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

Roumen Anguelov, Yves Dumont, Jean Lubuma and Eunice Mureithi

Mathematical Population Studies, 2013, vol. 20, issue 2, 101-122

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.

Date: 2013
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DOI: 10.1080/08898480.2013.777240

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