Author: Prof Jacek Banasiak (University of Pretoria)
Paper - Keynote Address
Long-term asymptotics in multiscale malaria models
Prof Jacek Banasiak (University of Pretoria)
Prof Jacek Banasiak (University of Pretoria) - Primary Author
Mathematical models of malaria are notoriously difficult due to the presence of (at
least) two interacting populations, human hosts, and mosquitoes. Fortunately for
modellers, these populations evolve at widely different time scales, which offers a
way to simplify the model using the tools from the singular perturbation theory.
However, to be relevant for the long-term dynamics of the models, the asymptotic
results must be uniform in time. In this talk, we present a survey of recent work on
these aspects of asymptotic analysis and show how they can be applied to achieve
a meaningful reduction in the complexity of some malaria models.
[1] J. Banasiak, A note on the Tikhonov theorem on an infinite interval, Vietnam Journal of Mathematics, 49(1), pp. 69-86 (2021)
[2] J. Banasiak, Some remarks on the renormalization group and Chapman-Enskog type methods in singularly perturbed problems, Mathematical Methods in the Applied Sciences, 43(18), pp. 10361-10380 (2020)
[3] J. Banasiak, R. Ouifki, W.A. Woldegerima, Some mathematical tools for
modelling malaria: A subjective survey, Biomath, 10(2), 2110029, (2021)
[4] E. Berettaa, V. Capasso, D. G. Garao, A mathematical model for malaria
transmission with asymptomatic carriers and two age groups in the human
population, Mathematical Biosciences, 300, 87–101, (2018)
Author: Prof Yves Dumont (CIRAD- UMR AMAP, University of Pretoria)
Paper - Keynote Address
On crop vector-borne diseases
Prof Yves Dumont (CIRAD- UMR AMAP, University of Pretoria)
Prof Yves Dumont (CIRAD- UMR AMAP, University of Pretoria) - Primary Author
In this talk I would like to present some examples of issues related to crop epidemiology, and in particular crop vector-borne diseases, for which Mathematical modeling can bring some new insights. The way plant diseases can spread are numerous, such that modeling [1-4] can become more complex, and thus more interesting, than standard human vector-borne diseases. Mathematical Modeling can also be helpful to derive new planting strategy [1] or new control strategies [2,3]. Unlike human vector-borne diseases, crop vector-borne diseases vectors can spread many plant diseases. For instance, Aphids are able to transmit several to hundreds of viruses on many crops. Plant viruses need vectors to survive. That is why, they have developed particular skills to enhance their survival, like host and vector manipulation. Modeling some vector preferences in temporal and spatiotemporal models [4] allow us to derive new results that can be useful to derive new vector control strategies.

[1] Roumen Anguelov, Jean Lubuma, Yves Dumont, Mathematical Analysis of Vector- Borne Diseases on Plants. In Guo, Y., Kang, M. Z., Dumont, Y. (Eds). The Fourth International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications, Shanghai, China, 31 October-3 November 2012. Beijing: IEEE Press, 22–29 (2012)

[2] Michael Chapwanya, Yves Dumont. Application of Mathematical Epidemiology to crop vector-borne diseases. The cassava mosaic virus disease case. In Miranda I. Teboh- Ewungkem; Gideon Akumah Ngwa. Infectious Diseases and our Planet, 7, Springer, 2021, Mathematics of Planet Earth, 978-3-030-50825-8

[3] Michael Chapwanya, Yves Dumont. On crop vector-borne diseases. Impact of virus lifespan and contact rate on the traveling-wave speed of infective fronts. Ecological Complexity 2018, 34, pp.119 - 133.

[4] Yves Dumont, Frédéric Hamelin, Frank Hilker, Spatiotemporal modeling of plant dis- eases and vector preferences. In preparation. 2022.
Author: Prof Winsto Garira, (University of Venda)
Paper - Keynote Address
The Transmission Mechanism Theory and its Application in the Development of Single Scale Models of Disease Dynamics
Prof Winsto Garira, (University of Venda)
Prof Winsto Garira, (University of Venda) - Primary Author
Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which span over three centuries now is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process. Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history, dating back to about three centuries now, that knowledge has not yet been formalized into a scientific theory. In this talk, I will discuss the formalization of this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system, disease dynamics is determined by transmission as the main dynamic disease process. I will also discuss how the transmission mechanism theory of disease dynamics has recently been extended by our research group into new radical scientific theory for multiscale modelling of infectious disease dynamics called the replication-transmission relativity theory. Throughout this talk, my aim is to show that our description of natural phenomena using scientific theories is a dynamic process because these scientific theories often only adequately describe the phenomenon studied up to a certain time. As time progresses, new knowledge often emerges as we refine the domains of observation to improve the accuracy of measurement and description.
Author: Prof J Lubuma (University of the Witwatersrand)
Presentation - Keynote Address
Ebola Virus Disease Spread and Control in War and Conflict Times
Prof J Lubuma (University of the Witwatersrand)
Prof J Lubuma (University of the Witwatersrand) - Primary Author
Prof M Chapwanya (University of Pretoria)
Dr Y Terefe (University of Free State)
Prof B Tsanou (University of Dschang)
In recent years, Ebola Virus Disease (EVD) outbreaks erupted in some African regions that are affected by war and conflict characterized by violence, destruction of Ebola Treatment Centers and escape of patients from hospitals to the bush. We develop a SIR-type model in which these disruptive events are suitably incorporated, and additional compartments are included to account for indirect/slow transmission through the contaminated environment. We compute the basic reproduction number of the model and use it to discuss the stability of disease-free and endemic equilibria. We construct a dynamically consitent nonstandard finite difference (NSFD) scheme. Using real data of the 2018-2020 EVD outbreak in the Democratic Republic of Congo (DRC), we undertake a statistical data analytics study, which supports the theory and leads to some recommendations to control the disease.
Author: Dr Henri Laurie (University of Cape Town)
Presentation - Keynote Address
Might age structure be a maximum entropy phenomenon?
Dr Henri Laurie (University of Cape Town)
Dr Henri Laurie (University of Cape Town) - Primary Author
I review recent publications on entropy in organisms and ecosystems. I then present a simple model population where thermodynamic entropy is invariant under age structure. Maximum information entropy in this case leads to uniform age structure. I then consider extending the model to more realistic populations
Author: Prof Anotida Madzvamuse (University of British Columbia)
Presentation - Keynote Address
Pattern formation on biological evolving domains and surfaces: Modelling, analysis and simulations
Prof Anotida Madzvamuse (University of British Columbia)
Prof Anotida Madzvamuse (University of British Columbia) - Primary Author
In this talk, I will present reaction-diffusion systems on evolving biological domains and surfaces. I will then present theoretical results demonstrating the generalisation of Turing diffusion-driven instability on evolving domains. I will demonstrate that the new conditions allow us to expand the family of models for pattern formation beyond the standard paradigm of long-range inhibition and short range activation. To support theoretical results, I will present finite element numerical simulations on growing domains for non-standard activator-activator kinetics as well as pattern formation on evolving surfaces. Here reaction-diffusion systems are posed on evolving hypersurfaces, the models are solved efficiently and robustly using the evolving surface finite element method. The theoretical outcomes challenge experimentalists to undertake experimental manipulations on domains that change in both space and time.
Author: Mr ES Ahiadu (University of Energy and Natural Resources)
Paper - Contributed talk
A Mathematical model for the transmission of the Black pod disease in a cocoa plantation
Dr BA Danquah (University of Energy and Natural Resources)
Mr ES Ahiadu (University of Energy and Natural Resources) - Primary Author
Dr BA Danquah (University of Energy and Natural Resources)
Black pod disease in cocoa is caused by fungi of the species Phytophthora palmivora or Phytophthora megakarya. The disease causes darkening of affected areas of cocoa trees and/or fruits and leads to significant reduction in crop yields and decreases lifespan of the plant. The disease affects the livelihood of farmers as well as the sustainability of the cocoa industry. In this study, we employed mathematical modelling and analysis to investigate the transmission of black pod disease in a cocoa plantation. An SEI model with variable population is used to assess the impact of cutting out approach, spacing or sanitation and post-exposure prophylaxis spraying on the dynamics of the black pod disease. In addition, we perform sensitivity analysis of the basic reproduction number with respect to the model parameters. The results show that apart from the per capita natural death rate of the cocoa trees, the top three parameters that govern the initial disease spread of the black pod disease are the contact rate, transmission probability, and planting rate of new trees. The effectiveness of the proposed control solution is shown by comparing the behaviour of controlled and uncontrolled systems. Numerical results show the impacts of the three controls in decreasing both exposed and infectious cocoa trees in the plantation.
Author: Dr J Malinzi (University of Eswatini)
Paper - Contributed talk
Dynamical survival analysis: from population to individual-based epidemic models
Dr J Malinzi (University of Eswatini)
Dr J Malinzi (University of Eswatini) - Primary Author
Due to the need for mathematical tractability, population-based epidemic models often ignore certain important characteristics of disease transmission patterns and the underlying populations. This often leads to inaccurate findings and poor forecasts [1]. In this work, the classical SIR epidemic model; which represents the transmission of populations from susceptible to infectious and recovered classes is reviewed. The review involves calculating the model thresholds of the basic reproduction ratio, the maximum possible number of infectives and the number of people that eventually end up being infected. Next, the SIR population-based epidemic model is transformed to a version that focuses on the fate of a single individual referred to as a survival dynamical system. I shall, using the approaches in KhudaBukhsh et al. [1], delve into the derivation of how population-level dynamics can simply imply probability laws for individual-level infection and recovery times which can be used for statistical inference.

1. W.R. KhudaBukhsh, B. Choi, E. Kenah, and G.A. Rempala, 2020. Survival dynamical systems: individual-level survival analysis from population-level epidemic models. Interface Focus, 10.1 (2020): 20190048.
Author: Dr TA Tegegn (Sefako Makgatho Health Science University and University of Pretoria)
Paper - Contributed talk
The contribution of vaccinated individuals in the transmission of COVID-19 after losing immunity: from mathematical modelling point of view
Dr TA Tegegn (Sefako Makgatho Health Science University and University of Pretoria)
Dr TA Tegegn (Sefako Makgatho Health Science University and University of Pretoria) - Primary Author
Dr YA Terefe (University of Free State)
Since its discovery in December 2019, in Wuhan China, COV-SAR-2 virus has infected well over half a billion people and claimed close to 7 million lives, by the \(9^{th}\) of September 2022.
The devastating effect of the pandemic, both socially and economically changed the way we lived and perceived our lives. Until vaccines were invented, our way of life seemed to adopt to new realities. The successful delivery of vaccines together with the tremendous effort from all stoke holders helped to slow down the spread of the virus and weaken its power so much so that people are starting to treat COVID-19 as if it is a seasonal flu. In this article we develop and analyse a mathematical model consisting of a system of deterministic ordinary differential equation to investigate the spread of the COVID-19 virus and contribution of vaccines in slowing down the pandemic. We have shown that the model exhibits a backward bifurcation during imperfect vaccination and recovery lead into temporary immunity for $\mathcal{R}_0<1$. With perfect vaccination and recovery guarantees permanent immunity, the disease-free equilibrium is globally asymptotically stable for $\mathcal{R}_0<1$ and unstable for $\mathcal{R}_0>1$. Numerical experiments are provided to support the theoretical analysis.
Author: Mr B MUFOYA (University of Venda)
Paper - Contributed talk
Multiscale modelling of infectious disease systems
Mr B MUFOYA (University of Venda)
Mr B MUFOYA (University of Venda) - Primary Author
Modelers of infectious disease systems are increasingly shifting towards a new modelling
framework called Multiscale modelling approach. This is because infectious disease
systems are complex systems that consist of multiple levels of organization and multiple scales. In this paper, we formulate a coupled multiscale model that integrates two adjacent scales at the macro-community level of organization (that is, the within-community scale and the between-community scale) where the whole pathogen life cycle is strictly inside the two hosts (vector host and vertebrate host) involved in the transmission of multi-hosts infections using Malaria as a paradigm. A key feature about this framework is that it distinguishes between-community transmission dynamics (global exchange of pathogen)
and the within-community transmission dynamics (local exchange of pathogen) during the entire transmission-replication cycle. The aim of this paper is to establish the
influence of the local transmission and global transmission parameters on the Malaria model dynamics. We develop an SIR-type multiscale model that illustrates the local transmission dynamics of malaria disease within the community and using graph-theoretic approach we represent the global transmission processes. We then extend this model to a stochastic model formulated by perturbing the system of ordinary differential equations using a stochastic Wiener process. From the numerical analysis, results show that an increase in the rates of migration of infected individuals from patch 2 to patch 1 leads to an increase in the Malaria burden in patch 1.
Author: Ms M. A. S Songa (University of Kwazulu-Natal)
Presentation - Contributed talk
A Modeling Formalism for Petri-nets
Ms M. A. S Songa (University of Kwazulu-Natal)
Ms M. A. S Songa (University of Kwazulu-Natal) - Primary Author
One of the applications of category theory is to provide formalisms for understanding the compositionality of open systems. These include Petri-nets, chemical reaction networks and Markov processes. One of the areas closely related to Rosen's metabolic repair networks is Petri-nets.

Recent discoveries provide formalisms for understanding the compositionality of open systems using decorated cospans and structured cospans. A key requirement for these constructions to work is the existence of finite colimits. The categories which arise in this way have pleasing properties. They are compact closed and self-dual (hypergraph). Hence, they are amenable to Rosen's arguments for closure to efficient causation in metabolic-repair networks.

Focusing on Petri-nets, we discuss the constructions which arise from decorated spans / structured cospans. We also discuss their role in providing a good formalism for understanding self-organisation in living systems.

Author: Dr Rendani Netshikweta (University of Venda)
Presentation - Contributed talk
A Nested Multiscale Modelling Framework for Characterizing HIV/AIDS as a Vector-borne Transmission Dynamics
Dr Rendani Netshikweta (University of Venda)
Dr Rendani Netshikweta (University of Venda) - Primary Author
Dr Kizito Muzhinji (University of Venda)
In the study of infectious disease systems, there has been a widespread appreciation of the fact that the transmission dynamics of infectious diseases can be classified into three main mechanisms, namely directly transmitted, environmentally transmitted, and vector-borne transmitted mechanisms. In recent years, we have witnessed efforts in which infectious disease systems that are directly transmitted in nature or even vector-borne transmitted diseases being studied as environmentally transmitted infections. This have been achieved by means of community pathogen load, a public health metric which measures a community's infectiousness. In this paper, we present a multiscale modelling framework that characterize directly transmitted infectious diseases as vector-borne transmitted infections using HIV/AIDS as a case study. We analyse numerically the multiscale model for HIV/AIDS dynamics presented using the nonstandard finite difference method (NSFDM). The NSFDM analysis results indicate that reducing the community viral load of both the population of female and male host respectively, is good for a individual but have a minimal impact on the transmission risk of the disease among individuals in the community. However, reducing both the infection rate of female and male has good benefits not only to individuals but to the community as a whole. Therefore, for a significant containment of HIV/AIDS more efforts should be directed to reduce the infection in both the population of males and females in the community.

Keywords: Infectious Disease Systems, HIV/AIDS Dynamics, Community Viral Load, Multiscale Modelling, Nonstandard Finite Difference Method (NSFDM)
Author: Mr K.A Maqele (University of Pretoria)
Presentation - Contributed talk
Beyond the tanh method - looking for explicit travelling wave solutions to partial differential equations
Mr ()
Mr K.A Maqele (University of Pretoria) - Primary Author
In this talk, we focus on general procedure for finding exact travelling wave
solutions for evolution equations with polynomial nonlinearities. We then
show that the well known methods such as the tanh-method, G'/G-method and
others are special case of the method to be presented.
Author: Dr HO Minoarivelo (Centre for Statistics in Ecology, Environment and Conservation SEEC, University of Cape Towniversity of Cape Town)
Presentation - Contributed talk
Mutualism creates empty ecological niches for invasion
Dr HO Minoarivelo (Centre for Statistics in Ecology, Environment and Conservation SEEC, University of Cape Towniversity of Cape Town)
Dr HO Minoarivelo (Centre for Statistics in Ecology, Environment and Conservation SEEC, University of Cape Towniversity of Cape Town) - Primary Author
Dr U Dieckmann (Complexity Science and Evolution Unit, Okinawa Institute of Science and Technology Graduate University, Japan)
Prof C Hui (BioMath group, Department of Mathematical Sciences, University of Stellenbosch)
Understanding how ecosystems are structured by species with different functional traits being packed through community assembly is a major challenge in ecology. Niche dynamics, rooted in the principle of competitive exclusion have been shown to be key determinants of such species packing. However, models based solely on competitive interactions have failed to explain the widely observed emergence and persistence of empty niches waiting to be exploited by alien invaders in many communities. Here, using the framework of adaptive dynamics [1], we build a theoretical model that accounts for eco-evolutionary feedbacks. We show how empty niches naturally emerge from the interplay of trait-mediated mutualistic and competitive interactions during community assembly. Specifically, we report that: first, empty niches result from a mutualism-induced impediment of trait evolution, trapping community assembly in a sub-optimal Nash equilibrium. Second, when biological invasions close a community by filling its empty niches, the community’s trait distribution becomes increasingly predictable. Third, successful invaders are more likely to establish outside the region of trait space benefiting from mutualism, especially if they are latecomers in the community-assembly process. Thus, mutualistic interactions can lead to the emergence and persistence of empty niches through complex eco-evolutionary feedbacks.

[1] Metz, J.A.J., Nisbet , R.M., Geritz, S.A.H. (1992): How should we define ‘fitness’ for general
ecological scenarios? Trends in Ecology and Evolution 7: 198–202.
Author: Mr Tiomela Tanefo SEDRIQUE ARNAUD (university of Yaounde I)
Presentation - Contributed talk
Computer simulation of the dynamics of a spatial SIR epidemic model with time delays in transmission and treatment
Mr Tiomela Tanefo SEDRIQUE ARNAUD (university of Yaounde I)
Mr Tiomela Tanefo SEDRIQUE ARNAUD (university of Yaounde I) - Primary Author
In human history, the spread of infectious diseases has repeatedly leads to epidemics, which could
cause a devastating disaster to the earth and mankind. when such diseases increase in incidence and
tend to spread geographically within decades, they can be defined as emerging infections. Diseases
that reappear after a significant decline are called reemerging diseases. Generally, the appearance
of these diseases always causes sanitary and economic crisis globally leading to planetary fluctuations, particulary in the low income countries like those in Africa. In this work, we analyze the
spatial-temporal dynamics of a susceptible-infected-recovered (SIR) epidemic model with time delays. To better describe the dynamical behavior of the model, we take into account the cumulative
effects of diffusion in the population dynamics, and the time delays in both the Holling type
II treatment and the disease transmission process, respectively. To this end, we perform linear
stability analyses at the disease-free and endemic equilibria, provide the expression of the basic
reproduction number and set conditions on the backward bifurcation using Castillos theorem. The
values of the critical transmission time delay, the treatment delays and the relationship between
them are established. As results, we show that the transmission and treatment time delays are
inversely proportional to the susceptible and infected diffusion rates. The analytical results are
numerically tested. The results show how the treatment rate significantly reduces the density of
infected population and ensures the transition from the unstable to the stable domain. Moreover,
the system is more sensible to the treatment in the stable domain. As conclusion, the density of
infected population increases with respect to the infected and susceptible diffusion rates. Both
effects of treatment and transmission delays significantly affect the behavior of the system. The
transmission time-delay at the critical point ensures the transition from the stable (low density) to
the unstable (high density) domain
Author: Dr A Ramanantoanina (University of Pretoria)
Presentation - Contributed talk
Population dynamics in a moving habitat
Dr A Ramanantoanina (University of Pretoria)
Dr A Ramanantoanina (University of Pretoria) - Primary Author
As the global climate changes, different species have limited options for their survival: to move and follow their suitable habitat, or to stay and adapt to the changing conditions. In this talk, we discuss the dynamics of populations in a moving habitat, with an emphasis on the spatiotemporal dynamics of mutualistic populations. We consider the cases where the habitat velocity is constant using integro-difference equations; then numerical simulations are used to investigate the frequency of extinction and the time to extinction in a moving habitat with varying velocity.
Author: Dr SM Kassa (Botswana International University of Science and Technology)
Presentation - Contributed talk
Impact of the WHO integrated stewardship policy on the control of methicillin-resistant Staphyloccus aureus : using a mathematical modeling approach
Dr YA Terefe (University of the Free State)
Dr SM Kassa (Botswana International University of Science and Technology) - Primary Author
Dr J.B.H Njagarah (Botswana International University of Science and Technology)
Methicillin-resistant Staphylococcus aureus (MRSA) is community and hospital-associated pathogen causing serious infections among populations by infiltrating into hospitals and surrounding environment. This main multi-drug resistant or antimicrobial resistance (AMR) bacterial pathogen is a threat to human health if not properly tackled and controlled. Tackling antimicrobial resistance (AMR) is one of the issues for the World Health Organization (WHO) to design a comprehensive set of interventions which also helps to achieve the end results of the developing indicators proposed by the same organization.

A deterministic mathematical model is developed and studied to investigate the impact of the WHO policy on integrated antimicrobial stewardship activities to use effective protection measures to control the spread of AMR diseases such as MRSA in hospital settings by incorporating the contribution of the healthcare workers in a hospital and the environment in the transmission dynamics of the disease. The model also takes into account the parameters describing various intervention measures and is used to quantify their contribution in containing the disease. The impact of combinations of various possible control measures on the overall dynamics of the disease under study is investigated.

The model analysis suggest that the contribution of the interventions: screening and isolating the newly admitted patients, improving the hygiene in hospital settings, decolonizing the pathogen carriers, and increasing the frequency of disinfecting the hospital environment are effective tools to contain the disease from invading the population. The study revealed that without any intervention, the disease will continue to be a major cause of morbidity and mortality in the affected communities. In addition, the study indicates that a coordinated implementation of the integrated control measures suggested by WHO is more effective in curtailing the spread of the disease than piecemeal strategies. Numerical experiments are provided to support the theoretical analysis.
Author: Mr A.E Phiri (University of Pretoria)
Presentation - Poster
The cell viability function of the non-uniformly distributed data
Mr A.E Phiri (University of Pretoria)
Mr A.E Phiri (University of Pretoria) - Primary Author
Cell viability of tumour cells under treatment is an important quantitative measure of
drug efficacy. Deriving cell viability is an essential step in cancer drug discovery. The work presented in the talk is based on the mechanistic model in [https://arxiv.org/pdf/2207.08449] of the inhibitionactivation dynamics in a cell population exposed to an inhibitor of its vital functions. Measuring the viability usually involves conducting a series of experiments and most often the experiments are costly. In the study in [https://arxiv.org/pdf/2207.08449], uniformly distributed data is used to fit the theoretically derived cell viability function. In this study, we exploit the same approach to derive the cell viability function suitable for non-uniformly distributed data. We use the experimental data from the inhibiting metabolite, namely CTCE-9908 to approximate the parameters at a 95% confidence interval. Further, we present the IC50 (that is, the concentration required to induce the death of at least 50% of the cancer population) as a function of time. Furthermore, we present the model of cell viability as a function of both concentration and time. The practical value of the latter is that one can obtain cell viability at a specific concentration and at a given time.
Author: Mr A J MATUSSE (University of Pretoria)
Presentation - Poster
Partially Degenerate Reaction-Diffusion System arising in Crop-Disease. The Case of Maize Lethal Necrosis
Mr A J MATUSSE (University of Pretoria)
Mr A J MATUSSE (University of Pretoria) - Primary Author
Prof M CHAPWANYA (University of Pretoria)
Prof Y Dumont (University of Pretoria; CIRAD, UMR AMAP-FRANCE; AMAP, UNiversity of Montpellier, CIRAD, CNRS, INRA, IRD, FRANCE)
Host infection by multiple pathogen genotypes is a crucial constrain in disease ecology and evolution. For instance, Maize Lethal Necrosis Disease (MLND) in Southern Africa results from synergistic interaction between the Maize Chlorotic Mottle Virus (MCMV) and potyviridae such as Sugarcane Mosaic Virus (SCMV). MCMV are transmitted by several vectors including, beetles, flower thrips and maize thrips Frankliniella Williams) in semi-persistent manner while SCMV are transmitted by aphids including Rhopalosiphum maidis, Rhopalosiphum padi, Myzus persicae, Schizaphis graminum in nonpersistent manner.

In this poster, we propose a partially degenerate co-infection vector borne-disease model in unbounded domain. We show some theoretical results on the existence of traveling wave solution when one of the virus is circulating. When both virus are circulating, we show the existence of traveling wave solutions through numerical simulations, for different invasion scenarios depending on the threshold parameters and initial conditions. We discuss the consequences of these traveling waves in terms of crop protection.

keywords: Crop disease, co-infection, synergistic interaction, partially degenerate reaction-diffusion system, traveling wave, numerical simulation.
Important Dates
Conference Duration
20 November 2022 - 23 November 2022
1 June 2022 - 10 November 2022 [CLOSED]
Call For Abstracts
1 June 2022 - 10 November 2022
Prof M Chapwanya
Contact Email
[email protected]
Contact Number
  • Keynote Address
  • Contributed talk
  • Poster