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Prof R (Roumen) Anguelov (HOD)

Tel: +2712 420-2874 / 2520 
Fax: +2712 420-3893
E-mail: [email protected]
Office: Mathematics 1-39.2

Position: Professor and Head of Department of Mathematics and Applied Mathematics, University of Pretoria
Academic qualifications: MSc(Sofia), PhD(Unisa)
NRF rating: B3

Open Access version of Articles

Fields of interest: Mathematics, Applications of Mathematics
Research interests: Applications of Mathematics to population dynamics and epidemiology: zoonotic diseases, vector-borne infections, mosquito control, gene-drive into population, ecological systems. Mathematics motivated by biological applications: dynamical systems, PDEs, impulsive PDEs, interval analysis, validated numerics, nonstandard finite difference method, image analysis.

Curriculum Vitae

Publications over the past five years:

Journal articles 

Roumen Anguelov, Nikolay Kyurkchiev, Svetoslav Markov, Some properties of the Blumberg’s hyper-log-logistic curve, Biomath 7 (2018), 1807317, http://dx.doi.org/10.11145/j.biomath.2018.07.317

Roumen Anguelov, Kenneth Dukuza, Jean M.‐S. Lubuma, Backward bifurcation analysis for two continuous and discrete epidemiological models, Mathematical Methods in the Applied Sciences  2018; 15 pages, https://doi.org/10.1002/mma.5138

Roumen Anguelov, Milen Borisov, Anton Iliev, Nikolay Kyurkchiev, SvetoslavMarkov, On the chemical meaning of some growth models possessing Gompertzian-type property, Mathematical Methods in the Applied Sciences  2018; 12 pages, http://dx.doi.org/10.1002/mma.4539

Roumen Anguelov, Claire Dufourd, Yves Dumont, Mathematical model for pest–insect control using mating disruption and trapping, Applied Mathematical Modelling 52 (2017) 437–457, http://dx.doi.org/10.1016/j.apm.2017.07.060

Salisu Usaini , Alun L Lloyd, Roumen Anguelov, Salisu M Garba, Dynamical behavior of an epidemiological model with a demographic Allee effect, Mathematics and Computers in Simulation 133 (2017), 311–325, http://dx.doi.org/10.1016/j.matcom.2016.04.010

Roumen Anguelov, Claire Dufourd, Yves Dumont, Simulations and parameter estimation of a trap-insect model using a finite element approach, Mathematics and Computers in Simulation 133 (2017), 47–75, http://dx.doi.org/10.1016/j.matcom.2016.04.010

Roumen Anguelov, Stephanus Marnus Stoltz, Stationary and oscillatory patterns in a coupled Brusselator model, Mathematics and Computers in Simulation 133 (2017), 39–46, http://dx.doi.org/10.1016/j.matcom.2015.06.002

Roumen Anguelov, Vitalii Akimenko, Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay, Journal of Biological Dynamics;11(1)(2016), 75-101, http://dx.doi.org/10.1080/17513758.2016.1236988

HM Tenkam, R Anguelov, I Fedotov, M Shatalov, Exact solution of the Mindlin-Herrmann model for longitudinal vibration of an isotropic rod, Journal of Engineering Mathematics 99 (2016) 185–201.

HM Tenkam, M Shatalov, I Fedotov, R Anguelov, Mathematical models for the propagation of stress wave in elastic rods: Exact solution and numerical simulation, Advances in Applied Mathematics and Mechanics 8 (2016), 257--27

Salisu Usaini, Roumen Anguelov, Salisu M. Garba, Dynamics of SI Epidemic with a Demographic Allee Effect, Theoretical Population Biology 106(2015), 1–13

R. Anguelov, P.W. Butler, C.H. Rohwer , M. Wild, Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular LULU-filters, Quaestiones Mathematicae 38(4)(2015), 463-482

Roumen Anguelov, Salisu M Garba, Salisu Usaini, Backward Bifurcation Analysis of Epidemic Model with Partial Immunity, Computers and Mathematics with Applications 68(9)(2014), 921-940

R. Anguelov, Y. Dumont, J. M.-S Lubuma, M. Shillor, Dynamically consistent nonstandard finite difference schemes for epidemiological models, Journal of Computational and Applied Mathematics, 255(2014), 161-182, http://dx.doi.org/10.1016/j.cam.2013.04.042.

C Dufourd, C Weldon, R Anguelov, Y Dumont, Parameter identification in population models for insects using trap data, Biomath 2(2)(2013), Article ID 1312061, 10 pages

R Anguelov, J H van der Walt, Algebraic and Topological Structure of Some Spaces of Set-valued Maps, Computers and Mathematics with Applications, 66(2013), 1643-1654.

R Anguelov, Y Dumont, J M-S Lubuma, E Mureithi, Stability Analysis and Dynamics Preserving Non-Standard Finite Difference Schemes for a Malaria Model, Mathematical Population Studies 20, 101–122, 2013

H Brettschneider, R Anguelov, CT Chimimba, A Bastos, A mathematical epidemiological model of gram-negative Bartonella bacteria: does differential ectoparasite load fully explain the differences in infection prevalence of Rattus rattus and Rattus norvegicus?, Journal of Biological Dynamics Vol. 6(2) (2012), 763–781

R Anguelov, Y Dumont, J M-S Lubuma, Mathematical modeling of sterile insect technology for control of anopheles mosquito, Computers and Mathematics with Applications 64 (2012) 374–389

R Anguelov, J M-S Lubuma, M. Shillor, Topological dynamic consistency of nonstandard finite difference schemes for dynamical systems, Journal of Difference Equations and Applications, 17 (12), (2011), 1769-1791

R Anguelov, E Popova, Topological structure preserving numerical simulations of dynamical models, Journal of Computational and Applied Mathematics 235 (2010) 358 -- 365

R Anguelov, I Fabris-Rotelli, LULU Operators and Discrete Pulse Transform for Multi-Dimensional Arrays, IEEE Transactions on Image Processing, 19(11), (2010), 3012-3023

R Anguelov, J M-S Lubuma, F Minani, A monotone scheme for Hamilton-Jacobi equations via the nonstandard finite difference method, Mathematical Methods in the Applied Sciences 33 (2010), 41—48.

R Anguelov, J M-S Lubuma, F Minani, Total variation diminishing nonstandard finite difference schemes for conservation laws, Mathematical and Computer Modelling, 51(2010), 160—166.

R Anguelov, C H Rohwer, LULU operators for functions of continuous argument, Quaestiones Mathematicae 32 (2), 2009, pp. 187–202.

R Anguelov, O F K Kalenda , The convergence space of minimal usco mappings, Czechoslovak Mathematical Journal Vol. 59 (134), 2009, pp. 101-128

R Anguelov, J K Djoko, J M-S Lubuma, Energy properties preserving schemes for BurgersEquation, Numerical Methods for Partial Differential Equations,  Vol 24 (1), 2008, pp.41-58.

R. Anguelov, Rational Extensions of C(x) via Hausdorff Continuous Functions, Thai Journal of Mathematics, Vol. 5 No. 2, 2007, pp. 261-272

R Anguelov, Algebraic Computations with Hausdorff Continuous Functions, Serdica Journal of Computing, Vol. 1 No. 4, 2007, pp. 443-454

R Anguelov, E E Rosinger, Solving Large Classes of Nonlinear Systems of PDE's, Computers and Mathematics with Applications, Vol. 53, 2007, pp. 491-507.

R Anguelov, S Markov and B Sendov, The Set of Hausdorff Continuous Functions – the Largest Linear Space of Interval Functions, Reliable Computing, Vol. 12, 2006, pp. 337-363.

R Anguelov, J H van der Walt, Order Convergence Structure on C(X), Quaestiones Mathematicae, Vol. 28 (4), 2005,  pp.425-457.

R Anguelov and E E Rosinger, Hausdorff Continuous Solutions of Nonlinear PDEs through the Order Completion Method, Quaestiones Mathematicae,Vol, 28(3), 2005, pp. 271-285.

R Anguelov, P Kama, J M-S Lubuma, On the non standard finite difference models of reaction-diffusion equations. Journal of Computational and Applied Mathematics, Vol. 175, 2005, pp. 11-29

R Anguelov, Dedekind order completion of C(X) by Hausdorff continuous functions, Quaestiones Mathematicae, Vol. 27, 2004,  pp. 153-170

R Anguelov, J M-S Lubuma, S K Mahudu, Qualitatively Stable Finite Difference Schemes for Advection-Reaction Equations, Journal of Computational and Applied Mathematics, Vol. 158/1, 2003, pp. 19-30

R Anguelov R, J M-S Lubuma, Nonstandard Finite Difference Method by Nonlocal Approximation, Mathematics and Computers in Simulation, Vol. 61/3-6, 2003, pp. 465-475

R Anguelov, J M-S Lubuma, Contribution to the Mathematics of the Nonstandard Finite Difference Method with Applications to Certain Discrete Schemes, Numerical Methods for Partial Differential Equations, Vol. 17(5), 2001, pp. 518-543.

R Anguelov, Wrapping Function of the Initial Value Problem for ODE: Applications, Reliable Computing, 5(2), 1999, pp.143-164.

R Anguelov, S Markov, Wrapping Effect and Wrapping Function, Reliable computing, 4(4), 1998, pp. 311-330.

R Anguelov, Spline-Fourier Approximations of Discontinuous Waves,  Journal of Universal Computer Science (J.UCS), Vol.4(2), 1998, pp. 110-113.

R Anguelov, Guaranteed Bounds for the Solution of the Wave Equation, Quaestiones Mathematicae, Vol. 19 (1-2), 1996, pp. 275-289.

R Anguelov, On the Convergence of Interval Methods for Systems of ODE with Interval Initial Condition, Annals of Sofia University, Mathematics, 80, 1988. (in Bulgarian)

R Anguelov, On the Wrapping Effect, Comptes Rendus de L’Academy Bulgare des Sciences, 1987.

R Anguelov, S Markov, An Interval Method for Systems of ODE, Lecture Notes in Computer Science, 212, 1986, pp. 103-108.

R Anguelov, S Markov, Extended Segment Analysis, Freiburger Intervall - Berichte, No 10, 1981, pp. 1 - 63

Conference proceedings

R Anguelov, S M Stoltz, Modelling of activator-inhibitor dynamics via nonlocal integral operators, in R. Anguelov, M. Lachowicz (Editors), Mathematical Methods and Models in Biosciences, Biomath Forum, Sofia, 2018, pp. 57-63, http://dx.doi.org/10.11145/texts.2017.12.233

R Anguelov, M Mabula, Asymmetric metric: an application to dealing with uncertainty. In MD Todorov (editor),  Proceedings of the 8th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’16), (22-27 June 2016, Albena, Bulgaria), AIP Conference Proceedings 1773 (2016), 050001-1–050001-7; doi: 10.1063/1.4964971.

R Anguelov, S Markov, Hausdorff Continuous Interval Functions and Approximations, M. Nehmeier et al. (Eds.): SCAN 2014, LNCS 9553, pp. 3–13, 2016, DOI: 10.1007/978-3-319-31769-4 1

R Anguelov, HMD Tenkam, Global Stability of Equilibrium of Multi-species Model with Cross Diffusion. M.D. Todorov (editor), Application of Mathematics in Technical and Natural Sciences (28 June – 3 July 2015, Albena, Bulgaria), AIP Conf. Proc. 1684, 050001-1–050001-7; doi: 10.1063/1.4934297

R Anguelov, Y Dumont, JM-S Lubuma, Mathematical Analysis of vector-borne diseases on plants.  In M Kang, Y Dumont and Y Guo (editors), 2012 IEEE 4th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA’12), (Shanghai, China), Institute of Electrical and Electronic Engineers (IEEE), Inc, 2012, pp 22-29, ISBN: 978-1-4673-0068-1

R Anguelov, Y Dumont, JM-S Lubuma, On non-standard finite difference schemes in Biosciences.  In MD Todorov (editor),  Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’12), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 212-223, ISBN: 978-0-7354-1099-2

R Anguelov, D Agbebaku, J H van der Walt, Hausdorff Continuous Solutions of Conservation Laws, In MD Todorov (editor), Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’12), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 151-158, ISBN: 978-0-7354-1099-2

R Anguelov, I Fabris-Rotelli, On the Axiomatization of Scale-Space Theory, In MD Todorov (editor), Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’12), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 159-167, ISBN: 978-0-7354-1099-2

R Anguelov, I Fabris-Rotelli, Locally Monotone Approximations of Real Functions on Graphs, Proceedings of the International Conference on Constructive Theory of Functions, 3-10 June 2010,  Sozopol, Bulgaria, Marin Drinov Academic Publishing House, Sofia, 2012, pp. 21-29.

R Anguelov, Y Dumont, J M-S Lubuma, Mathematical Modeling of Sterile Insect Technology for Control of Anopheles Mosquito, In Ch Christov and MD Todorov (eds), Proceedings of the 3rd International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (Albena, Bulgaria), American Institute of Physics - AIP Conference Proceedings 1404, (2011), pp 155-161, ISBN: 978-0-7354-0976-7

R Anguelov, Y Dumont, J M-S Lubuma, Monotone Dynamical Systems: Application to population models, Proceedings of the Annual Meeting of the Bulgarian Section of SIAM, 20-21 December 2010, Sofia, pp. 7-10.

R Anguelov, H Brettschneider, A Bastos, A case of multi-vector and multi-host epidemiological model: Bartonella infection, In Ch Christov and MD Todorov (eds), Proceedings of the 2d International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’10), (21-27 June 2010, Sozopol,Bulgaria), American Institute of Physics - AIP Conference Proceedings 1301, (2010), pp 175 - 187, ISBN: 978-0-7354-0856-2

R Anguelov, Structurally Stable Numerical Schemes for Applied Dynamical Models, Proceedings of the 7th International Conference on Large Scale Scientific Computations, 3-8 June 2009, Sozopol, Bulgaria, Lecture Notes in Computer Science, 5910 (2010), pp. 557—565.

R Anguelov, S Markov, F Minani, Hausdorff Continuous Viscosity Solutions of Hamilton-Jacobi Equations, Proceedings of the 7th International Conference on Large Scale Scientific Computations, 3-8 June 2009, Sozopol, Bulgaria, Lecture Notes in Computer Science, 5910 (2010), pp. 241—248.

R Anguelov, E Popova, Reliable Simulations for Applied Dynamical Models, In TE Simons, G Psihoyios and Ch Tsitouras (editors), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2009, (18-22 September 2009, Rethymno, Crete, Greece), American Institute of Physics Conference Proceedings 1168, 2009, USA, Vol 2, pp. 1205-1209.

R Anguelov, Y Dumont, J M-S Lubuma, M Shillor, Dynamically consistent non-standard finite difference schemes for the MSEIR epidemiological model, In TE Simons, G Psihoyios and Ch Tsitouras (editors), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2009, (18-22 September 2009, Rethymno, Crete, Greece), American Institute of Physics Conference Proceedings 1168, 2009, USA, Vol 2, pp. 1213-1216

R Anguelov, Y Dumont, J M-S Lubuma, M Shillor, Comparison of some standard and non-standard numerical methods for the MSEIR epidemiological model, In TE Simons, G Psihoyios and Ch Tsitouras (editors), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2009, (18-22 September 2009, Rethymno, Crete, Greece), American Institute of Physics Conference Proceedings 1168, 2009, USA, Vol 2, pp. 1209-1212.

R Anguelov, H Kojouharov, Continuous Age-Structured model for bovine tuberculosis in African  buffalo, 1st International Conference on Application of Mathematics in Technical and Natural Sciences, 22-27 June 2009, Sozopol, Bulgaria, AIP Conference Proceedings Volume 1186 (2009), pp. 443-450.

R Anguelov, J Djoko and J M-S Lubuma, Numerical schemes that preserve properties of the solutions of the Burgers equation for small viscosity. In: A. Abdulle, et al. (Eds), Multiscale problems in biomathematics, physics and mechanics: modelling, analysis and numerics, Gakuto International Series in Mathematical Sciences and Applications, 2009, pp. 279--302.

R Anguelov, Dynamically Consistent Schemes for Epidemiological Models, Proceedings of the Annual Meeting of the Bulgarian Section of SIAM, 22-23 December 2008, Sofia, pp. 11--14

R Anguelov, I Fabris-Rotelli, Discrete Pulse Transform of Images, Proceedings of ICISP 2008, Lecture Notes in Computer Science 5099, 2008, pp. 1-9

R Anguelov, S Markov, Numerical Computations with Hausdorff Continuous Functions,  In: T. Boyanov et al. (Eds.),  Numerical Methods and Applications 2006 (NMA 2006), Lecture Notes in Computer Science  4310,  Springer, 2007, 279-286.

R Anguelov, J Djoko, P Kama, J M-S Lubuma, On Elementary Stable and Dissipative Nonstandard Finite Difference Schemes for Dynamical Systems, in T. Simos, G. Maroulis (Eds), Recent Progress in Computational Sciences and Engineering (Selected papers from the International Conference on Computational Methods in Sciences and Engineering, 27 October - 1 November 2006, Greece), Lecture Series on Computer and Computational Sciences, Volume 7A, VSP/Brill, 2006.

R Anguelov, F Minani, F., Nonstandard Finite Difference Schemes for Hamilton-Jacobi Equations, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, 15-19 September 2006, Greece, Wiley-VCH, Weinheim, 2006, pp. 28-31.

R Anguelov, LULU Operators and Locally δ-monotone Approximations, Proceedings of the International Conference on Constructive Theory of Functions, 1-7 June 2005, Varna, Bulgaria, Marin Drinov Acad. Publ. House, Sofia, 2006, pp. 22-34.

R Anguelov, S Markov, B Sendov, Algebraic Operations on the Space of Hausdorff Continuous Interval Functions, Proceedings of the International Conference on Constructive Theory of Functions, 1-7 June 2005, Varna, Bulgaria, Marin Drinov Acad. Publ. House, Sofia, 2006, pp. 35 - 44.

R Anguelov, S Markov, B Sendov, On the Normed Linear Space of Hausdorff  Continuous Functions, Proceedings of the Fifth International Conference on "Large Scale Scientific Computations", June 6-10, 2005, Sozopol, Lecture Notes in Computer Science, Springer,  Vol. 3743, 2006,  pp. 281 - 288.

R Anguelov, P Kama. J M-S Lubuma, Nonstandard theta method and related discrete schemes for the reaction-diffusion equation, In: T E Simos (editor), Proceedings of the International Conference of Computational Methods in Sciences and Engineering, World Scientific, Singapore, 2003, pp. 24-27.

R Anguelov, J M-S Lubuma, On the Nonstandard Finite Difference Method, keynote lecture at the 43rd Annual Congress of the South African Mathematics Society (SAMS), October 2000, Notices of SAMS, Volume 31 (3), 2000, pp.143-152.

R Anguelov, J M-S Lubuma, On the Mathematical Foundation of the Nonstandard Finite Difference Method, in B Fiedlers and K Groger (editors): International Conference on Differential Equations (Equadiff '99), 1-7 August 1999, Berlin, World Scientific, 2000, pp.1401-1403.

R Anguelov, On the Construction of Interval Numerical Methods for Initial Value Problems, in: Numerical methods and Applications, Ed B Sendov, Publ. House of the Bulgarian Academy of Sciences, 1989, pp. 18-22.

R Anguelov, P Bochev, G Grosev, S Markov, Highly Accurate and Save Numerical Computations via Interval and Advanced Computer Arithmetic, in: Numerical Methods and Applications, Ed. B Sendov, Publ. House of the Bulgarian Academy of Sciences, 1989, pp.23-27.

R Anguelov, Software for Automatic Differentiation with Application to Ordinary Differential Equations, International Conference on Numerical Methods and Applications, Sofia, 1984, Publ. House of the Bulgarian Academy of Sciences, 1985, pp.157 – 164

R Anguelov, S Markov, Two-Sided Approximation of the Solution of the Initial Value Problem for Systems of Ordinary Differential Equations Involving Inexact Data, Proceedings of the International Conference on Constructive Theory of Functions, Varna, 1984, Publ. House of the Bulgarian Academy of Sciences, 1984, pp. 125 -127.

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