Prof JM-S (Jean) Lubuma

E-mail: [email protected]

Position: Emeritus Professor
DST/NRF SARChI Chair: Mathematical Models and Methods in Bioengineering and Bioscience

Academic qualifications: MSc, PhD (Louvain)
NRF rating: A2

Link to SARChI Chair
Link to personal page
Open Access version of articles

Fields of interest: Science awareness
Research interests: Partial/ordinary differential equations; dynamical systems; numerical analysis (finite element/difference method, boundary element methods, etc.); function spaces (distributions, Sobolev, etc); integral equations of potential theory

Publications over the past five years:

Journal articles
Chapwanya M, Lubuma J.M.-S., Mickens RE  Nonstandard finite difference schemes for Michaelis-Menten type reaction-diffusion equations.  Numerical Methods for Partial Differential Equations, 29(1)(2013), 337-360

Anguelov R, Dumont Y, Lubuma JM-S, Mureithi EW  Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model.  Mathematical Population Studies, 20(2013), 101-122(available online DOI: 10.1080/08898480.2013.777240).

Anguelov R, Dumont Y, Lubuma JM-S., Shillor M  Dynamically consistent nonstandard finite difference schemes for epidemiological models.  Journal of Computational and Applied Mathematics, 255(2014), 161-182

Hassan AS, Garba SM, Gumel A, Lubuma JM-S  Dynamics of mycobacterium and bovine tuberculosis in a human-buffalo population.  Computational and Mathematical Methods in Medicine, 2014, Article ID 912306, 20 pages

Chapwanya M, Lubuma JM-S, Mickens RE  Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences.  Computers and Mathematics with Applications, 68(2014), 1071-1082 (available online DOI: 10.1016/j.camwa.2014.04.021)

Garba SM, Gumel A, Hassan AS, Lubuma JM-S  Switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation.  Applied Mathematics and Computation, 258(2015), 388-403

Appadu AR, Lubuma JM-S, Mphephu N Computational study of three numerical methods for linear and non-linear advection-diffusion-reaction equations.  Progress in Computational Fluid Dynamics 17(2)(2017), 114-129

Aderogba AA, Chapwanya M, Djoko JK, Lubuma JM-S  Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation.  International Journal of Computer Mathematics 93(11)(2016) 1833–1844

Djoko JK, Lubuma JM-S Analysis of a time implicit scheme for the Oseen model driven by nonlinear slip boundary conditions. Journal of Mathematical Fluid mechanics 18(2016), 717–730

Lubuma JM-S· Terefe YA A nonstandard Volterra difference equation for the SIS epidemiological model, RACSAM 109(2015), 597–602

Bowonga S Lubuma JMS Tsanou B Global stability of a two-patch cholera model with fast and slow transmissions. To appear in Mathematics and Computers in Simulation

Hussaini N, Lubuma JM-S, Barley K, Gumel AB Mathematical analysis of a model for AVL–HIV co-endemicity Mathematical Biosciences 271 (2016) 80–95

Terefe YA, Chapwanya M, Lubuma JM-S Analysis and dynamically consistent nonstandard discretization for a rabies model in humans and dogs. RACSAM 110(2016), 783–798

Manyombe ML, Mbang J, Lubuma JM-S, Tsanou B Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers. To appear in Mathematical Biosciences and Engineering

Terefe YA, Lubuma JM-S Global stability for the continuous and discrete SIS-diffusion epidemiological models. Quaestiones Mathematicae 40(2)(2017), 161–176

Tsanou B, Lubuma JM-S Moremedi GM, Shava RK A Simple Mathematical Model for Ebola in Africa. Journal of Biological Dynamics 11(2016), 42–74   

Djoko JK, Lubuma JM-S and Mbehou M On the numerical solution of the stationary power-law Stokes equations: A penalty finite element approach. Journal of Scientific Computing 69(2016),1058–1082

Tsanou B Bowonga S Lubuma JMS Global stability of a two-patch cholera model with fast and slow transmissions. Mathematics and Computers in Simulation 133(2017), 142–164

Appadu R, Djoko JK, Gidey H and Lubuma JM Analysis of Multilevel Finite Volume Approximation of 2D Convective Cahn-Hilliard Equation. Japan Journal of Industrial and Applied Mathematics 34(2017), 253–304

Tsanou B, Bowong S, Lubuma J, Mbang J  Assessing the impact of the environmental contamination on the transmission of Ebola virus disease (EVD)Journal of Applied Mathematics and Computing 55(2017) 205-243

Tsanou B, Bowong S, Lubuma JMS, Manyombe MLM Modeling Ebola virus disease transmissions with resevoir in a complex virus life ecology. Mathematical Biosciences and Engineering 15(1)(2018) 21-56

Tsanou B, Lubuma JMS, Tassé AJO, Tenkam HM Dynamics of host-reservoir transmission of Ebola with spillover potential to humans. Electronic Journal of Qualitative Theory of Differential Equations 14(2018) 1-32

Berge T, Chapwanya M, Lubuma JMS, Terefe YA A Mathematical model for Ebola epidemic with self-protection measures. Journal of Biological Systems 26(1)(2018) 107-131

Lerata MB Lubuma JMS Yusuf AA Continuous and discrete dynamical systems for the declines of honeybee colonies. Math Meth Appl Sci. 41(2018) 8724–8740

Gumel AB, Lubuma JMS, Sharomi O, Terefe YA Mathematics of a sex-structured model for syphilis transmission dynamics. Math Meth Appl Sci. 41(2018) 8488–8513

Anguelov R, Dukuza K, Lubuma JM-S Backward bifurcation analysis for two continuous and discrete epidemiological models. Math Meth Appl Sci. 41(2018) 8784–8798

Tsanou B, Tassé AJO, Tenkam HM, Lubuma JMS Mathematical modeling of contact tracing 6 as a control strategy of Ebola virus disease. International Journal of Biomathematics 11(7)(2018) 1-36

Chapwanya M, Jejeniwa OA, Appadu AR, Lubuma JMS An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations. To appear in International Journal of Computer Mathematics

Manyombe MLM, Mbang J, Tsanou B, Bowong JS, Lubuma JMS Mathematical analysis of a spatio-temporal model for the population ecology of anopheles mosquito. Mathematical Models in Applied Sciences 43(6)(2020) 3534-3555

Usain S, Hassan AS, Garba SM, Lubuma JM-S Modeling the transmission dynamics of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) with latent immigrants. Journal of Interdisciplinary Mathematics 22(6)(2019) 903-930

Tsanou B, Kamgang JC, Lubuma JMS, Danga DEH Modeling pyrethroids repellency and its role on the bifurcation analysis for a bed net malaria model. Chaos, Solitons and Fractals 136(2020) 109809 1-18J

Ndongo Teytsa HM, Tsanou B, Bowong S, Lubuma JMS Bifurcation analysis of a phage-bacteria interaction model with prophage induction. Mathematical Medicine & Biology 38(1)(2021) 28-58

Anguelov R, Banasiak J, Bright C, Lubuma JMS, Ouifki R The big unknown: The asymptomatic spread of COVID-19. Biomath 9(2020) 2005103

Garba S, Lubuma JM-S, Tsanou B Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa. Mathematical Biosciences 328(2020) 108441 1-14

Anguelov R, Berge T, Chapwanya M, Djoko JK, Kama P, Lubuma JM-S, Terefe Y Nonstandard finite difference method revisited and application to the Ebola virus disease transmission dynamics. Journal of Difference Equations and Applications 26(6)(2020) 818-854

Ndongmo Teytsa HM, Tsanou B, Bowong S, Lubuma JM-S Coupling the modeling of phage-bacteria interaction and cholera epidemiological model with and without optimal control. Journal of Theoretical Biology 521(2021) 110537

Chapwanya M, Lubuma JM-S, Lutermann H, Matusse A, Nyabadza F, Terefe YA Mathematical modeling and analysis of Cannabis epidemic in a South African province. To appear in Journal of Statistics & Management Systems

Fossi AF, Lubuma JM-S, Tadmon C, Tsanou B Mathematical modeling and nonstandard finite difference scheme analysis for the environmental and spillover transmissions of Avian Influenza A model. Dynamical Systems 36 (2021) 212-255

Aziz-Alaoui MA, Lubuma JMS, Tsanou B Prevalence-based modeling approach of schistosomiasis: global stability analysis and integrated control assessment. Computational and Applied Mathematics 40(24)(2021) 1-38

Books and/or Chapters in books
Lubuma J, Mureithi E and Terefe Y  Nonstandard discretizations of the SIS epidemiological model with and without diffusion. In: A Gumel (editor), Mathematics of Discrete and Continuous Dynamical Systems, AMS Contemporary Mathematics book series. Volume in honour of Ronald E Mickens' 70th birthday, American Mathematical Society 2014, Vol 618, pp 113-132, ISBN: 978-0-8218-9862-8, 978-1-4704-1686-7

Conference proceedings
Lubuma JM-S, Mickens RE  Diffusion versus cross diffusion in Biosciences: challenges in designing nonstandard finite difference schemes.  In RJ Daverman, G Benkart, ML Lapidus, M Miller and SH Weintraub (editors), Abstracts of papers presented to the American Mathematical Society (AMS), (San Diego, USA), American Mathematical Society, 2013, 34(1)(171)(2013), pp 265, ISSN: 0192-5857

Chapwanya M, Lubuma JM-S  An Operator splitting method for the advection diffusion reaction equation for problems in porous flow.  In TE Simos, G Psihoyios and Ch Tsitouras (editors), Proceedings of the International Conference of Numerical Analysis and Applied Mathematics 2013 (ICNAAM 1013), (Rhodes, Greece), American Institute of Physics – AIP Conference Proceedings 1558, 2013, pp 253-256, ISBN: 978-0-7354-1184-5

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