Publications in peer-reviewed journals

  1. Lubuma, J. M.-S. 1987.  Comportement des coefficients de Fourier de la solution d'un problème de Dirichlet à domaine polygonal. Annales de la Société Scientifique de Bruxelles. Vol. 99 No. II-III, 97-114. MR 88h: 35032, Zbl. Math. 635.35019.
  2. Lubuma, J.M.-S. 1987. Opérateur intégral de Neumann pour le Laplacien à frontière non lisse. Bulletin de la Société Mathématique de Belgique, Vol. 39B No. 2, 215-236. MR 88i: 31003, Zbl. Math. 633.45004.
  3. Dauge, M., Lubuma, J.M.-S. and Nicaise, S. 1987. Coefficients des singularités pour le problème de Dirichlet sur un polygone. Comptes Rendus de l'Académie des Sciences de Paris Série I Sciences Mathématiques. Vol. 304 No. 16, 483-486. MR 88f: 35038, Zbl. Math. 619.35033.
  4. Lubuma, J.M.-S. and Taleb, A. 1989. Méthode de projection pour le problème de Stokes sur un polygone. Les Annales de l'Ecole Nationale des Ingénieurs de Tunis. Vol. 3 No. 1, 31-42.
  5. Bourlard. M., Dauge, M., Lubuma, J.M.-S. and Nicaise, S. 1990. Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques I: Résultats généraux pour le problème de Dirichlet. Modélisation Mathématique et Analyse Numérique. Vol. 24 No. 1, 27-52. MR 91b: 35032.
  6. Bourlard, M., Dauge, M., Lubuma, J.M.-S. and Nicaise, S. 1990. Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques II: Quelques Opérateurs particuliers. Modélisation Mathématique et Analyse Numérique. Vol. 24 No. 3, 343-367. MR. 91g: 35010.
  7. Lubuma, M.-S. 1990. Méthode variationnelle et équations intégrales pour le problème de Stokes. Cahiers Mathématiques, Université d'Oran. Vol. 2, pp 17.
  8. Chettab, M. and Lubuma J.M.-S. 1991. Coefficients of singularities and mixed methods for the mixed Dirichlet-Neumann problem for the Stokes operator on a polygon. Journal of Computational and Applied Mathematics. Vol. 35, 139-157. Zbl. Math. 728.65101.
  9. Bourlard, M., Dauge, M., Lubuma, J.M.-S. and Nicaise, S. 1992. Coefficients of the singularities for elliptic boundary value problems on domains with conical points III: Finite element methods on polygonal domains. SIAM Journal of Numerical Analysis. Vol. 29 No. 1, 136-155. MR 93a: 65146.
  10. Lubuma, J.M.-S. and Nicaise, S. 1992.  Méthodes d'éléments finis raffinés pour le problème de Dirichlet dans un polyèdre. Comptes Rendus de l'Académie des Sciences de Paris Série I Sciences Mathématiques. Vol. 315, 1207-1210. MR 94a: 65058, Zbl. Math. 782.65134.
  11. Chidume, C. and Lubuma, J.M.-S. 1992. Solution of the Stokes system by boundary integral equations and fixed point iterative schemes. Journal of the Nigerian Mathematical Society, Vol. 11 No. 3, 1-17. MR 95m: 65205.
  12. Lubuma, J.M.-S. 1993. Error estimates in projective solutions of the Radon equation. Journal of Computational and Applied Mathematics. Vol. 45, 309-319. MR 94g: 31003, Zbl. Math. 771.65094.
  13. Lubuma, J.M.-S. 1993. Classical solutions of two-dimensional Stokes problems on non smooth domains I: The Radon integral operators. Mathematical Methods in the Applied Sciences. Vol. 16 No. 9, 643664. MR 94j:35130, Zbl. Math. 787.65086.
  14. Lubuma, J.M.-S. 1993. Classical solutions of two-dimensional Stokes problems on non smooth domains II: Collocation method for the Radon equation, Mathematical Methods in the Applied Sciences. Vol. 16 No. 9, 665-679. MR 94j: 35131, Zbl. Math. 787.65087.
  15. Lubuma, J.M.-S. and Nicaise, S. 1994. Dirichlet problems in polyhedral domains I: Regularity of solutions. Mathematische Nachrichten. Vol. 168, 243-261. MR 95h:35061.  Zbl. Math. 0844.35014.
  16. Lubuma, J.M.-S. and Nicaise, S. 1994. Méthode de fonctions singulières pour problèmes aux limites avec singularités d'arêtes. Comptes Rendus de l'Académie des Sciences de Paris Série I Sciences Mathématiques. Vol. 319, 1109-1119. MR 95h: 65066.
  17. Lubuma, J.M.-S. and Nicaise, S. 1995. Dirichlet problems in polyhedral domains II: Approximation by FEM and BEM. Journal of Computational and Applied Mathematics, Vol. 61, 13-27. MR 96k: 65073. Zbl. Math. 0840.65110.
  18. Lubuma, J.M.-S. and Nicaise, S. 1999. Finite element method for elliptic problems with edge singularities, Journal of Computational and Applied Mathematics, Vol. 106, 145-168, MR 2000j:65115.
  19. Lubuma, J.M.-S. and Nicaise, S. 2000. Edge behaviour of the solution of the Stokes problem with applications to the finite element methods, Proceedings of the Royal Society of Edinburgh, Vol. 130A, 107-140. MR2001b:35245. Zbl. Math. 0936.65130.
  20. Lubuma, J.M.-S., Nicaise, S. and Paquet, L. 2000. Integral equations for elliptic problems with edge singularities with applications to the Fourier boundary element method, Numerical Functional Analysis and Optimization, Vol. 21, 743-779. MR 2001f:65144. Zbl. Math. 0984.35055.
  21. Anguelov, R. and Lubuma, J.M.-S. 2001. Contributions to the mathematics of the nonstandard finite difference method and applications, Numerical Methods for Partial Differential Equations, Vol. 17, 518-543. MR 1849163 (2002e:65104). Zbl. Math. 0988.65055.
  22. Anguelov, R. and Lubuma, J.M.-S. 2003. Nonstandard finite difference method by nonlocal approximation, Mathematics and Computers in Simulation, Vol. 61, 465-475. MR 1984145. Zbl. Math. 1015.65034.
  23. Anguelov, R.,  Lubuma, J.M.-S. and Mahudu, K.S. 2003. Qualitatively stable finite difference schemes for advection reaction equations, Journal of Computational and Applied Mathematics. Vol. 158, 19-30. MR 2013601 (2004k:65127). Zbl. Math. 1040.65074.
  24. Lubuma, J.M.-S. and Roux, A. 2003. An improved theta method for systems of ordinary differential equations, Journal of Difference Equations and Applications. Vol. 9, 1023-1035. MR 202165 (2004i:65055). Zbl. Math. 1042.65059.
  25. Anguelov, R., Kama, P. and Lubuma, J.M.-S. 2005. On non-standard finite difference models of reaction-diffusion equations, Journal of Computational and Applied Mathematics, Vol. 175, 11-29. MR2105666 (2005k:65163).
  26. Dumont, Y. and Lubuma, J.M.-S. 2005. Non-Standard finite-difference methods for vibro-impact problems, Proceedings of the Royal Society of London, Series A:  Mathematical, Physical and Engineering Sciences. Vol. 461, 1927-1950. MR 2152572 (2006a:70002).
  27. Lubuma, J.M.-S. and Patidar, K.C. 2006. Uniformly convergent non-standard finite difference methods for self-adjoint singular perturbation problems, Journal of Computational and Applied Mathematics, Vol 191, 228-238.  MR2219927 (2006k:65194).
  28. Dumont, Y. and Lubuma, J.M.-S. 2007. Non-standard finite difference schemes for multi-dimensional second-order systems in nonsmooth mechanics, Mathematical Methods in Applied Sciences, Vol. 30, 789-825 (available online at www.interscience.wiley.com; DOI: 1002/mma.811)
  29. Lubuma, J.M.-S. and Patidar, K.C. 2007. Non-standard finite difference methods for singularly perturbed problems possessing oscillatory/layer solutions,  Applied Mathematics and Computation, Vol. 187, 1147-1160 (available online at www.interscience.wiley.com; DOI: 10.1016/j.amc.2006.09.011)
  30. Lubuma, J.M.-S. and Patidar, K.C. 2007. Solving singularly perturbed advection reaction equation via non-standard finite difference methods, Mathematical Methods in the Applied Sciences, Vol. 30, 1627-1637 (available online at www.interscience.wiley.com; DOI: 10.1002/mma.858)
  31. Lubuma, J.M.-S. and Patidar, K.C. 2007. ε-Uniform non-standard finite difference methods for nonlinear singularly perturbed boundary-value problems, Advances in Mathematical Sciences and Applications, Vol 17, 651-665. MR2374144
  32. Anguelov, R., Djoko, J.K. and Lubuma, J.M.-S. 2008. Energy properties preserving finite difference schemes for the Burger’s equation, Numerical Methods for Partial Differential Equations, Vol. 24, 41-59. MR 2371347 (available online at www.interscience.wiley.com; DOI: 10.1002/num20227).
  33. Lubuma, J.M.-S. 2008. Fourier series and integral equation method for the exterior Stokes problem, Numerical Methods for Partial Differential Equations, Vol. 24, 699-727, MR 2402570 (available online at www.interscience.wiley.com; DOI: 10.1002/num20273).
  34. Lubuma, J.M.-S. and Patidar, K.C. 2009. Reliable finite element methods for self-adjoint singular perturbation problems,  Quaestiones Mathematicae-Journal of the South African Mathematical Society, Vol 32(3), 397-413. MR2569097
  35. Lubuma, J.M.-S. and Patidar, K.C. 2009. Towards the implementation of the singular function method for the singular perturbation problem, Applied Mathematics and Computation, Vol. 209, 68-74 (available online at www.sciencedirect.com; DOI: 10.1016/j.amc.2008.06.026).
  36. Anguelov, R., Lubuma, J.M.-S. and Minani, F. 2010. Total variation diminishing non-standard finite difference schemes for conservation law, Mathematics and Computer Modelling, Vol. 51, 160-166 (available online at www.sciencedirect.com; DOI: 10.1016/j.mcm.2009.08.038). 
  37. Anguelov, R., Lubuma, J.M.-S. and Minani F. 2010. A monotone scheme for Hamilton-Jacobi equations via the non-standard finite difference method, Mathematical Methods in Applied Sciences, Vol. 33, 41-48 (available online at www.interscience.wiley.com; DOI: 10.1002/mma.1148).
  38. Chin, P.M., Djoko, J.K. and Lubuma, J.M.-S.  2010. Reliable numerical schemes for a linear diffusion equation on a nonsmooth domain,  Applied Mathematics Letters , Vol. 23, 544-548 (available online at www.sciencedirect.com, DOI: 10.1016/j.aml.2010.01.008).
  39. Garba, S.M., Gumel, A.B. and Lubuma J.M.-S. 2011, Dynamically consistent nonstandard finite difference method for an epidemic model, Mathematical and Computer Modelling, Vol 53, 131-150 (available online at www.sciencedirect.com, DOI: 10.1016/j.mcm.2010.07.026).
  40. Anguelov, R., Lubuma, J.M.-S. and Shillor, M. 2011,  Topological dynamic consistency of non-standard finite difference schemes for dynamical systems,   Journal of Difference Equations and Applications, Vol. 17, No. 12, 1769-1791 (available online at www.informaworld.com, DOI: 10.1080/10236198.2010.488226). 
  41. Anguelov, R.,  Dumont, Y. and  Lubuma, J.M.-S.  2012, Mathematical modeling of sterile insect technology for control of anopheles mosquitoes, Computers & Mathematics with Applications, Vol. 64, 374-389, (available online DOI: 10.1016/j.camwa.2012.02.068).
  42. Chapwanya, M., Lubuma, J.M.-S. and Mickens, R.E. 2012, From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: Design of nonstandard finite difference schemes, Computers & Mathematics with Applications, Vol. 64, 201-213, (available online DOI: 10.1016/j.camwa.2011.12.058).
  43. Chapwanya, M., Lubuma, J.M.-S. and Mickens, R.E. 2013, Nonstandard finite difference schemes for Michaelis-Menten type reaction diffusion equations, Numerical Methods for Partial Differential Equations, Vol 29, No. 1, 337-360, (available online at www.sciencedirect.com, DOI: 10.1002/num.21733)
  44. 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).
  45. 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
  46. 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
  47. 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)
  48. ​Garba, S., Gumel, A.B., Hassan, S. and Lubuma, J.M.-S, 2015, Switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation, Applied Mathematics and Computation, Vol 258, 388-403 (http://dx.doi.org/10.1016/j.amc.2015.01.088).
  49. Lubuma JM-S, Terefe YA  A nonstandard Volterra difference equation for the SIS epidemiology model.  Appeared online Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A Matemáticas (RACSAM) (available online DOI 10.1007/s13398-014-0203-5).
  50. ​​​Barley K., A.B. Gumel, A.B. Hussaini, N. and Lubuma, J.M-S, 2016,  Mathematical Analysis of a Model for AVL-HIV Co-endemicity, Mathematical Biosciences, Vol. 271, 80-95, (http://dx.doi.org/10.1016/j.mbs.2015.10.008)
  51. ​​Chapwanya, M, Lubuma, J.M.-S. and Terefe, Y.A. 2016, Analysis and dynamically consistent nonstandard discretization for a rabies model in humans and dogs, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Vol 110 , 783-798 (http://dx.doi.org/10.1007/s13398-015-0266-y)
  52. Aderogba, A.A., Chapwanya, M., Djoko, J.K. and  Lubuma, J.M.-S.  2016, Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation, International Journal of Computer Mathematics, Vol 93 (11), 1833-1844. (http://dx.doi.org/10.1080/00207160.2015.1076569).
  53. Djoko, J.K., Lubuma, J.M.-S. and  Mbehou, M. , 2016, On the numerical solution of the stationary power-law Stokes equations: A penalty finite element approach: A penalty finite element approach, Journal of Scientific Computing, Vol 69, 1058-1082, (http://dx.doi.org/10.1007/s10915-016-0227-4).  
  54. Djoko, J.K. and Lubuma, J.M.-S., 2016, Analysis of a time implicit scheme for the Oseen model driven by nonlinear slip boundary conditions, Journal of Mathematical Fluid mechanics, Vol 18, 717-730, (http://dx.doi.org/10.1007/s00021-016-0254-9).
  55. Luther, M, Mbang, J, Lubuma, J.M.-S. and Tsanou, B., 2016, Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers, Mathematical Biosciences and Engineering, Vol 13 (4), 813-840 (http://dx.doi.org/10.3934/mbe.2016019)
  56. Tsanou, B, Lubuma, J.M.-S., Bowong, S. and Mbang, J, 2017,  Assessing the impact of the environmental contamination on the transmission of Ebola Virus Disease (EVD), Journal of Applied Mathematics and Computing, Vol 55, 205-243 (http://dx.doi.org/10.1007/s12190-016-1033-8)
  57. Berge, T, Lubuma, J.M-S, Moremedi, G.M., Morris, N. and R. K. Shava, R.K., 2017,  A simple mathematical model for Ebola in Africa, Journal of Biological Dynamics, Vol 11 (1), 42-74 (http://dx.doi.org/10.1080/17513758.2016.1229817)
  58.  Berge, T., Bowong, S. and Lubuma, J.M.-S., 2017, Global stability of a two-patch cholera model        with fast and slow transmissions, Mathematics and Computers in Simulation,  Vol 133, 142-164, (http://dx.doi.org/10.1016/j.matcom.2015.10.013) 
  59. Appadu, A.R., Djoko, J.K., Gidey, H.H. and Lubuma, J.M-S, 2017, Analysis of multilevel finite volume approximation of 2D convective Cahn-Hilliard equation, Japan Journal of Industrial and Applied Mathematics, Vol 34, 253-304, (http://dx.doi.org/10.1007/s13160-017-0239-y)
  60. Appadu, R., Lubuma, J.M-S. and Mphephu, N, 2017, Computational study of three numerical methods for some linear and nonlinear advection-diffusion-reaction problems, Progress in Computational Fluid Dynamics, An International Journal (PCFD), Vol 17, Issue no 2,114-129, (http://dx.doi.org/10.1504/PCFD.2015.10001164)
  61. Lubuma, J.M.-S. and Terefe, A.Y., 2017, Global stability of the continuous and discrete SIS-diffusion epidemiological model, Quaestiones Mathematicae- Journal of the South African Mathematical Society, Vol 40, Issue no 2, 161-76,   
    (http://dx.doi.org/10.2989/16073606.2017.1283369).
  62. Berge, T., Bowong, S., Lubuma, J.M.-S., Manyombe, L.M. 2018, Modeling Ebola virus disease transmissions with reservoir in a complex virus life ecology, Mathematical Biosciences and Engineering, Vol 15 (1), 21-56, (http://dx.doi.org/10.3934/mbe.2018002)
  63. Gumel, A., Lubuma, J.M.-S., Sharomi, O. and Terefe, Y.A, 2018, Mathematics of a sex-structured model for Syphilis transmission dynamics, Mathematical Methods in the Applied Sciences, In Press (http://dx.doi.org/10.1002/mma.4734).
  64. Berge, T.; Chapwanya, M., Lubuma, J.M.-S. and Terefe, Y.A. 2018, A mathematical model for Ebola epidemic with self-protection measures, Journal of Biological Systems, Vol 26 (1), 107-131 (http://dx.doi.org/10.1142/S0218339018500067)
  65. Berge, T, Lubuma, J.M-S., Tassé, A.J.O. and Tenkam, H.M. 2018, Dynamics of host-reservoir transmission of Ebola with spillover potential to humans, Electronic Journal of Qualitative Theory of Differential Equations, Vol. 14, 1–32 (https://doi.org/10.14232/ejqtde.2018.1.14)
  66. Berge, T, Tassé, A.J.O., Tenkam, H.M. and Lubuma, J.M-S., 2018, Mathematical modeling of contact tracing as a control strategy of Ebola virus disease, International Journal of Biomathematics, Vol 11, no. 7, 1850093 (36 pages) (https://doi.org/10.1142/S1793524518500936)
  67. Lerata, M., Lubuma, J.M.-S. and Yusuf, A., 2018, Continuous and discrete dynamical systems for the declines of honeybee colonies, Mathematical Methods in the Applied Sciences, Vol 41, 8724-8740 (https://doi.org/10.1002/mma.5093).
  68. Anguelov, R., Dukuza, K. and Lubuma, J.M.-S., 2018, Backward bifurcation analysis for two continuous and discrete epidemiological models, Mathematical Methods in the Applied Sciences, Vol 41, 8784-8798. (https://doi.org/10.1002/mma.5138).
  69. Appadu, R., Chapwanya, M, Jejeniwa, A. and Lubuma, J.M-S. 2018, An explicit nonstandard finite difference scheme for the FitzHugh-Nagumo equations, International Journal of Computer Mathematics (GCOM), Article ID: GCOM 1546849, Accepted, (https://doi.org/10.1080/00207160.2018.1546849)
  70.  Usain, S., Hassan, A.S., Garba, S.M., Lubuma, J.M.-S., 2019, Modelling the transmission   dynamics of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) with latent  immigrants. Journal of Interdisciplinary Mathematics, Vol 22 (6), 903-930. (https://doi.org/ 10.1080/09720502.2019.1692429).
  71.  Mann Manyombe, Mbang, J. M.L.,Bowong, Tsanou, B. and S., Lubuma, J. 2020, Mathematical analysis of a spatio-temporal model for the population ecology of anopheles  mosquito, Mathematical Methods in the Applied Sciences, Vol 43 (6), 3524-3555. (https://doi.org/10.1002/mma.6136).
  72. Tsanou, B., Kamgang, Jean C., Lubuma, J.M.-S. and Houpa Danga, D.E. 2020, Modeling pyrethroids repellency and its role on the bifurcation analysis for a bed net malaria model, Chaos, Solitons and Fractals, Vol. 136, 109809 (https://doi.org/10.1016/j.chaos.2020.109809).
  73. Anguelov, R., Banasiak, J., Bright, C., Lubuma, J.M-S. and Ouifki, R., 2020, The big unknown: the asymptomatic spread of COVID-19, Journal BIOMATH, Vol 9 (1), COVID-19 Research Communication, (http://dx.doi.org/10.11145/j.biomath.2020.05.103).
  74. Anguelov, R., Berge, T., Chapwanya, M., Djoko, J.K., Kama, P., Lubuma, J.M-S and Terefe, Y., 2020, Nonstandard finite difference method revisited and application to the Ebola Virus Disease transmission dynamics, Journal of Difference Equations and Applications, In Press. (https://doi.org/10.1080/10236198.2020.1792892).
  75. Bowong, S., Lubuma, J., Ndongmo Teytsa, H.M. and Tsanou, B., 2020, Bifurcation analysis of a phage-bacteria interaction model with prophage induction, Mathematical Medicine & Biology, Accepted

    Papers submitted for publication or in preparation:
     
  76. Aziz-Alaoui, M.A., Lubuma, J. and Tsanou, B., 2019, Prevalence-based modeling approach of schistosomiasis: global stability analysis and integrated control assessment, Submitted.
  77. Tassé, A.O., Tsanou, B., Lubuma, J.M.-S. and Woukeng, J.L., 2020. Assessment of effective isolation, safe burial and vaccination optimal controls for an Ebola epidemic model, Submitted 
  78. Berge, T., Garba, S. and Lubuma, J.M-S., 2020, From SARS-CoV and MERS-CoV to COVID-19 pandemic: challenges in modelling the transmission dynamics in South Africa
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