito ecology, parasite dispersal, mosquito dispersal on a spatial landscape, and human stratification by behavior, travel, age, sex, bed net usage, and care-seeking among others. The framework further provides a platform for quantifying and synthesizing transmission that occurs at a particular time and place by keeping track of the mosquito and human position. As a case study, we provide a three-habitat, two patches, and two human-stratified models describing mosquito ecology and malaria dynamics in the modular framework. This is analyzed with steady states and reproductive numbers to prove mathematical consistency and biologically meaningful output. From this study, it is noted that the modular framework makes it easy to develop and extend this existing model to incorporate other factors including exogenous forcing, drug resistance, and vector control among others. It is also easy to modify the functional response and some basic parameters that may affect the outcome while maintaining robustness

A new model for earthquake induced oscillations of high-rise structures, (using an adapted Timoshenko beam model) is analyzed. The earthquake is modeled as a force acting on the foundation via so-called soil-structure interaction. Existence of solutions, modal analysis and convergence of the modal solution will be briefly considered. Numerical experiments (using the Finite element method) investigating the dynamic behavior of such a structure will also be discussed.

The distance between two vertices in a connected graph is the length of a shortest path between those two vertices. The diameter of a strong digraph or connected graph is the largest of the distances between its vertices. An orientation of an undirected graph is a digraph obtained from the original graph by assigning a direction to each edge. The oriented diameter of a graph is the minimum diameter amongst all orientations of the graph. It is computationally difficult to find the oriented diameter of a given graph. Hence, bounds on it are of interest.
A cut vertex of a graph is a vertex whose removal, together with any incident edges, disconnects the graph. A block is a maximal connected subgraph of the original graph that has no cut vertex. A block graph is a graph in which every block is a clique.
In this talk, we give an upper bound on the oriented diameter of a bridgeless graph in terms of order and number of blocks. Furthermore, this bound is sharp. As a corollary, we obtain a sharp upper bound on the oriented diameter in terms of order and number of cut vertices. We also give an upper bound on the oriented diameter of a bridgeless block graph in terms of order.
This is joint work with Peter Dankelmann and Megan Jane Morgan.

This talk explores the realm of positive model theory, which focuses on formulas preserved by homomorphisms [1][4]. It is well known that these are "positive existential formulas," which are constructed using atomic formulas and falsity while employing only conjunction, disjunction, and the existential quantifier, but excluding negation or the universal quantifier. The Keisler-Shelah Isomorphism Theorem, a cornerstone in classical model theory, asserts that structures are "elementarily equivalent" (meaning they satisfy the same first-order sentences) if and only if they possess isomorphic ultrapowers. Keisler originally proved this theorem under the assumption of the Generalized Continuum Hypothesis [Thm. 2.4, 2], which was later shown to be unnecessary by Shelah [p. 244, 5]. This talk aims to establish a positive model theory counterpart to Keisler's theorem

We say two structures are "positively equivalent" if they satisfy the same positive existential sentences. A new construction called a "prime product" captures positive equivalence by replacing the index set of an ultraproduct with a poset and using a "prime filter" of the poset's upward-closed sets. Traditional ultraproducts are a special case obtained when the poset is the identity relation. This generalization not only preserves positive existential formulas, akin to a positive version of ?o?›' Theorem, but also perserves the universal closure of implications between them, referred to as "basic h-inductive sentences." Consequently, it becomes possible to characterize classes of models of h-inductive theories as those closed under isomorphisms, prime products, and ultraroots.

The central result of this talk establishes that, under the Generalized Continuum Hypothesis (GCH), two structures satisfy the same positive existential sentences if and only if they have isomorphic prime powers of ultrapowers. This conclusion holds even in the absence of the GCH, provided that prime powers are replaced by prime products. But ultrapowers remain indispensable, as there exist positively equivalent structures lacking isomorphic prime powers. The findings presented here have been compiled in the paper [3].

[1] I. Ben-Yaacov. Positive model theory and compact abstract theories. Journal of Mathematical Logic, 3:85–118, 2003.
[2] H. J. Keisler. Ultraproducts and elementary classes. Indagationes Mathematicae, 23:477–495, 1961.
[3] T. Moraschini, J. J. Wannenburg, and K. Yamamoto. Elementary equivalence in positive logic via prime products. The Journal of Symbolic Logic, 1-18, doi:10.1017/jsl.2023.50, 2023.
[4] B. Poizat and A. Yeshkeyev. Positive Jonsson Theories. Logica Universalis, 12:101–127, 2018.
[5] S. Shelah. Every two elementarily equivalent models have isomorphic ultrapowers. Israel Journal of Mathematics, 10:224–233, 1971.

The COVID-19 pandemic was first experienced in Wuhan City, China, in December 2019. It spread globally and has since subsided. In this research article, we propose a mathematical model for studying the transmitting dynamics of COVID-19 taking into consideration precautions of wearing face masks and quarantine. We study the stability analysis of the model equilibria. The global stability analysis of the equilibria is done using Lyapunov functions.

A quasi-equation is an implication (such as a cancellative law) whose premises and conclusion constitute a finite set of equations. A quasivariety is a class K of similar algebras that can be axiomatized by quasi-equations. It has the joint embedding property (JEP) if it is generated by a single algebra A (i.e., the valid quasi-equations of A axiomatize K). It is structurally complete if, moreover, the free denumerably-generated algebra in K can serve as A. A consequence of this demand, called 'passive structural completeness' (PSC), is that the nontrivial members of K all satisfy the same existential positive sentences.

We prove that if K is PSC then it still has the JEP, and if it has the JEP and its nontrivial members lack trivial subalgebras, then its relatively simple members all belong to the universal class generated by one of them. Under these conditions, if K is relatively semisimple then it is generated by one K-simple algebra. We also prove that a quasivariety of finite type, with a finite nontrivial member, is PSC iff its nontrivial members have a common retract.

The theory is then applied to the variety of De Morgan monoids, where we isolate the sub(quasi)varieties that are PSC and those that have the JEP, while throwing fresh light on those that are structurally complete. The results illuminate the extension lattices of intuitionistic and relevance logics. For further details, see [1].

References:

[1] T. Moraschini, J.G. Raftery and J.J. Wannenburg: Singly generated quasivarieties and residuated structures. Mathematical Logic Quarterly 66(2) (2020), 150-172.

Agriculture production yield varies with weather changes. This causes farmers incur loses. For instance, extreme temperature leads to low maize yield. This study describes temperature weather derivatives in Agriculture markets which are incomplete markets in nature and applies risk management hedging technique. It focuses on hedging crop yield against extreme temperatures during irrigation farming which is being done without green house. This study's primary goal is to hedge maize crop yields using temperature derivatives. This is achieved by: (i) Developing a daily average temperature stochastical model. (ii) Deriving statistical properties of the model based on the historical data of 31 years of our sample space (1990 – 2020 Kasungu District Temperature data). (iii) Pricing temperature derivatives to hedge maize crop yield. The study's findings suggest that the temperature will rise gradually but steadily. This scenario does not offer a positive outlook for agriculture production since it can be damaged by a rise in temperature. The weather index is GDD (growing degree day) and the pricing is done by temperature down and out call barrier option. Premium for weather derivative options has been calculated as $3.50 per GDD index contract. The pricing model devised can be applied in the agricultural sector by farmers who are interested in hedging temperature-related weather risks. Other weather-related companies that depend on heat can utilize it to price weather derivatives. The findings based on this study assist financial institutions likewise the government in creating products that will benefit farmers.
Key words: Incomplete market, Weather derivatives, Growing Degree Day, Temperature, Mean reversion, the Wiener process, Ornstein-Uhlenbeck, temperature barrier option pricing.

In this work, we propose a reaction diffusion model representing microbial populations responding to environmental changes, such as availability or depletion of the growth-liming nutrient. We establish conditions under which microbial population oscillations (boom-and-bust) may occur, a phenomenon that has been observed in population dynamics. Existence of travelling wavefronts is established for the proposed partially degenerate reaction diffusion system. Numerical simulations are provided to support theoretical results.

This study explores the dynamics of childbearing transitions among women, employing a discrete time multiprocess modeling approach based on data from the South African Population Research Institute (SAPRIN). Childbearing transitions are pivotal events in a woman's life, and understanding the factors and patterns associated with these transitions is crucial for informed policy-making and healthcare interventions. Utilizing a rich dataset of 117,171 women, we examine the transitions across various age groups, calendar years, and residency statuses. Our analysis reveals nuanced insights into how these transitions evolve over time, with a focus on identifying complex transitions that may have significant implications for maternal and child health outcomes. By employing discrete time multiprocess modeling techniques, we aim to provide a comprehensive understanding of childbearing dynamics, shedding light on the diverse factors influencing women's reproductive decisions in the South African context. This research offers valuable insights for policymakers and healthcare practitioners working to improve maternal and child health outcomes in South Africa.

This paper presents a comprehensive approach to dynamic portfolio management by leveraging the Fokker-Planck initial value problem. It considers a portfolio composed of a risk-free bond (Bond) and two stocks (Stock 1 and Stock 2). The weights of the two stocks, denoted as π1 and π2, vary over time, but their sum is equal to π. By solving the Fokker-Planck equation, we demonstrate how one can calculate π1 or π2, which, in turn, fixes the other. We apply this methodology to assess the impact of extreme events on investment strategies, providing insights into the adaptive nature of portfolio management during times of economic uncertainty.

Keywords: Dynamic portfolio management, Fokker-Planck equation, Economic uncertainty, Extreme events, Adaptability

Category: Financial Mathematics

The analysis of spatial point pattern data is typically done to expand the basic understanding of the first- and second-order properties of the point process that generated the data. First and second order properties of spatial point patterns are estimated using density and distance-based measures. These measures rely on the specification of the window domain. Thus, correct specification of a window domain and the use of an appropriate distance metric to quantify proximity on the chosen window is important in the analysis of point pattern data. The typical approaches used for window selection are the smallest rectangular bounding window and convex windows. In some situations, however, points may be constrained by environmental phenomena or observational factors. Covariate information should thus be incorporated into the selection of an appropriate window domain. We propose a new algorithm for selecting the point pattern domain based on spatial covariate information and without the restriction of convexity, allowing for better estimation of the true domain. The use of nonconvex windows constructed using the algorithm necessitates the use of a norm alternative to the Euclidean distance, since this distance does not respect window boundaries. In the case where movement between points is constrained by a connected physical path on the window, it is important to define distance using a measure that is representative of this path since these will affect the estimates used to characterize first- and second-order properties. Consideration is also given herein to this topic.

In this work, we consider a financial market model where the price of a risky asset is modeled by a skew geometric Brownian motion (GBM). We derive bounds on the scale function related to the skew GBM driving the price of the risky asset. We solve an ordinary differential equation for the scale function and obtain its bounds based on certain parameters and constants. Utilizing these bounds, we show that the expectation of the skew GBM is also bounded.

Keywords: Scale function, skew geometric Brownian motion.

Analytical solutions to solute transport equations can predict the fate and transport of contaminants in soil or groundwater systems and provide reference for validating numerical models. However, when the solute transport equation is coupled with heat, the corresponding analytical solutions are rarely reported due to the complexity of these models. This paper presents an analytical solution to the solute transport equation coupled with heat for the case of modeling solute transport in a vertical section of a homogenous infinite aquifer. In earlier work [1], analytical solutions to the solute transport equation in both finite and infinite aquifer were presented, but Soret effect was not considered. Heat can, however, significantly impact the movement of concentration front. In our study, we couple the solute equation with a generalized classic heat diffusion equation by assuming negligible Dufour effect and consider a one-way coupled model. The repeated integral transformation method (RITM) is utilized to obtain the analytical solutions to the proposed coupled model. As a limiting case, a comparison with analytical solution [1], equation (21) and other literature findings is done to validate our results. The influences of the thermopheresis effect and other model parameters are presented graphically using MATLAB R2015a. In comparison, our results show that movement of contaminant in the medium is affected by the presence of heat, in particular along the direction of flow, consistent with the literature. The analysis of longitudinal and transverse concentration profiles suggest that the proposed solutions are applicable for monitoring of groundwater contaminants and risk assessment.

This study explores the dynamics of childbearing transitions among women, employing a discrete time multiprocess modeling approach based on data from the South African Population Research Institute (SAPRIN). Childbearing transitions are pivotal events in a woman's life, and understanding the factors and patterns associated with these transitions is crucial for informed policy-making and healthcare interventions. Utilizing a rich dataset of 117,171 women, we examine the transitions across various age groups, calendar years, and residency statuses. Our analysis reveals nuanced insights into how these transitions evolve over time, with a focus on identifying complex transitions that may have significant implications for maternal and child health outcomes. By employing discrete time multiprocess modeling techniques, we aim to provide a comprehensive understanding of childbearing dynamics, shedding light on the diverse factors influencing women's reproductive decisions in the South African context. This research offers valuable insights for policymakers and healthcare practitioners working to improve maternal and child health outcomes in South Africa.

We propose a nonparametric method to test the validity of the whole model in the framework of GLMs when the response is a count variable. The solution is a multiple permutation test based on the combination of the p-values of the partial tests on the significance of the single regression coefficients. Through a simulation study, the power behavior of the proposed test is compared with the likelihood ratio test of the two most commonly used approaches for count data: the Poisson regression and the Negative Binomial regression.

The effects of temperature-dependent viscosity and thermal conductivity together with water, maginzium oxide and silver hybrid nanofluid in a porous medium flow heat transfer on a rotating cone examine. The system of partial differential equations representing the flow transformed to diamensionless ordinary differential equations by using suitable similarity transformation. Overlapping grid multidomian spectral quasilinearization method used to generate results. For selected parameters comparative study between different combinations of fluid conducted and results are presented.
It is observed that the main flow of the hybrid nanofluid enhances compared to the mono-nano fluid as the coupling number increases (as the fluid micropolar). The application of studies like this can be found in the atomization process of liquids.

In this research, we introduce a new generalized family of distributions called the Risti'c and Balakhrisnan or Gamma Type II Exponentiated Half Logistic-Topp-Leone-G (RB-TII-EHL-TL-G) distribution. This generalized family of distributions is being introduced because of its ability to address the limitations of earlier families, increased flexibility, and enhanced tail behavior. Some statistical properties of the model including moments, moment generating function, conditional moments, moment of residual and reversed residual life, distribution of order statistics, R'enyi entropy and stochastic orders are derived. The performance of the estimates is assessed via Monte Carlo simulation using different estimation techniques, namely, the maximum likelihood (MLE), Cram'er-von-Mises (CVM), ordinary least squares (OLS), weighted least squares (WLS), and Anderson-Darling (AD). Using the root mean square error (RMSE) and average bias (Abias), the MLE technique was found to be the best technique to estimate the model parameters. By fitting the RB-TII-EHL-TL-W a special case of the RB-TII-EHL-TL-G distribution to two real-world data sets from different fields, we demonstrate its superiority over nested and some existing equi-parameter non-nested models in the literature.

This paper aims to provide an alternative approach to modelling heavy tailed insurance claims data by proposing a comprehensive analysis of two component non-Gaussian composite models and mixture models. Composite and mixture models have gained attraction in actuarial literature because they provide flexible methods of curve-fitting for claims data. 256 composite models derived from 16 popular parametric distributions are studied. The composite models are developed by piecing together two distributions at a threshold value. A catalogue of 38 mixture models is considered - of which half are mixture models of the same parametric distribution with different parameters and the other half are mixture models of different parametric distributions. The mixture models are developed as a convex combination of two distributions.
The objective of this paper is to provide a comprehensive data-driven analysis of three categories of loss distributions - standard, composite and mixture loss distributions. Two real insurance datasets from different industries - the South African taxi claims data and the popular Danish fire claims data - are considered. When a few common loss distributions (i.e. exponential, gamma, Weibull, Pareto, lognormal and Burr) were considered for the taxi claims data, the lognormal and Pareto distributions were proposed to be the best for that insurance dataset.
In this paper, the list of fitted common distributions is extended from 6 to 19, and it is observed that there are some common loss distributions that provide a better fit than the lognormal and Pareto distributions when evaluating the fit using goodness of fit measures.
The complex composite and mixture models are compared to the common loss distributions using the same goodness of fit measures. Risk measures (or key risk indicators) are evaluated for informed risk management decisions and the appropriateness of the proposed models is also measured by comparing theoretical risk measures to the empirical results.

We investigate a trivariate polynomial associated with rooted trees. It generalises a bivariate polynomial for rooted trees that was recently introduced by Liu [1].
We show that this polynomial satisfies a deletion-contraction recursion and can be expressed as a sum over maximal antichains. Several combinatorial quantities can be obtained as special values, in particular the number of antichains, maximal antichains and cutsets.
We prove that two of the three possible bivariate specialisations characterise trees uniquely up to isomorphism. One of these has already been established by Liu, the other is new. For the third specialisation, we construct non-isomorphic trees with the same associated polynomial.
We finally find that our polynomial can be generalised in a natural way to a family of posets that we call V-posets. These posets are obtained recursively by either disjoint unions or adding a greatest/least element to existing V-posets.

[1] P. Liu, A tree distinguishing polynomial, Discrete Appl. Math. 288 (2021), 1–8.

Background: Causal effect estimates are required to guide key decision-making across a wide range of important areas such as healthcare. Randomization (of treatment or exposure) is the gold standard approach for establishing a causal effect of a treatment or exposure on an outcome. However, randomisation is not always feasible or ethical, and estimates can only be inferred from observational studies which are subject to confounding. Hence, methods that can provide sufficient adjustment for confounding are crucial. An additional challenge in estimating causal effects is also encountered from observational data with clustering structure. Clustered data are ubiquitous and statistical procedures for such data may leverage the clustering structure to achieve better results. Procedures that ignore the clustering are prone, among other issues, to cluster-level confounding. Moreover, such grouped data can show considerable imbalances across groups (i.e., varying cluster sizes). This can present further challenges in statistical analyses and may require appropriate methods or adjustments to account for the imbalance to make accurate inferences.
Objectives: This study aims to evaluate methods for estimating causal effects on binary outcomes in the presence of unbalanced clustered data.

Methods: Various propensity score-based approaches have been proposed including propensity score matching and propensity score weighting with corresponding variations for multilevel data depending on the outcome and the propensity score models. Using simulation, twenty methods for the estimation of the average treatment effect on the exposed units. The evaluation considered thirty-six scenarios including two response surfaces (parallel and non-parallel); three outcomes intra-class correlation (ICC) groups ( low, medium and high); three effect size estimates (0.5, 1, 2); and two scenarios for unobserved cluster-level confounding (assuming present/not present).

Results: Multilevel data may offer the opportunity to estimate the causal effect of non-randomized exposure both within the subpopulation of exposed individuals and the overall population. Importantly, when all the cluster-level confounders are observed and adjusted for, cluster-unconscious approaches, i.e., methods that ignore clustering can provide consistent estimates as cluster-aware models (based on fixed or random effect models), especially when the ICC is low. On the other hand, when there is unobserved cluster-level confounding, cluster-unconscious approaches are more sensitive and biased than cluster-aware approaches. The magnitude of bias is influenced by both the size of the ICC and the characteristics of the outcome response surface. A larger ICC is associated with a higher bias, while a non-parallel response surface is linked to increased bias. All the methods struggle to uncover small effects. Irrespective of the scenario, methods that perform the best in terms of the relative bias from the true value are methods that allow for clustering at least at one stage of the estimation

Conclusion: Both cluster-unconscious and cluster-aware approaches provided consistent estimates of the causal effects of a non-randomized exposure but procedures that allow for clustering structure are necessary when the outcome ICC is high. We cannot rely on the assumption of no-unobserved cluster-level confounding.

Compartmental and state space models have long been used in modelling disease dynamics. However, how they relate to each other has not been fully explored. In this work, we discuss the two types of models. We transform an SIR compartmental model to a state space model in both deterministic and stochastic forms. Other non-conventional compartmental models are also discussed. We note that a compartmental model may as well be defined as a state space model if its output is defined.

We present the development, analysis and numerical simulation of a mechanobiochemical model for 2D and 3D cell migration. The model couples biochemical reactions and biomechanical forces. Force balance equation is used to model the mechanical properties for displacement, while the dynamics of the actin and myosin concentration are described by two reaction-diffusion equations. The moving grid finite element method is employed to obtain an approximate solution to the model system. The numerical results are supported by linear stability theoretical results close to the bifurcation points during early stages of cell migration.

Abstract:

It is well known that if a and b are Banach algebra elements then

ab = ba implies exp(a)exp(b)=exp(b)exp(b)=exp(a+b).

However, this statement has no obvious converse. Wermuth in [3] used the notion of the spectra of a and b being 2πi-congruence-free to show the converse being true. Schmoeger in [1] and [2] shows that it is possible to provide a very short proof of the Wermuth result if one employs the notion of an inner derivation on a Banach algebra. In this talk we detail the results by Wermuth and Schmoeger as well as giving counter-examples showing that without such conditions the converse fail to hold.

[1] C. Schmoeger, A Remark on Commuting Exponential in Banach Al- gebras, Proceedings of the American Mathematical Society, Vol. 127 (1999), Pg. 1337-1338.
[2] C. Schmoeger, A Remark on Commuting Exponential in Banach Alge- bras II, Proceedings of the American Mathematical Society, Vol. 128 (2000), Pg. 3405-3409.
[3] E.M.E. Wermuth, A Remark on Commuting Operator Exponentials, Proceedings of the American Mathematical Society, Vol. 125 (1997), Pg. 1685-1688.

The University of Botswana is mandated to review and redesign its curricula every five years. The study is part of a larger project that continues to investigate the use of Intelligent Systems for all critical aspects of curriculum design. As the number of courses grow, and also due the proliferation of multi-disciplinary programs, the mapping of prerequisites has become a complex problem, requiring measures that monitor consistency and integrity of course requirements. Literature highlights the importance of discovering an ideal prerequisite skill structure. This research studies the validation of prerequisite structure in an existing university curriculum using a Data Science approach with a view to assist the redesign of the curriculum. Various approaches that employ Data Science exist in Literature such as using clustering algorithms and association rules to identify effective prerequisites but with poor results. Others use Bayesian Belief Networks to predict student performance in future semesters based on the design of academic programs, and linear regression to quantify strengths of relationships between prerequisite and post-requisite skills.
The study applies Regression methods to a Computer Science curriculum on courses offered in the first year. The applied datasets consist of student records for students that passed and completed all first-year courses within the period 2014-2015 Semester 1 to 2022-2023 Semester 2. The University of Botswana starts its academic year with Semester 1 around August and ends with Semester 2 around June of the following year. The experiments and the results demonstrate the correlations and dependencies of the first-year courses and how a Data Science approach could be applied to validate the prerequisite structures.

In a targeted terminal wealth generated by bond and risky assets, where the proportion of a risky asset is gradually being phased out, we propose a divestment model in a risky asset compensated by growth in a bond (insurance). The model includes the phase down rate of the risky asset, c(t), the variable proportion, π, in a risky asset and the interest rate, r, of the bond. To guide the growth of the total wealth in this study, we compared it to the Oksendal and Sulem [1] total wealth for which c(t) = 0, and π was a constant. We employed the Fokker Planck equation to find the variable moment, π(t), and the associated variance. We proved the existence and uniqueness of the first moment by Feller’s criteria. We have found a pair (c(t), r∗) for each π(t) which guarantees a growing total wealth. We have addressed the question whether this pair can reasonably be achieved to ensure an acceptable phase down rate at financially achievable interest rates, r∗.

Pneumonia is recorded to be one of the major causes of death among children under five years of age and adults over 65. It is reported that more than 2 million deaths occur in developing countries due to pneumonia each year. The eorts for early detection, effective treatment, and minimizing the transmission of pneumonia are possible if the dynamics of the disease are well understood. In this research, a model for the transmission dynamics of pneumonia is developed to investigate the effect of a pathogen-contaminated environment, and the significance of community and hospital-based care on disease management. The basic properties of the model including positivity and boundedness, existence, and stability of equilibria were determined. The basic reproduction number, (R_0) was derived and was used to study the model properties. It has a locally asymptotically stable disease-free equilibrium when the reproduction number is less than one, in which case the disease will be contained. The conditions for the existence of the endemic equilibrium and the possibility of backward bifurcation were also established. Sensitivity analysis was performed to determine the parameters with the greatest influence on the reproduction number, from which the results revealed that transmission rate through the contaminated environment and contact rate through person-to-person have the most significant potential of increasing the disease burden when increased, while effective treatment and increased decay rate of virus from the environment have the greatest possibility of minimizing the number of infections. Numerical simulations were performed to illustrate the analytical results as
well as establish the long-term behavior of the disease. It was observed that effective treatment interventions either in the hospital or community-based care can accelerate the containment of the disease. On the contrary, the infection may stay longer in the community in situations with increased contact with infected individuals either in hospital or community-based care. We recommend that the community- based care be enhanced in the disease management process to cater for communities where hospitals are far from reach and in resource-limited settings. We further recommend training of community-based caregivers on the transmission dynamics of pneumonia and its management and
prevention strategies. More still, practicing good hygiene, and applying more control measures such as vaccination and isolation of the infected is essential in containing the disease.

Let G be a connected graph. The eccentricity of a vertex v of G is the distance
from v to a vertex farthest from v. The eccentric sequence of G is the
non-decreasing sequence of the eccentricities of the vertices of G.

In this talk we present bounds on on several graph invariants - including metric dimension,
number of leaves and Wiener index - for trees in terms of their eccentric sequence.

This is joint work with Audace Dossou-Olory.

Disease incidence forecasting is critical in guiding disease
control strategies, resource distribution, and healthcare system preparedness.
Linear time series models such as autoregressive (AR) models are
incapable of capturing time dynamics of highly infectious diseases. This
study proposes Smooth Transition Autoregressive models for modeling
non-linear dynamics of disease incidence. Using simulations studies, our
proposed methods were able to capture the regime-switching behavior of
disease incidence data compared to the standard AR forecasting model.
In an analysis of COVID-19 data in African countries, our methods outperformed
the conventional AR model in short-term forecasting, demonstrating
potential in infectious disease forecasting.
Keywords: Autoregressive model; Bayesian; Hierarchical; Model; COVID-
19; Infectious Disease; Forecasting

This research aims to evaluate the performance of single models and their combinations for forecasting the volatility of tourism demand. The main thrust of this research is on developing a comprehensive understanding of how different modelling approaches can contribute to accurate volatility forecasts. The seasonal autoregressive integrated moving average (SARIMA) model is employed in the construction of the mean equation. In addition, three single models are utilized for estimating the volatility of monthly tourist arrivals to South Africa: the generalized autoregressive conditional heteroskedasticity (GARCH) family models, the innovative smooth transition exponential smoothing (STES) model and the error-trend-seasonal exponential smoothing (ETS-ES) model. Three combining methods which are the simple average (SA), minimum variance (MV), and novel smooth transition (ST) were used in model adequacy checking. The research contributes to the field of tourism demand forecasting in South Africa and beyond by providing insights into the efficacy of different modelling approaches and their combinations for volatility forecasting. It offers valuable directions for future research in this area, aiming to enhance the accuracy and reliability of tourism demand volatility forecasts.

Keywords: Forecast combining method; tourism demand volatility; exponential smoothing; SARIMA-GARCH family models; SARIMA-ES family methods.

Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of similar strength in online gaming, and for players to track their own strength over time. Most implemented rating systems assume only win/loss outcomes, and treat occurrences of ties as the equivalent to half a win and half a loss. However, in games such as chess, the probability of a tie (draw) is demonstrably higher for stronger players than for weaker players, so that rating systems ignoring this aspect of game results may produce strength estimates that are unreliable. We develop a new rating system for head-to-head games that explicitly acknowledges a tie as a third outcome, and that the probability of a tie may depend on the strengths of the competitors. Our approach relies on time-varying game outcomes following a Bayesian dynamic modeling framework, and that posterior updates within a time period are approximated by one iteration of Newton-Raphson evaluated at the prior mean. The approach is demonstrated on a large dataset of chess games played in International Correspondence Chess Federation tournaments.

Malaria remains a health challenge globally despite more than 100 years of research. Malaria is a vector borne disease caused by Plasmodium parasites, with Plasmodium falciparum being the deadliest and most prevalent in Africa. P. falciparum transmission is driven by ecological factors including those that favor Anopheles breeding sites and thus Anopheles populations. Understanding the ecology of malaria and its vectors is an essential component of successful malaria control. In sub-Saharan Africa, agriculture is an important aspect of this ecology. According to the United Nations (UN) projections Africa’s population will double to 2.5 billion in 2050, with much of the growth occurring in rural areas. Such growth places considerable demand on Africa’s food supply and governments are considering large scale agricultural projects to meet this increased need. Agriculture development may undermine efforts to eliminate malaria.
While numerous factors influence the transmission dynamics of malaria, the role of agricultural practices has not been extensively studied. This study aims to develop a comprehensive mathematical model to explore the impact of agriculture on malaria transmission. Environmental reservoirs, influenced by irrigation practices, play a pivotal role in triggering mosquito breeding. We consider factors such as water irrigation, which can provide breeding grounds for mosquitoes; the use of pesticides, which may affect mosquito populations.
Preliminary results indicate that agricultural practices can lead to an increase in the mosquito population, thereby elevating the risk of malaria transmission. On the other hand, the proper use of pesticides and management of irrigation systems can mitigate this risk. The model also suggests that optimal rainfall and temperature can act as triggers in the environmental reservoir that will be favorable for the Anopheles populations.
This study underscores the importance of integrating malaria control measures into agricultural practices. This modelling framework allows for simulating and analyzing various scenarios, aiding in the development of targeted interventions for effective malaria control and elimination strategies.

Malaria is an infectious disease caused by several malaria parasites, including Plasmodium falciparum. The Anopheles mosquitoes are the vehicle of infection to humans, with Anopheles gambiae and Anopheles funestus being the most common in Africa. The fight with malaria has been going on for approximately 30 million years. Drug resistance led to the introduction and recommendation by the World Health Organisation to administer artemisinin-based combination therapies (ACTs). However, artemisinin resistance which emerged almost a decade ago in Cambodia is fast spreading and negating all the efforts to eliminate malaria through repeated malaria attacks due to the survival of malaria parasites in the red blood cells of an infected person. Artemisinin resistance is the delay in malaria parasite clearance within 72 hours after the administration of artemisinin-based therapy. In this study we aim to explore the progression and severity of malaria and effectiveness of ACTs in the presence of both resistant and sensitive parasites assuming a struggling healthcare system.

In this study we hypothetically simulated artemisinin resistance scenarios in a country with struggling health care facilities. A country of one million people, with 80% susceptible population and struggling healthcare systems. We used a deterministic compartmental mathematical model to model two scenarios, first one where the sensitive parasite only is present and in the second scenario both parasites are in circulation. In addition, we assessed the parasite evolutionary process for both struggling health care systems and well-resourced health care systems. We assessed malaria severity peaks and treated peaks for both parasites. We put some restrictive assumptions for example the inexistence of human mobility and human population is well mixed.

As expected, the findings showed that artemisinin resistant infections are more severe relative to artemisinin sensitive infections. The simulated plot shows a higher severity peak for artemisinin resistant infections relative to artemisinin sensitive infections. The increased severity is a result of many factors which include delayed treatment and long hospitalization/prolonged disease. The prolonged illness as shown by the rate of recovery comparison between the two parasites, time taken to recover from an artemisinin resistant infection is longer than the time to recover from artemisinin sensitive infection.

The findings of this study are a reference to policy makers in planning healthcare facilities, robust malaria surveillance system and ultimately the need to have an alternative to ACTs. The prolonged stay in health care facilities bring both direct and indirect costs.

This article introduces a new statistical distribution called the Heavy-Tailed-Type II Exponentiated Half Logistic-Gompertz-G (HT-TIIExHL-G-G) distribution. We provide various structural properties of this
distribution, such as the quantile function, linear representation, moments, generating function, and estimation using the maximum likelihood method. We carried out simulation study to explore the estimation
of the model parameters through several established techniques. The
analysis showcased their numerical efficiency and performance. Furthermore, through the utilization of the maximum likelihood technique, we
use a special instance from the HT-TIIExHL-G-G family of distributions family of distributions to show its practical application. This is achieved by fitting
it to three real-world data examples from health care and engineering
disciplines.

After the discovery of fractal structures of financial markets, enormous efforts has been dedicated to finding accurate and stable numerical schemes for solving fractional Black-Scholes partial differential equations. This work therefore serves to propose a numerical scheme for pricing double barrier options, written on an underlying stock whose dynamics are governed by a non-standard fractal stochastic process. The resultant model is of a time fractional nature and is herein referred to as a time-fractional Black-Scholes model. The presence of the time-fractional derivative helps in capturing the time-decaying effects of the underlying stock while capturing the globalized change in underlying price price and barriers. In this paper we present the construction of the proposed scheme, analyse it in terms of its' stability and convergence as well as present two numerical examples on pricing double knock-in barrier option problems. The results herein suggest that, the proposed scheme is unconditionally stable and convergent with order $\mathcal{O}(h^2+k^{2})$

In most applications, parametric monitoring schemes are used to monitor the majority of industrial and non-industrial processes in order to improve the quality of the outputs or services. However, parametric monitoring schemes are known to underperform when the normality assumption is not met or when there is not enough information about the symmetry or asymmetry nature of the process underlying distribution. Hence, in this paper, a new nonparametric Phase II Shewhart-type double sampling (DS) monitoring scheme based on the precedence statistic is proposed in order to efficiently monitor quality processes when the underlying process distribution departs from normality. The performance is investigated using the average run-length (ARL), standard deviation of the run-length (SDRL), expected ARL (EARL) and expected average number of observations to signal (EANOS) and the average sample sizes (ASS) metrics. The latter metrics are computed using Monte Carlo simulation and exact formulae. In general, it is shown that the new DS precedence scheme outperforms the existing basic Shewhart precedence scheme with and without supplementary runs-rules in many situations. A real-life illustrative example based on a filling process of milk bottles is provided to demonstrate the application and implementation of the new DS precedence monitoring scheme.

In supervised classification, dataset shift occurs when for the units in the test set a change in the distribution of a single feature, a combination of features, or the class boundaries, is observed with respect to the training set. As a result, in real data applications, the common assumption that the training and testing data follow the same distribution is often violated. Dataset shift might be due to several reasons; the focus is on what is called “concept shift”, namely the conditional distribution P(x|y) differs from training to test set. Random perturbation of variables or units when building the classifier can help in addressing this issue. Evidence of the performance of the proposed approach is obtained on simulated and real data.

The heat transfer in the longitudinal fin of a convex parabolic shape is examined in this research. We use the power law to model the temperature distribution, thermal conductivity, and heat transfer coefficient, which vary non-linearly with temperature. The boundary conditions that we have selected are the step change in base heat flow and the step change in base temperature. We employ Lie symmetries to overcome the issue. Two local symmetries were allowed by the governing equation for the convex parabolic profile in the case where m=n and two additional symmetries in the situation where m is not equal to n. The initial non-linear PDE was transformed into non-linear ODEs by the local symmetries. Both steady-state and transient-state solutions were examined. In certain circumstances, the solutions achieved the desired step shift. The effects of the thermo-geometric parameter and the exponent on temperature are studied. The fin efficiency is also examined.

Let 1<= p <= infinity and 1<= r <=p* where p* is the conjugate index of p. We introduce and study the mid (p, r)-compact sets and operators. We begin by introducing and defining the mid (p, r)-compact subsets of a Banach space X and the mid (p, r)-compact operators between Banach spaces X and Y. The set of mid (p; r)-compact operators between Banach spaces X and Y will be denoted by K^mid_(p,r)(X, Y ). We prove that the ideal ( K^mid_(p,r)(X, Y ), k^mid_(p,r)(-)) is a quasi-Banach operator ideal. We will also introduce and study the (p, r)-limited sets of Banach spaces. We prove that the set K^mid_(p,r)(X, Y ) consists of (p, r)-limited sets. Other results with regard to this ideal K^mid_(p,r) and the (p, r)-limited sets will also be proved.

In the era of social media, the analysis of Twitter data has become increasingly essential for understanding the dynamics of online discussions. This research introduces an approach for tracking the spatial and temporal evolution of topics in Twitter data. Leveraging the spatial and temporal labels provided by Twitter for tweets, we propose the Clustered Biterm Topic Model. This model combines the Biterm Topic Model with K-medoid clustering to uncover the intricate topic development patterns over space and time.

To enhance the accuracy and applicability of our model, we introduce an innovative element: a covariate-dependent matrix. This matrix incorporates essential covariate information and geographic proximity into the dissimilarity matrix used by K-Medoids clustering. By considering the inherent semantic relationships between topics and the contextual information provided by covariates and geographic proximity, our model captures the complex interplay of topics as they emerge and evolve across different regions and timeframes on Twitter.

The proposed Clustered Biterm Topic Model offers a robust and versatile tool for researchers, policymakers, and businesses to gain deeper insights into the dynamic landscape of online conversations, which are inherently shaped by space and time.

In this talk, we address the problem of covariance matrix and factor model estimation in large dimensions under the low rank plus sparse assumption. Existing estimators based on principal component analysis fail to catch low rank components characterized by non-spiked eigenvalues, as in that case the established asymptotic consistency of principal components defaults. For this reason, UNALCE (UNshrunk ALgebraic Covariance Estimator), an alternative estimator based on the solution of a low rank plus sparse decomposition problem, has been developed. Existing solutions perform estimation by recovering principal components and sparsifying the residual covariance matrix, while UNALCE recovers the low rank plus sparse decomposition by least squares minimization under nuclear norm plus l1 norm penalization.
In the literature, the best known algorithm to numerically solve this problem is soft thresholding plus singular value thresholding. We study the convergence of this algorithm and we prove consistency for the subsequent estimators of the low rank and the sparse covariance matrix component under specific assumptions on the eigenvalues of the low rank component matrix and the number of on-zeros in the residual component matrix. These conditions allow both the identification of the underlying low rank and sparse matrix varieties and the optimization of the provided solution in terms of fitting, by introducing the unshrinking of estimated eigenvalues. This means that algebraic consistency is established for UNALCE estimators beyond the usual parametric one.
The new UNALCE procedure is compared with the existing ones under the same conditions. The performance of our minimizer is described in a wide simulation study, where various low rank plus sparse settings are simulated according to different parameter values.
It results that the UNALCE approach returns the covariance matrix estimate with the least possible dispersed eigenvalues among all the matrix pairs having the same rank of the low rank component and the same support of the sparse component, respectively. In addition, parametric consistency in various norms and the exact recovery of the latent rank and
the residual sparsity pattern are guaranteed, provided that latent eigenvalues present a larger scale than the maximum number of nonzero residual covariances per
row as the dimension diverges.
In the end, the approximate factor model which generates low rank plus sparse covariance matrix decompositions can be succesfully recovered. In fact, we prove that Bartlett’s and Thompson’s loadings and factor scores estimated via UNALCE provide the tightest possible uniform error bound in Euclidean norm. Simulation results show that UNALCE is particularly effective with respect to POET for recovering the proportion of latent variance, as well as the proportion of residual covariance and the number of residual non-zeros. In addition, UNALCE exactly recovers the latent rank and the residual sparsity pattern, showing also optimal fitting properties. UNALCE factor model estimates are then proved to be particularly effective if latent eigenvalues are not so spiked and the residual component is very sparse, even when the dimension is much larger than the sample size.
Two real data-sets, regarding UK market data and ECB supervisory data respectively, provide further insights about the usefulness of UNALCE in practical applications.

We deal with the existence of quadratic variation obtained from various deterministic paths that incorporate jumps as well as the existence of quadratic variation defined in other ways, for example along shifted partitions. We establish relationships between these variations. Additionally, we provide examples of deterministic paths where the quadratic variation exists as the limit of normalized truncated variation while the quadratic variation obtained along shifted partitions does not exist. Furthermore, we discuss examples of deterministic paths where the quadratic variation converges to different limits for distinct choices of sequences

Keywords: Quadratic variation, deterministic paths, truncated variation, model-free price paths.

The implementation of statistical techniques in on-line surveillance of financial markets has been frequently studied more recently. As a novel approach, statistical control charts which are famous tools for monitoring industrial processes, have been applied in various financial applications in the last three decades. The aim of this study is to propose a novel application of control charts called profile monitoring in the surveillance of the cryptocurrency markets. In this way, a new control chart is proposed to monitor the price variation of a pair of two most famous cryptocurrencies i.e., Bitcoin (BTC) and Ethereum (ETH). Parameter estimation, tuning and sensitivity analysis are conducted assuming that the random explanatory variable follows a symmetric normal distribution. The triggered signals from the proposed method are interpreted to convert the BTC and ETH at proper times to increase their total value. Hence, the proposed method could be considered a financial indicator so that its signal can lead to a tangible increase of the pair of assets. The performance of the proposed method is investigated through different parameter adjustments and compared with some common technical indicators under a real data set. The results show the acceptable and superior performance of the proposed method.

Many researchers have shown interest in profile monitoring; however, most of the applications in this field of research are developed under the assumption of normal response variable. Little attention has been given to profile monitoring with non-normal response variables, known as general linear models (GLM) which consists of two main categories (i.e., logistic and Poisson profiles). This paper aims to monitor Poisson profile monitoring problem in Phase II and develops a new robust control chart using support vector regression (SVR) by incorporating some novel input features and evolutionary training algorithm. The new method is quicker in detecting out-of-control (OOC) signals as compared to conventional statistical methods. Moreover, the performance of the proposed scheme is further investigated for Poisson profiles with both fixed and random explanatory variables as well as non-parametric profiles. The proposed monitoring scheme is revealed to be superior to its counterparts, including the likelihood ratio test (LRT), multivariate exponentially weighted moving average (MEWMA), LRT-EWMA and other machine learning-based schemes. The simulation results show superiority of the proposed method in profiles with fixed explanatory variables and non-parametric models in nearly all situations while it is not able to be the best in all the simulations when there are with random explanatory variables. A diagnostic method with machine learning approach is also used to identify the parameters of change in the profile. It is shown that the proposed profile diagnosis approach is able to reach acceptable results in comparison with other competitors. A real-life example in monitoring Poisson profiles is also provided to illustrate the implementation of the proposed charting scheme.

With the increase in scale of mining, hand sorting has become challenging and inefficient, hence over the years sensor based sorting has been introduced to increase retrieval rates, give more effective concentration, and thus reducing overall recovery costs. Wotruba et al (2014) presents sensor based sorting machines as a means to find and distinguish single raw material particles by using sensors rather than having direct contact with the particles. According to Reidel et al (2009), X-ray transmission sorters are an example of sensor based sorting machines which uses the particular atomic density of the input materials to determine the individual material constituents. These machines use image segmentation algorithms but their efficiency declines when dealing with small sized particles which are usually highly irregular in shape and there is variability in their sizes. Though these machines have some performance constraints they offer high potential to be highly efficient if their existing shortfalls are overcome hence the need to improve their current performance by improving on how their image analysis in the XRT sorting process is done as this is what determines the detection effectiveness and efficiency. Semantic Image segmentation is a computer vision technique that involves subdividing an image into sub-regions based on similar characteristics. This research tackles the problem of image segmentation of overlapping, touching and multi-faceted small particles from X-ray transmission images which is applied in improving efficiency of sensor based sorting of small rock particles in the context of mineral waste recovery. In our study, we explore classical image segmentation techniques as applied to the stated problem domain. Evidently from literature no standard image segmentation solution exist for this problem context, but a solution is built by evaluating and proposing an appropriate technique to apply at each of the general overlapping particles segmentation stages which are preprocessing and de-noising, image binarization, contour estimation, and post-processing and filtering. A categorization framework of which technique can be most appropriate at each of these phases for any given overlapping dataset, is proposed. The purpose of the framework is to guide research by attempting to provide some structure to the selection of different techniques in building a solution pipeline. We provide a case study on how our proposed categorization framework could be of benefit by implementing two solution pipelines for solving the given problem using the given X-ray Transmission image dataset and carrying out a visual analysis.

HIV/AIDS is still a global health burden and causes a significant number of morbidity and mortality. This study aims to explore time-dependent biomarkers and the time to death of HIV/AIDS patients jointly using the Bayesian estimation technique. The application of joint modeling is a statistical approach that simultaneously analyses multiple longitudinal outcomes and time-to-event data which recently become very crucial in medical research. The data for this study is obtained from Ethiopia, Felege Hiwot Comprehensive Referral Hospital from patients’ registration cards. A total of 571 patients' registration cards were accessed and their information is recorded for the current study. From a total of 571 patients, there are 315 female and 256 male patients with 52.2% and 48.8% respectively. The two longitudinally measured biomarkers, CD4 count and weight, were first transformed to square root and logarithmic transformation techniques respectively to make the data normally distributed. This study shows that the CD4 counts and weight of patients are significantly associated biomarkers with the time to death of the patients. The estimated association parameter for CD4 count is significantly associated at the current time and the weight of the patient is significantly associated at its slope. In this Bayesian joint model estimation, both the CD4 count and weight of the patients have negative estimated posterior mean association parameters which indicate that the hazard of death decreases as the CD4 count and weight of the patients increase. The presence of one or more diseases (comorbidity) in HIV/AIDS patients has also a significant effect on time to death and has a higher risk of death of the patients. The use of both longitudinal and time-to-event data jointly gives a more robust estimation and this will help the patient-specific intervention.
Keywords: Joint modeling, HIV/AIDS, longitudinal measure, Biomarkers

Semi-parametric mixture of Gaussian non-parametric regressions (SPGMNRs) are a flexible class of Gaussian mixtures of regression models. These models assume that the component regression functions (CRFs) are non-parametric functions of the covariates whereas the mixing proportions and variances are constant (parametric).
However, local-likelihood estimation of the non-parametric (CRFs) poses a computational challenge. Traditional EM optimization of the local-likelihood functions is not appropriate due to the label-switching problem. Separately applying the EM algorithm on each local-likelihood function will likely result in wiggly and non-smooth CRFs. This is because the local responsibilities calculated at the local E-step of each EM are not guaranteed to be aligned at each local M-step. A simple but effective approach to prevent any misalignment is to use the same (global) responsibilities at each local M-step. Thus, the goal is to obtain these global responsibilities.
In this presentation, we propose a novel two-step approach to address label-switching. In the first step, we maximize each local-likelihood function separately to obtain the local responsibilities. In the second step, based on an appropriate objective function, we choose one set of the local responsibilities from the first step as the global responsibilities. The performance and practical usefulness of the proposed method is evaluated using a simulated dataset and a real dataset.

In this talk, we discuss a necessary and suffiecient conditions for a weak topology to coincide with the original topology on the set C(X) of continuous real valued functions on X. It is known that for a topological space (X,τ), τu ⊂ τ where τu is a weak topology. Some cases where equallity between the two topologies are known.
For example, τ = τu, then the space X is completely regular. The converse is not there in general. Therefore our discussion will be focused on conditions where τ = τu and also consider some examples to illustrate the difference between the two topologies.
References
[1] F. Azaranah, F. Monshoor , R. Mohamadian A generalization of the m-Topology on C(X) finer than the m-Topology, Filomat, 2017 , 2509-2515

With diclofenac, ibuprofen and aspirin acting as controls, we demonstrate how graph irregularity index and eccentricity can be used to craft a prototype predictive model for identifying compounds with pain killing abilities. We, in the process, discover compounds that are superior than the well-known standard analgesics.

Compositional data sets, i.e., a dataset with observations that are proportional and are
subject to non-negativity and unit-sum constraints arise naturally in a variety of domains,
including agriculture, archaeology, biology, economics, environment, geography, geology,
medicine, and psychology. There is a strong footprint in the literature on the Dirichlet
distribution for modeling these types of data sets, followed by several generalizations of the
Dirichlet distribution with more flexible structures. In this paper, by applying square root
transformations on the Dirichlet and alternative candidates, novel contributions, are developed on the positive orthant of the hypersphere. Therefore, we consider n-variate distributionshaving joint probability distributions defined as functions of x1, . . . , xn, with the constraint x1+x2+...+xn = 1 . A visual display will shed light on the flexibility of these contributions. These distributions can be used to model compositional data or data clustered in some areas between ellipses.

Control charts, which are one of the major tools in the Statistical Process Control (SPC) domain, are used to monitor a process over time and improve the final quality of a product through variation reduction and defect prevention. As a novel development of control charts, referred to as profile monitoring, the study variable is not defined as a quality characteristic; it is a functional relationship between some explanatory and response variables which are monitored in such a way that the major aim is to check the stability of this model (profile) over time. Most of the previous works in the area of profile monitoring have focused on the development of different theories and assumptions, but very little attention has been paid to the practical application in real-life scenarios in this field of study. To address this knowledge gap, this paper proposes a monitoring framework based on the idea of profile monitoring as a data-driven method to monitor the internet usage of a telecom company. By definition of a polynomial model between the hours of each day and the internet usage within each hour, we propose a framework with three monitoring goals: (i) detection of unnatural patterns, (ii) identifying the impact of policies such as providing discounts and, (iii) investigation of general social behaviour variations in the internet usage. The results shows that shifts of different magnitudes can occur in each goal. With the aim of different charting statistics such as Hoteling T^2 and MEWMA, the proposed framework can be properly implemented as a monitoring scheme under different shift magnitudes. The results indicate that the MEWMA scheme can perform well in small shifts and has faster detection ability as compared to the Hoteling T^2 scheme.

The hulls of linear codes over finite fields have been of interest and extensively studied due to

their wide applications. In this work, we study the hermitian hull of constacyclic codes over a

finite semi-local ring. The main tool for the characterization of the hermitian hull of

constacyclic codes is given in term of their generator polynomials. We also establish the

dimension and the average hemitian hull dimension of constacyclic codes over finite ring.

Finally, we provide a formula for the average dimension of the hermotian hull of constacyclic codes with some upper and lower bounds over a finite semi local ring.

Multivariate analysis and time series modelling are essential data analysis techniques that provide a comprehensive approach for understanding complex datasets and supporting data-driven decision-making. Multivariate analysis involves the simultaneous examination of multiple variables, enabling the exploration of intricate relationships, dependencies, and patterns within the data. Time series modelling, on the other hand, focuses on data evolving over time, facilitating the detection of trends, seasonal patterns, and forecasting future values. In addition to the multivariate and time series analysis techniques, we expand our focus to include machine learning, a field dedicated to developing algorithms and models for data-driven predictions and decisions. The primary contribution of this research is the development of an innovative R Shiny application known as the Advanced Modelling Application (AM application). The AM application revolutionizes multivariate analysis, machine learning, and time series modelling by bridging the gap between complexity and usability. With its intuitive interface and advanced statistical techniques, the application empowers users to explore intricate datasets, discover hidden patterns, and make informed decisions. Interactive visualizations and filtering capabilities enable users to identify correlations, dependencies, and influential factors among multiple variables. Moreover, the integration of machine learning algorithms empowers users to leverage predictive analytics, allowing for the creation of robust models that uncover latent insights within the data and make accurate predictions for informed decision-making. Additionally, the application incorporates state-of-the-art algorithms for time series analysis, simplifying the analysis of temporal patterns, forecasting future trends, and optimizing model parameters. This ground-breaking tool is designed to unlock the full potential of data, enabling users to drive impactful outcomes.

This research essay provides an overview of the career and research contributions of Prof Maxim Finkelstein, a distinguished professor in the Department of Mathematical Statistics and Actuarial Science at the University of the Free State (UFS). Since his arrival at the institution, 25 years ago, he has authored and co-authored over 200 publications in ISI or Web of Science indexed journals as well as 3 monographs that made significant contributions to reliability studies. This contribution is through research output, collaboration, and editorial activities. His expertise lies in the field of mathematical theory of reliability with application, focusing on modelling and analysing shocks, failure rates and repairs of systems over time. This area of research is highly theoretical and is considered challenging to grasp, especially its practical applications. However, over the course of this project, it is demonstrated that the work serves as the foundation to many disciplines in science and engineering, and additionally provides a framework for analysing and modelling the ability of a system and/or object performing its intended function over its lifetime.

A characteristic feature of living organisms is their response to the environment in search for food or reproduction opportunities. This presentation is devoted to the investigation of the pattern formation of the Holling-Tanner predator-prey model with predator-taxis. We first summarize the qualitative properties of the model where a threshold for the appearance of pattern formation is specified. Secondly, we provide numerical simulations to support the theoretical findings.

Length-biased sampling has been well recognized in various fields such as economics, industrial reliability, etiology applications, and studies related to epidemiology, genetics, and cancer screening. Assessing the relationship between risk factors and survival time under biased data has been a longstanding statistical challenge, specially in length-biased data.
Due to the structure of the observed length-biased data is different with the target population, estimation of covariate effect using observed length-biased data is inappropriate using traditional methods. In this review, we focus on discussing the existing methods for estimating regression coefficients in Cox regression and several semiparametric linear models, including accelerated failure time, additive hazard, proportional odds, and transformation models in the context of observed length-biased data and informative right censoring. Furthermore, we conduct a comparative study using the Oscar dataset to compare the performance of biased correction methods with traditional methods.

The challenge of addressing unbalanced count data distributions in spatial count analysis prompts questions about the suitability of the Poisson model. Furthermore, the limitations of traditional methods become apparent when parametric models struggle to capture the intricate relationships between variables, particularly when covariates have uncleared functional forms and exhibit complex or unspecified spatial patterns.

To tackle these challenges, we propose the adoption of an innovative Bayesian hierarchical modeling approach. This methodology combines non-parametric techniques with a modified dispersed count model known as the Gamma-count model, which is based on renewal theory. This approach equips us to effectively handle the complexities of count data marked by unequal dispersion, nonlinear associations between variables, and intricate spatial patterns.

To showcase the adaptability and effectiveness of our proposed approach, we conduct a comprehensive simulation study to assess its performance across a range of scenarios, thereby providing a robust validation of its capabilities. Additionally, we apply this methodology to disease mapping, with a specific focus on the examination of lung cancer data. This research contributes to a broader understanding of spatial count analysis and paves the way for addressing complex count data challenges.

The human gut microbiome consists of all the microbes that make up the human intestinal
tract, and many diseases are associated with certain microbial compositions in the gut. First, a mathematical model describing the growth of gut microbiome inside and on the wall of the gut is developed based on the chemostat model with wall growth. Both the concentration and flow rate of the nutrient input are time-dependent, which results in a system of non-autonomous differential equations. First the stability of each meaningful equilibrium is studied for the autonomous counterpart. Then the existence of pullback attractors and its detailed structures for the nonautonomous system are investigated using theory and techniques of nonautonomous dynamical systems. In particular, sufficient conditions under which the microbiome vanishes or persists are constructed. Numerical simulations are provided to illustrate the theoretical results. Then a second model is developed describing the growth of one beneficial bacterial populationwith time-varying controlled rate of the input flow of the nutrient. First the stability of each meaningful equilibrium is studied for a constant input case. Then schemes are developed using optimal control theory to find an optimal time-varying rate of input flow. Numerical comparison simulations are provided

World Rugby’s ranking system for national teams in rugby union is an adjustive rating system in which the two competing teams in a match exchange rating points based on a comparison between the match result and the predicted match outcome. For the match result, the teams are assigned 0 for a loss, 0.5 for a draw and 1 for a win. The predicted outcome, also scaled from 0 to 1, is the probability of a team beating the opponent and is calculated in terms of the relative strength of each team and home advantage, if applicable. With World Rugby’s system, the match result is considered more important than the margin of victory. Consequently, a team does not gain any rating points for a narrow loss to an opponent with a higher rating. Therefore, in this research an adjustive rating system is presented in which margin of victory is directly used in the calculation of the rating points. The two rating systems are applied to and compared for the 20 teams who competed in the 2023 Rugby World Cup.

Abstract: Optimal control is a very paramount area of research both in theory and application. The financial market is constituted of a risk-free asset and a risky asset whose price process is subjected to the uncertain random differential equation with Poisson jump. Based on the concept of an uncertain random process, optimal uncertain random differential game strategies in insurance and finance is dealt with. A two-player, non zero-sum uncertain differential game is presented. The goal of each investor is to maintain business competitive advantage over the other by sustaining or increasing the difference between the respective surplus of the two companies. In general each investor tries to maximise his terminal wealth. Ultimately, the dynamic programming approach is employed to obtain the explicit expressions of equilibrium investment strategies and value functions for the constant absolute risk-averse and constant relative risk-averse utility function.

Many species are experiencing significant range shifts due to climate change. In this talk, we present and analyze an integro-difference model that incorporates growth and dispersal in a shifting habitat. We extend existing models [1] by considering that population growth depends on the local habitat quality. The dispersal phase comprises two components: a habitat-dependent dispersal rate and a dispersal kernel, which reflects the dispersal distance. The model is used to assess the impact of climate change on population dynamics and to investigate the effect of different dispersal rates. We focus on both the profile of the populations and their persistence in the shifting habitat. Consistent with existing literature for single-species models, our results suggest that only species with intermediate dispersal ability can persist. We further identify the range of dispersal rates, respectively, for the persistence and the extinction of the species.

[1] Harsch et al. Moving forward: insights and applications of moving-habitat models for climate change ecology. Journal of Ecology 105 (2016), 1169-1181. https://doi.org/10.1111/1365-2745.12724

The lack of Information Communication Technology (ICT) integration in South African education has become a significant concern, as it limits the quality of education and teachers’ preparedness for a digital world. Despite the efforts of the government to provide schools with ICT infrastructure, research has shown that many teachers are not effectively integrating technology into their teaching practices. Consequently, this study aimed to explore the perceptions and self-efficacy among mathematics and non-mathematics teachers in South African schools. The Technology Acceptance Model (TAM) (Davis, 1989) was adopted to investigate the significant differences between mathematics and non-mathematics teachers concerning their ICT perceptions and self-efficacy. In the context of this study, TAM provided a lens to understand these teachers' willingness or resistance to adopt ICT in their teaching practices. The Statistical Package for the Social Sciences (SPSS) version 28 was used for descriptive and inferential statistics. The descriptive statistics include percentages, measures of location (means and medians) and measures of spread (standard deviations and interquartile ranges), while the inferential statistics consist of the nonparametric Mann-Whitney U test used for testing for significant differences between ordinal responses of two independent groups (mathematics vs non-mathematics teachers). Sixty-eight teachers from seven schools in the Nama Khoi Municipality situated in the Namakwa district of the Northern Cape province of South Africa were conveniently sampled based on their geographical accessibility (n = 38 mathematics teachers; n = 30 non-mathematics teachers). The majority of these teachers aged between 27 and 31 years (standard deviation = 2.239) and the gender distribution was 50 females, 15 males, and 3 prefer not to say. This study used a quantitative research design, employing a cross-sectional survey approach to explore these teachers' perceptions and self-efficacy in primary (n = 4) and secondary (n = 3) schools. A questionnaire consisting of closed-ended demographic and ordinal Likert scale questions was distributed face-to-face to the participants. Results showed that mathematics teachers generally reported significantly lower self-reported scores regarding their knowledge of ICT applications tailored for diverse learners and their ability to adapt technology for various teaching activities compared to non-mathematics teachers. Mathematics teachers felt more inadequately equipped with the essential technical skills to utilise technology to its fullest potential compared to non-mathematics teachers. Furthermore, results revealed a significant difference in perceptions of resistance to embracing ICT changes, with mathematics teachers likely exhibiting more resistance or perceiving more resistance among their peers. Results also showed that mathematics teachers perceived a greater barrier to accessing high-quality online resources compared to their counterparts who are not teaching mathematics. The study provided insights into the perceptions and self-efficacy of mathematics teachers and non-mathematics teachers regarding ICT integration in the South African education landscape. This study furthermore contributed to the literature on mathematical sciences, and the results could be generalised to other municipalities with similar characteristics. Results suggest that there is a need for specialised training programs focusing on ICT tools specifically for mathematics education, given the knowledge and adaptability gap observed among mathematics teachers. These programs should emphasise hands-on experience and real-world applications to enhance mathematics teachers' confidence and skills.

Keywords: ICT, Mathematics, Mann-Whitney U, Mathematical Sciences, Quantitative, Questionnaire, Self-efficacy

References
Davis, F. D. (1989). Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS Quarterly, 13(3), 319-340. Retrieved from http://www.jstor.org/stable/249008

The global community is growing increasingly concerned about the mathematical achievement of South African schoolchildren. From the reports of the well-known international large-scale international study, the Trends in International Mathematics and Science Studies (TIMSS), which investigates aspects of mathematical performance, South Africa’s abysmal learner mathematics achievement has once again taken centre stage. South Africa participated in TIMSS 2019 at Grade 5 and Grade 9 levels; the focus of this study is on the Grade 5 level where South Africa scored 374, which is well below the international benchmark of 500. TIMSS establishes the minimum benchmark at 400 points, with a score above 400 indicating the acquisition of fundamental mathematical skills. Only 37% of South African learners acquired basic mathematical knowledge (score above 400), indicating that 63% of South African learners do not possess basic mathematical knowledge (Reddy et al., 2020). In recent years, South Africa has implemented numerous intervention programs intended to enhance the educational system (Zenex Foundation, 2020). Consequently, these poor results in mathematics are alarming.

Poor safety in schools can be a significant hindrance to academic success, and addressing this issue is a vital step toward improving the overall educational landscape in South Africa. In line with the principles enshrined in the South African Constitution, which seeks to safeguard the rights and welfare of all its citizens, it is imperative to emphasise the fundamental right of every child to access equitable education that is not only devoid of harm but also fosters a safe and conducive learning environment. This commitment is not just a matter of policy; it is a legal imperative, as stipulated in the South African Children’s Amendment Act No. 41 of 2007, which mandates the reporting of incidents of violence against schoolchildren to law enforcement agencies (Republic of South Africa, 2008). Despite the legislative framework in place, the disheartening reality persists that stories of dreadful and distressing events in South African schools continue to dominate news headlines. The very essence of education hinges on the creation of an environment where learners can learn, grow, and thrive without fear or intimidation.

In a concerted effort to shed light on these pressing issues of unsafe South African schools and poor mathematics performance, a comprehensive investigation was conducted into the safety factors associated with Grade 5 mathematics achievement in the South African educational landscape. The study employed a quantitative research design rooted in a deductive approach and underpinned by a positivist philosophical stance. To conduct this inquiry, a secondary data analysis method was employed, using data collected in the 2019 TIMSS cycle for respondents from South Africa. Maslow’s Hierarchy of Needs (Maslow, 1943) was used as theoretical framework, wherein safety and security represent one of the fundamental needs that must be met before individuals can fully realise their potential. In this context, addressing safety concerns in education is a crucial step toward allowing learners to progress towards fulfilling their academic potential.

The study’s main objective was to construct a model that could elucidate the complex interplay of safety factors impacting Grade 5 mathematics achievement in South Africa. This model encompassed ten variables: one dependent variable (Grade 5 mathematics achievement) and nine independent variables (gender, socio-economic status (SES), and seven components related to various safety aspects within school environments). The analysis was carried out using sophisticated multi-level techniques, facilitated by Hierarchical Linear Modeling (HLM) software. The results of this comprehensive analysis revealed a set of salient factors that stood out as significant predictors of Grade 5 mathematics achievement in South Africa. Among these significant predictors were issues related to feelings of insecurity at school, incidents involving theft or intentional damage to property, instances of physical harm or threats, the SES of the learners, the safety of school buildings and grounds, as well as the prevalence of intimidation or verbal abuse directed at teachers and staff.

In conclusion, this study underscores the profound impact of safety factors within the South African educational context on the mathematics achievement of Grade 5 learners. It is evident that these factors are intricately linked to the learners’ ability to learn and thrive in an academic environment. The results of this research bring into sharp focus the urgent need for proactive measures and policy interventions to mitigate the pervasive issues of insecurity and violence within South African schools. These results should serve as a clarion call for stakeholders in the education system, policymakers, and the broader society to collaborate and work towards the creation of a safer and more nurturing educational environment for all South African learners. In light of these results, it is important to consider a range of recommendations and proposals aimed at addressing these pressing issues and ensuring that the right to education, as enshrined in the South African Constitution, is upheld and safeguarded for all children in the country. This study, thus, underscores the significance of acknowledging the multifaceted challenges within the South African education system, emphasising the need for collective efforts to create a secure and supportive educational milieu for the nation’s youth.

Keywords: mathematics achievement; multi-level analysis; school safety; TIMSS 2019

References

Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50(4), 370–396. https://doi.org/10.1037/h0054346

Reddy, V., Winnaar, L., Juan, A., Arends, F., Harvey, J., Hannan, S., Namome, C., & Zulu, N. (2020). TIMSS 2019 highlights of South African grade 5 results in mathematics and science. Department of Basic Education. Retrieved from https://www.timss-sa.org/publication/timss-2019-highlights-of-south-african-grade-5-results-in-mathematics-and-science

Republic of South Africa. (2008). Children’s Amendment Act, 2007 (Act No. 41 of 2007). Pretoria: Government Printers

Zenex Foundation (2020, 18 February). New Zenex study provides a valuable overview of maths teaching and learning programmes. Retrieved from https://www.zenexfoundation.org.za/new-zenex-study-provides-a-valuable-overview-of-maths-teaching-and-learning-programmes/early-grade-research-knowledge/

Background: In recent years, the field of personalized medicine has witnessed remarkable advancements, particularly in the domain of joint modeling. Prior research in personalized screening predominantly concentrated on univariate joint modeling, which involved the examination of a single longitudinal outcome and a single time-to-event outcome. Nevertheless, real-world data often encompass multiple longitudinal outcomes and diverse event types, including recurrent or competing events. This necessitates the adoption of multivariate modeling. While multivariate joint models have been explored for various types of outcomes, such as continuous, binary, ordinal, or mixed types, their application in personalized screening, particularly in the context of data from the sub-Saharan African region, remains relatively limited. This project represents a pioneering effort in the study of HIV disease progression in resource-limited settings. It employs multivariate joint models to analyze both longitudinal and time-to-event data within the framework of personalized screening, marking a significant milestone, particularly for South Africa.

Methods: Our aim was to introduce a practical and straightforward methodology designed to personalize screening intervals for multiple longitudinal outcomes within the framework of multivariate joint longitudinal and time-to-event models. Our method uses patient-specific cumulative-risk of HIV progression. If the risk is above a predefined threshold, we schedule a visit. This methodology was applied to estimate the optimal timing for the next measurement of CD4 count and viral load, utilizing contemporary HIV data from the SAPIT study conducted by the Centre for the AIDS Programme of Research in South Africa (CAPRISA). Our primary objective was to formulate personalized screening schedules for patients, taking into account their regularly monitored CD4 counts and viral loads, along with relevant baseline covariates. These individualized screening plans will empower healthcare professionals to proactively design interventions and promptly adjust treatment strategies, ultimately reducing the risk of mortality. This study represents a significant contribution to the field of personalized medicine, particularly in the context of HIV disease progression in resource-limited settings and highlights the novel application of multivariate joint models for more effective healthcare interventions.

Results: In the SAPIT dataset, CD4 counts, and viral loads were scheduled at baseline and at every six months. Our model suggested more frequent visits for very sick individuals with CD4 counts less than 100. Whereas for healthy individuals with CD4 > 500, the model suggested less frequent visits.

Conclusion: Our methodology allowed for flexibility, enabling adjustments in screening intervals based on the evolving health status of the patient. For instance, if a patient’s CD4
count or viral load shows significant fluctuations, the model can adapt, leading to
more frequent tests. Similarly, if the patient’s health remains stable over a period,
the intervals between screenings can be extended, reducing the frequency of unnecessary
tests. By integrating CD4 count and viral load data into personalized risk assessments,
healthcare providers can tailor screening intervals for HIV patients effectively.
This patient-centered approach not only optimizes healthcare resources but
also enhances patient experience by minimizing unnecessary medical procedures while ensuring timely interventions when needed. 

Students with disabilities attending regular universities tend to need more support from the university and their peers. Whether in class or outside the classroom, students with disabilities have some difficulties with social participation. This paper will find out more about the interaction of students with disabilities and their peers , what sort of interaction they have ,how often they interact with other students either those with disabilities or those without disabilities and what triggers this sort of interaction. During a lecture at the University of Malawi ,Chancellor College(UNIMA), at least 100 students were observed, 50 were sampled of which 5 of them have disabilities. Out of these 5 students 4 have visual impairment and one with a walking disability. All 50 students were given questionnaires to fill , where they were also asked to nominate 5 friends each. Students with and without disabilities were asked about their learning experiences in the classroom with their peers and lecturers and about what measures can be taken in order to accommodate everyone without segregation. An observation was also done during the lecture hours, in order to observe how they class is conducted and the behavior of the students with and without disabilities was also observed. The data collected was entered into Gephi to analyze. Using social network analysis, results showed that these students with disabilities have fewer friends, engage less in classroom activities and have small social networks. The big difference in the social participation of students with disabilities and their peers indicates that there is need for change of how lectures are conducted and also finding ways of how to increase the social networks of students with disabilities. These ways could be training more teachers in special needs education, grouping the students with disabilities and their peers and also conducting extra curricular activities for the students.

A key focus area in the development of medical technologies in the past decade has been toward providing personalized medicine, where medicinal treatments are catered to the individual. This is due to the dynamic nature of diseases such as HIV/AIDS, cancer, type I bipolar disorder, schizoaffective disorder, etc. where prognosis varies significantly by individual. In longitudinal clinical trials, biostatisticians often seek to model repeatedly measured biomarkers of diseases such as HIV, such as viral load, with at least one time-to-event point of interest, for example, the development of AIDS. Over the past three decades a methodological approach for this, known collectively as joint modelling of longitudinal and time-to-event data, has been rigorously developed. At its core, the joint model seeks to model the association, through various approaches, between the time-to-event and the longitudinal processes. Numerous R packages have been developed to estimate joint models. To name a few, there are JMbayes2, joineRML and lcmm, among others depending on what the use cases for analysis might be. JMbayes2 and joineRML could be considered for univariate and multivariate joint models, where more functionality in the former is catered more to Bayesian modelling and not necessarily the latter. However, lcmm is built for univariate and multivariate latent class joint models, a rising area of burgeoning research in the world of joint models that seek to combine concepts of finite mixture models, such as model-based clustering, with joint models. Although some of these packages are new, they inherit statistical architectures from older packages by the same key authors. This arguably makes these packages some of the more mature frameworks available for building joint models in R. JMbayes2, in particular, is less than six months old but its use for modelling joint data holds promise. This presentation will discuss some of the underlying statistical assumptions of these packages and the estimation process for each package for comparison. Moreover, the author will explore, showcase and apply how these packages work for univariate and multivariate cases with the aid of two separate datasets for HIV/AIDs and psychiatric disease. This work will ultimately showcase the work done during the course of the author's doctoral candidature to date, as well as discuss potential areas of future research.

Background: In human genetics, heterozygote advantage (heterosis) has been
detected in studies that focused on specific genes but not in genome-wide
association studies (GWAS). For example, heterosis is believed to confer
resistance to certain strains of malaria in patients heterozygous for the sickle-cell
gene, haemoglobin S (HbS). Yet the power of allelic tests can be substantially
diminished by heterosis. Since GWAS (and haplotype-associations) also utilize
allelic tests, it is unclear to what degree GWAS could underachieve because
heterosis is ignored.
Methods: In this study, a two-step approach to genetic association testing in
malaria studies in a GWAS setting that may enhance the power of the tests was
proposed, by identifying the underlying genetic model first before applying the
association tests. Generalized linear models for dominant, recessive, additive, and
heterotic effects were fitted and model selection was performed. This was
achieved via tests of significance using the MAX and allelic tests, noting the
minimum p-values across all the models and the proportion of tests that a given
genetic model was deemed the best. An example dataset, based on 17 SNPs,
from a robust genetic association study and simulated genotype datasets, were
used to illustrate the method. Case-control genotype data on malaria from Kenya
and Gambia were used for validation.
Results and conclusion: Results showed that the allelic test returned some false
negatives under the heterosis model, suggesting reduced power in testing genetic
association. Disparities were observed for some chromosomes in the Kenyan and
Gambian datasets, including the sex chromosomes. Thus, GWAS and haplotype
associations should be treated with caution, unless the underlying genetic model
had been determined.
Keywords: Allelic test; Case-control study; Genome-wide association; Malaria;
MAX test

The focus of this study will be to apply principal component analysis (PCA) as a tool to identify the major sources of air pollution variation in Gaborone, Botswana. The concentrations for each criteria pollutant, Nitric Oxide (NO), Nitrogen Dioxide (NO2), Nitrogen Oxides (NOx), Ozone (O3), Sulfur Dioxide (SO2), and Carbon Monoxide (CO) will be established using PCA. In addition, PCA will be used to construct a temporal overall air quality assessment index to find the period of best air quality along the year. PCA will also be used to group the parameters and estimate the interrelationships between the loadings of the parameters in each component. The data will be collected through a monitoring station in Gaborone called Civic Centre, and it will involve the measurements of O3, NO, NO2, NOx, SO2, and CO for the year 2019. These air quality parameters will then be analyzed using PCA seasonally and yearly.

Characterization of solar energy behavior under intermediate-sky conditions in Mozambique

1 Fernando Mucomole; 2 Carlos Silva & 3 Lourenço Magaia

1 Eduardo Mondlane University, Faculty of Sciences, Department of Physics, Mozambique,
1 Eduardo Mondlane University, Faculty of Sciences, CPE – Centre of Research in Energies,
2 University of Lisbon, Instituto Superior Técnico, Department of Mechanical Eng., Portugal
3 Eduardo Mondlane University, Faculty of Science, Department of Mathematics and Informatics, Mozambique.

Corresponding author’s email: [email protected]

The use of solar energy using photovoltaic systems is increasing in many regions of the world. However, not all locations have the same capacity to generate an equitable flow of energy at the output of a similar photovoltaic generating system; this is due to the substantial reduction in solar energy upon arrival at the surface of the earth, which is conditioned by the characteristics of the sky types of each location. To do this, we characterize the behavioral variability of intermediate-sky days at each location under short measurement interval conditions. Only data with the intermediate-sky nomenclature were analyzed, which are the most problematic in terms of high variability of photovoltaic solar energy. Using a sample of clear-sky index data with a measurement interval of 60,0 seconds, measured in the projects of the Eduardo Mondlane University, the National Energy Fund of Mozambique and the National Institute of Meteorology of Mozambique, totaling around 18 measurement stations by traditional radiometers. The statistical analysis of the clear-sky index probability density function for intermediate-sky days is located in the range of 0,0274 to 0,0771, presenting for any average clear-sky index values, high values of deviation from the clear sky index about 0,6473. The results do not show any considerable discrepancies in the temporal evolution behavior between locations, with a correlation of the clear sky index between the stations along the channel. It can be concluded that on intermediate sky days the probability density shows a slight decrease, since the frequency of clear sky index variation values in the range outside -1,0 to 1,0 is higher.

Keyword: Intermediate-sky, characterization, behavior, variability, photovoltaic.

Bibliography: 1 – Twidell, John & Weir, Tony (1996), Renewable Energy Resources, https://doi.org/10.4324/9781315766416; 2 – Mucomole, F. V. Et al. (2023), Temporal Variability of Solar Energy Availability in the Conditions of the Southern Region of Mozambique, https://doi.org/10.54536/ajenr.v2i1.1311; 3 – Perez, R.et al. (2016), Spatial and Temporal Variability of Solar Energy, Foundations and Trens in Renewable Energy, USA, New York, 2016. doi:10.1561/2700000006.

Investigators in the fields of interventions, social science, and epidemiology frequently encounter the task of dissecting the impact of exposure into various causal pathways that operate through specific intermediary variables. Previous studies have suffered from methodological limitations as they did not account for interactions between exposure and mediator. Assessing mediation without accounting for interactions leads to biased estimates. This paper introduces the concept of decomposing the total effect into three components: a direct effect, an indirect effect, and an interactive effect. An Aalen additive model including a product term for the exposure and mediator term was developed. The methods were further illustrated with practical approach to real Kenya Demographic health survey data. Disentangling the pathways between education and Under Five Child Mortality, also requires a statistical methodology that allows interactions between exposure and mediators. Interaction between education and maternal income was estimated. Most of the total effect is attributable to pure direct effect and part of it is attributable to pure indirect effect. and A given proportion is ascribed to an interaction between no education level and maternal income
From this investigation we see that though significant portion of the effect of maternal education in Under Five Child Mortality is mediated by raising maternal income, it is the interaction between maternal education and maternal income in the popular of these cases of mediation that conveys about reduction in under Five Child Mortality. Computations for all data sets was implemented using the freely available R-software package.

{Key Words: [ mediation; Child mortality; Aalen additive model; Total effect].}

Spectral analysis is very important in the study of Banach algebra and in particular C*-algebras and their extensions. In this paper, we provide in details, a partial solution to the open problem regarding the spectral extension (SE) property in Banach algebras. Let $\mathcal{A}$ be a non-unital C*-algebra and let $\mathcal{A}^{I} = \mathcal{A} \oplus{\mathcal{C}_{I}}$ be the unitized form of $\mathcal{A}$. It is known that if $\mathcal{A}$ satisfies the SE property then $\mathcal{A}^{I}$ also satisfies SE property. The interesting open question is: Does the converse holds? Therefore, in this note we characterize strong spectral extension and give conditions when the converse holds for $\mathcal{A}^{I}.$ We also provide applications in the structural characterization of norm-attainability criterion in a general Banach space setting.

Although Rwanda's HIV prevalence has declined, many people are still acquiring or living with it. Among other methods of HIV prevention, condoms are a safe and reliable method in addition to preventing pregnancy and other sexually transmitted infections, especially when used properly. This study determined the prevalence of and factors associated with condom use during last sexual intercourse among reproductive-aged women in Rwanda using data from the cross-sectional, nationally representative Rwanda Demographic and Health Survey (RDHS) conducted in 2019/2020. A geo-additive logistic regression model was applied to determine the factors associated with condom use as well as spatial variations in condom use. All analyses from the model were adjusted for unequal sampling probabilities using survey weights. Results showed a 10.8% prevalence of condom use. The odds of condom use during last sex were significantly lower for women who lived with a man (adjusted odds ratio [aOR]= 0.10, CI=0.08:0.13) and those from the Southern region (aOR=0.69, CI= 0.52 to 0.92) but were significantly higher for those with primary education (aOR=1.38, CI= 1.00:1.88). Also, the rich were more significantly associated with condom use compared to the poor (aOR=1.53, 95% CI= 1.20:1.93). Those who had three or more sexual partners had higher odds of condom use than those with one partner (aOR=3.12, CI= 2.50:3.89). Based on the results, health promotion interventions aimed at raising awareness of HIV prevention should, therefore, target the groups and districts that were found to have a low prevalence of condom use.

Assessment of the risk of emergence of avian influenza in Senegal according to the health approach using data modeling of migratory birds

Sow Mouhamadou Moustapha1, Diallo Binta1, Ndour Khady1, Dame Diongue1, Diouf Nicolas1 et Dia Ndeye Méry1
1. Gaston Berger University of Senegal

Highly pathogenic avian influenza (HPAI) outbreaks in wild birds and poultry are no longer a rare phenomenon in west Africa. In the last 3 years, HPAI outbreaks in particular those caused by H5 viruses that emerged in north Senegal in 2021 have been occurring with increasing frequency in the country. Between 2021 and 2023, many outbreaks HPAI were identified in Senegal resulting in mass mortalities among poultry and wild birds. In 2021, 750 great white pelicans (Pelecanus onocrotalus) (740 juveniles and 10 adults) were found dead by rangers in the Djoudj Nation Bird Sanctuary. The sanctuary welcomes thousands of Palearctic and Afroprotical migratory birds every year as a refuge. In the same year, the Ministry of Environment documented 8,887 pelicans.
The goal of this study is to value the emergence risk of HPAI from the migratory birds in Senegal by using modulization.
Specifically:
• Identify the most species at risk;
• To identify the period of highly risk emergence of HPAI;
• Value the risk of emergence of HPAI
• Predict the risk of HPAI emergency.
The WHOA and Westland database on migratory birds in Senegal was used for the modeling. We used data on birds at risk of avian flu, with 10 species on the red list. Thus, after cleaning the data, we used the Chi-square test (<0.05) to evaluate the months where the risk of avian flu emergence is higher, with a p-value applied of <0.001. For modeling prediction, linear regression with the least-squares method was used.
On average, between 1990 and 2022, 300,000 species of the ten bird families at risk of avian influenza were recorded in Senegal, with a steady increase since 2015. Since then, the number of birds at risk has almost doubled, from 300,000 to 500,000, making the emergence of HPAI more frequent in this region. This visualization shows that the months of July, February and January are the most at risk for epidemics. This is confirmed by recent epidemics that have occurred at these times of year. The risk of occurrence is estimated at 20.45 at a 95% confidence interval; t(29; 0.025). The prediction on the number of species at risk, a risk factor for HPAI epidemics over the next 10 years, gives a total population size of 114,806.558 (?‚?144 752.25) and the model parameters: mean error (1.9227e-009); mean absolute error (88279) and bias proportion, UM (0).
This study is the first to estimate the risk from wild birds of the emergence of avian influenza in Senegal. With an estimated risk of 20. 00, it is necessary to set up integrated monitoring of migratory birds and thermal sensor systems in order to anticipate variations. The model is not perfect, given the number of observations, but it gives an idea of the importance of zoonosis management.
Keywords: avian influenza; migratory bords; risk assessment; date modeling; One Health

This study aims to forecast the potential COVID-19 trends and determine how long a wave could be, taking into consideration the current vaccination rates. The model is calibrated using South African reported data for the first four waves of COVID-19, and the data for the fifth wave are used to test the validity of the model forecast. The model is qualitatively analyzed by determining equilibria and their stability, calculating the basic reproduction number R0 and investigating the local and global sensitivity analysis with respect to R0. The impact of vaccination and control interventions are investigated via a series of numerical simulations. Based on the fitted data and simulations, we observed that massive vaccination would only be beneficial (deaths averting) if a highly effective vaccine is used, particularly in combination with nonpharmaceutical interventions. Furthermore, our forecasts demonstrate that increased vaccination coverage in SSA increases population immunity leading to low daily infection numbers in potential future waves. Our findings could be helpful in guiding policy makers and governments in designing vaccination strategies and the implementation of other COVID-19 mitigation strategies.

One-health stresses on an integrated, unifying approach that aims at sustainably balancing and optimizing the health of people, animals and the ecosystems. As one way of ensuring sustainable interactions of different systems in the ecosystem, this study uses a One-health (OH) approach to compare performance of Local-, Kuroiler- and Black Australrorp chickens raised under semi-intensive management system in Malawi. This aim is necessitated by an increase in poultry and livestock production system by urban residents, keeping chickens and other small livestock in the backyards, to respond to an increasing demand for local chickens unlike broilers. However, previous studies have shown that performance of semi-intensive poultry maybe largely affected by genetic, epigenetic and environmental factors which in turn affect both the environment and human health. We present some preliminary findings.

Impact of Demography on the Dynamics of Malaria

J. Banasiak, University of Pretoria, [email protected]
S. Y. Tchoumi, University of Pretoria, [email protected]
R. Ouifki, North West University, [email protected]


Epidemiological models should account for the vital dynamics when the disease duration is comparable with the lifespan of affected individuals, the disease is lethal or recurring, or when we study the disease's long-term impact on the population. The authors often use ad hoc or generic population equations to describe the vital dynamics. In the talk, using a malaria model as an example, we shall show that the used population model can dramatically affect the dynamics of the disease. Therefore, the selection of the latter requires extreme care.

1. J. Banasiak, R. Ouifki, S. Tchoumi, Impact of demography on the dynamics of malaria with transmission-blocking drugs.

Approach for sizing a photovoltaic system to power a Mobile Health Clinic

1 Fernando Mucomole; 2 Carlos Silva & 3 Lourenço Magaia

1 Eduardo Mondlane University, Faculty of Sciences, Department of Physics, Mozambique (Mz),
1 Eduardo Mondlane University, Faculty of Sciences, CPE – Centre of Research in Energies, Mz,
2 University of Lisbon, Instituto Superior Técnico, Department of Mechanical Eng., Portugal, Lisbon;
3 Eduardo Mondlane University, Faculty of Science, Department of Mathematics and Informatics, Mz.

Corresponding author’s email: [email protected]



The treatment and diagnosis of local diseases in a mobile health clinic powered by a photovoltaic solar system is an efficient alternative as it provides energy without oscillation, assisting in uninterrupted treatment, and sustainable as it can be applied in regions that do not yet benefit from the connection. to the conventional electrical network. Motivated by the above, the materialization and design methodology of a mobile health clinic with the capacity to treat two patients simultaneously is presented. A sample of solar radiation data from the years 2020, 2021 and 2022 from the National Institute of Meteorology of Mozambique was used to estimate the months with the highest and lowest solar radiation, and using the method for sizing autonomous photovoltaic systems which consists of sizing the photovoltaic arrangement based on energy needs, the power of the photovoltaic generator was determined. The internal and external dimensions of the mobile health clinic were determined, analyzing the internal and external environment. The power supply system was standardized using efficient lamps for room lighting and a thermometer was used to measure temperature. To keep the temperature constant, a thermostat was used. Next, the photovoltaic system was designed for the mobile health clinic. In this task, energy needs were first surveyed by creating a table in which clinical treatment loads and clinical material were organized according to their powers and hours of operation and daily energy consumption was calculated. Based on the total energy consumption required, the photovoltaic modules, solar batteries, charge controller, and inverter, components of the mobile health clinic's photovoltaic systems, were sized. It was possible to conclude that the daily energy consumption of the mobile clinic is 864.44 Wh/d. For good performance and long durability of the photovoltaic system, it must be composed of three monocrystalline solar modules, with a nominal power of 100 W each, a bank of sealed solar batteries with a capacity of 459 Ah, a solar inverter with an apparent power of 400 W. , a 240W charge controller, with current (20A continuous) and several cables with a minimum cross-sectional area of 1.5 mm2.

Keyword: solar clinic, photovoltaic, sizing, health, diseases.

Bibliography: 1 – Mucomole, F. V. Et al. (2023), Temporal Variability of Solar Energy Availability in the Conditions of the Southern Region of Mozambique, https://doi.org/10.54536/ajenr.v2i1.1311; 2 – Twidell, John & Weir, Tony (1996), Renewable Energy Resources, https://doi.org/10.4324/9781315766416; 3 – Perez, R.et al. (2016), Spatial and Temporal Variability of Solar Energy, Foundations and Trens in Renewable Energy, USA, New York, 2016. doi:10.1561/2700000006.