Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model

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Authors

Anguelov, Roumen
Dumont, Yves
Lubuma, Jean M.-S.
Mureithi, Eunice W.

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Routledge

Abstract

When both human and mosquito populations vary, forward bifurcation occurs if the basic reproduction number R0 is less than one in the absence of disease-induced death. When the disease-induced death rate is large enough R0 = 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 speci c algebraic decomposition into infective and non-infected humans and mosquitoes. Stability results are extended and the possibility of backward bifurcation is clari ed. A dynamically consistent nonstandard nite di erence scheme is designed.

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Keywords

Bifurcation analysis, Dynamic consistency, Global asymptotic stability, Malaria, Nonstandard finite difference

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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: An International Journal of Mathematical Demography, 20:2, 101-122, DOI: 10.1080/08898480.2013.777240