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Department of Mathematics and Applied Mathematics
       
  Prof JM-S (Jean) Lubuma
 

Open Access version of articles



Tel: +2712 420-2222 / +2712 420-2520
Fax: +2712 420-3893
E-mail: jean.lubuma@up.ac.za
Office: Mathematics Building 1-39.3

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

Link to SARChI Chair

Academic qualifications: MSc, PhD (Louvain)
NRF rating: B2

Link to personal page

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 

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

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

Chin PM, Djoko JK, Lubuma J.M.-S. Reliable numerical schemes for a linear diffusion equation on a nonsmooth domain. Applied Mathematics Letters 23(2010), 544-548

Garba S, Gumel A, Lubuma J.M.-S.  Dynamically-consistent non-standard finite difference method for an epidemic model.  Mathematical and Computer Modelling, 53(2011), 131-150

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

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

Chapwanya M, Lubuma J.M.-S., Mickens RE  From enzyme kinetics to epidemiological models with Michaelis-Menton contact rate: Design of nonstandard finite difference schemes.  Computers & Mathematics with Applications, 64(2012), 201-213

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.  Accepted for publication (available online DIO: org/10.1016/j.camwa2014.04.021), and University of Pretoria Technical Report, No. UPWT2013/25, 15 pages

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
Mureithi EW, Lubuma JM-S  A vector-borne epidemic disease model with treatment.  In AG Ahmad, AR Salleh, AM Ishak, AS Rambely, H Ismail, LC Yeub, M Darus, NJZ Mamat, NRM Suradi, R Ahmad, RM Nazar, SH Jaaman and Z Isa (eds.), Proceedings of the 2nd International Conference on Mathematical Sciences (ICMS2) 2010, (Kuala Lumpur, Malaysia), University of Kebangsaan, Malaysia, 2010, pp 758-765, ISBN: 978-967-5878-03-9

Lubuma JM-S, Mureithi EW, Terefe Y  Analysis and dynamically consistent numerical schemes for the SIS model and related reaction diffusion equation.  In CI Christov and MDTodorov (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 168-175, ISBN: 978-0-7354-0976-7

Anguelov R, Dumont Y, Lubuma JM-S, Mathematical modeling of sterile insect technology for control of Anopheles Mosquito.  In CI Christov and MDTodorov (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

Anguelov R, Dumont Y, Lubuma JM-S  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’11), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 212-223, ISBN: 978-0-7354-1099-2

Anguelov R, Dumont Y, Lubuma JM-S  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

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