Research

Selected Publications in Peer-reviewed Journals

• Chapwanya M. and Dumani P. Existence of traveling waves in a spatial model of bacteria quiescence. Proceedings of the Royal Society A. 479(2278), 2023
• Chapwanya M. and Dumani P. Spatio-temporal dynamics of microbial population under nutrient limiting conditions. Applied Mathematics and Computation, 456, 128138, 2023.
• Chapwanya M. and Dumani P. Stationary and oscillatory patterns in microbial population under environmental stress. Math. Comput. Simul. 210, 370 - 383, 2023.
• Chapwanya M. and Kenyon E.  On mathematical modeling of the transmission of Grapevine leafroll-associated virus 3 (GLRaV-3) by the vine mealybug, Planococcus ficus. J. Biol. Systems, 31(01), 185 - 213, 2023. 
• Chapwanya M., J-M.S. Lubuma and Y.A. Terefe and Tsanou B. Analysis of war and conflict effect on the transmission dynamics of the tenth Ebola outbreak in the Democratic Republic of Congo. Bull. Math. Biol., 84:136, 2022. 
• Banda H., Chapwanya M., and Dumani P. Pattern formation in the Holling-Tanner predator-prey model with prey-taxis. A nonstandard finite difference approach. Math. Comput. Simul., 196, 336 - 353, 2022.
• Chapwanya M. and Dumani P., Environmental considerations on the spread of rabies among African wild dogs (Lycaon pictus) with control measures. Math. Methods Appl. Sci., 45(8), 4124 - 4139, 2022
• Chapwanya M., Lubuma J.M-S., Lutermann H., Matusse A., Nyabadza F., and Terefee Y., A mathematical model for the cannabis epidemic in a South African province with a nonlinear incidence rate. Journal of Statistics and Management Systems, 24, 1627 - 1647, 2021.
• Chapwanya M., Matusse A. and Dumont Y., On synergistic co-infection in crop diseases. The case of the Maize Lethal Necrosis Disease. Applied Mathematical Modelling, 90, 912-942, 2021.
• Anguelov R., Berge T., Chapwanya M., Djoko J.K., Kama P., Lubuma J.M.-S., and Terefe Y., Nonstandard finite difference method revisited and application to the Ebola virus disease transmission dynamics. Journal of Difference Equations and Applications, 26(6), 818-854, 2020.
• Chapwanya M., Dozva R., and Muchatibaya G., A nonstandard finite difference technique for the singular Lane-Emden type equations. Engineering Computations, 35(5), 1566 – 1578, 2019
• Chapwanya M., Jejeniwa O.A., Appadu A.R. and Lubuma J.M-S., An explicit nonstandard finite difference scheme for the FitzHugn-Nagumo equations. International J. Computer Mathematics, 96(10), 1993 – 2009, 2019.
• Aderogba A.A. and Chapwanya M. Positivity preserving and bounded nonstandard finite difference scheme for the Hodgkin-Huxley system of equations. Japan Journal of Industrial and Applied Mathematics, 35, 773 – 785, 2018.
• Berge T., Chapwanya M., Lubuma J.M.-S. and Terefe Y.A. A mathematical model for Ebola epidemic with self-protection measures. Journal of Biological Systems, 26(1), 107 – 131, 2018.
• Chapwanya M. and Y. Dumont. On crop vector-borne diseases. Impact of virus lifespan and contact rate on traveling wave speed of infective fronts. Ecological Complexity, 34, 119 – 133, 2018.
• A.R. Appadu, M. Chapwanya and O.A. Jejeniwa. Some optimized schemes for 1D KdV equation. Progress in Computational Fluid Dynamics an Int. J., 17(4)(2017),  250-266.
• Aderogba AA, Chapwanya M, J.K. Djoko and J-M.S. Lubuma. Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation. Computers and Mathematics with Applications, 93:11, 1833 – 1844, 2016.
• Chapwanya M. and Lubuma J-M.S and Terefe Y.A. Analysis and dynamically consistent nonstandard discretization for a Rabies model in humans and dogs. RACSAM 110:783-798, 2016
• Winstanley HF, Chapwanya M. Fowler AC. and O’Brien SBG. A 2D channel-clogging biofilm model, Journal of Mathematical Biology, 71:647-668, 2015.
• Aderogba AA and Chapwanya M, An explicit nonstandard finite difference scheme for the Allen-Cahn equation. Journal of Difference equations and Applications, 21:10, 875 – 886, 2015.
• M. Chapwanya and N.N. Misra. A mathematical model of meat cooking based on polymer-solvent analogy. Applied Mathematical Modelling, 39(14): 4033-4043, 2015
• Chapwanya M. and Misra NN. A soft condensed matter approach towards mathematical modelling of mass transport and swelling in food grains, Journal of Food Engineering, 145: 37 – 44, 2015
• Chapwanya M., Lubuma, JM-S. and Mickens, R.E. Positivity preserving nonstandard finite difference schemes for cross diffusion equations in biosciences. Computers & Mathematics with Applications, 68: 1074 – 1082, 2014.
• A.C. Fowler and M. Chapwanya, The instability theory for the formation of ribbed moraine, drumlins and mega-scale glacial lineation, Proceedings of the Royal Society A, 470(2171): 20140185, 2014
• A.A. Aderogba, M. Chapwanya and J. K. Djoko. On the fractional step-splitting scheme for the Cahn-Hilliard equation. Journal of Engineering Computations, 31(7):1151 – 1168, 2014
• Chapwanya M., Lubuma, JM-S. and Mickens, R.E. Non-standard finite difference schemes for Michaelis-Menten type reaction diffusion equations. Numerical Methods for Partial Differential Equations, 29(1): 337–360, 2013
• Chapwanya M., Lubuma, JM-S. and Mickens, R.E. From Enzyme Kinetics to Epidemiological Models with Michaelis-Menten Contact Rate: Design of Nonstandard Finite Difference Schemes. Computers & Mathematics with Applications, 64:201–213, 2012.
• Chapwanya M., Fowler, A.C. and Clark, C.D. Numerical computations of a theoretical model of ribbed moraine formation. Earth Surface Processes and Landforms, 36:1105–1112, 2011
• Winstanley H.F., Chapwanya M., McGuinnes M.J. and Fowler A.C. A polymer-solvent model of biofilm growth. Proceedings of the Royal Society A., 467:1449–1467 2011.
• Chapwanya M. and Stockie J.M. Numerical simulations of a non-equilibrium model for gravity-driven fingering in unsaturated porous media. Water Resources Research. 46, W09534, 2010.
• Chapwanya M., O’Brien S.B.G. and Williams JF. A perturbation solution for bioremediation in a porous medium with bio clogging. Journal of Computational and Applied Mathematics. 234:2709–2723, 2010
• Rojas J., Burke M., Chapwanya M. Hewitt I. Korobeinikov A. Meere M., McCarty S., O’Brien M., Vo Thi Ngoc Tuo and Winstaanley H. Modeling of Autothermal Thermophylic Aerobic Digestion. Mathematics in Industry Case Studies Journal. 2:34–63, 2010.
• Chapwanya M., Stockie J.M. and Liu W. A model for reactive porous transport during re-wetting of hardened concrete. Journal of Engineering Mathematics. 65(1):53–73, 2009.
• Chapwanya M. and O’Brien S.B.G. Corner and start-up singularities in porous flow. Journal of Computational and Applied Mathematics. 176(1): 163–177, 2005.

Book Chapters

• Chapwanya M. and Dumani P., Dynamics preserving nonstandard finite difference scheme for a microbial population model incorporating environmental stress. To appear in: Gumel (eds) AMS Contemporary Mathematics series honoring the 80th birthday of Ronald Mickens, 2023. 
• Chapwanya M. and Dumont Y., Application of mathematical epidemiology to crop-vector-borne diseases: the case of cassava mosaic virus. In Teboh-Ewungkem M.I., Ngwa G.A. (eds). Infectious diseases and our Planet Earth. Mathematics of the Planet Earth, vol. 7, Springer Cham, https://doi.org/10.1007/978-3-030-50826-5_4, 2021.

Selected Published Study Group & Conference Papers

• Aderogba AA, Chapwanya M and OA Jejeniwa. Finite difference discretisation of a model for biological nerve conduction. AIP Conference Proceedings, 1738, 030009, 2016.
• Aderogba AA, Chapwanya M, and Djoko JK, Numerical approach for the solution of the oscillatory 1D Schrodinger equation. Procceedings of the 9^th South African Conference on Computational and Applied Machanics (SACAM 2014) CD-ROM, ISBN 978-0-62058994-9, 2014.
• Chapwanya M and Lubuma JM-S, An operator splitting method for advection diffusion reaction equations arising in porous flow. AIP Conference Proceedings, 1558: 253 – 256, 2013.
• Aderogba AA., Chapwanya M., and Djoko JK. Traveling wave solutions of the Kuramoto-Sivashinsky equation: A computational study. AIP Conference Proceedings. 1479: 777–780, 2012.
• Spin coated substrate for cell growth. Proceedings of the 75^th European Study Group with Industry, University of Limerick, ESGI75, (2010)
• Chapwanya M and Stockie JM. A mathematical model for the reactive transport and self-desiccation in concrete. AIP Conference Proceedings 1168(2): 1453-1456, (2009)
• Modeling wastewater treatment. Proceedings of the 70th European Study Group with Industry, University of Limerick, ESGI70, 107-139, (2009)
• Modeling the release of an encapsulated breaker. Proceedings of the 10th PIMS Industrial Problem Solving Workshop, Simon Fraser University, 2006
• Chapwanya M. and O'Brien S.B.G. Modeling bioremediation in a porous medium with small bio clogging. Journal of Mathematical Modeling and Analysis Conference Proceedings. 6570, 2005. ISBN 9986-05-924-0.