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Stability Analysis and Dynamics Preserving Nonstandard Finite Difference Schemes for a Malaria Model

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  • ROUMEN ANGUELOV
  • YVES DUMONT
  • JEAN LUBUMA
  • EUNICE MUREITHI

Abstract

When both human and mosquito populations vary, forward bifurcation occurs if the basic reproduction number R 0 is less than one in the absence of disease-induced death. When the disease-induced death rate is large enough, R 0 = 1 is a subcritical backward bifurcation point. The domain for the study of the dynamics is reduced to a compact and feasible region, where the system admits a specific algebraic decomposition into infective and non-infected humans and mosquitoes. Stability results are extended and the possibility of backward bifurcation is clarified. A dynamically consistent nonstandard finite difference scheme is designed.

Suggested Citation

  • Roumen Anguelov & Yves Dumont & Jean Lubuma & Eunice Mureithi, 2013. "Stability Analysis and Dynamics Preserving Nonstandard Finite Difference Schemes for a Malaria Model," Mathematical Population Studies, Taylor & Francis Journals, vol. 20(2), pages 101-122, June.
    • Handle: RePEc:taf:mpopst:v:20:y:2013:i:2:p:101-122
    DOI: 10.1080/08898480.2013.777240
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    Cited by:

    1. Dayan, Fazal & Rafiq, Muhammad & Ahmed, Nauman & Baleanu, Dumitru & Raza, Ali & Ahmad, Muhammad Ozair & Iqbal, Muhammad, 2022. "Design and numerical analysis of fuzzy nonstandard computational methods for the solution of rumor based fuzzy epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).

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