Journal
MATHEMATICAL POPULATION STUDIES
Volume 20, Issue 2, Pages 101-122Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/08898480.2013.777240
Keywords
bifurcation analysis; dynamic consistency; global asymptotic stability; malaria; nonstandard finite difference
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Funding
- French Ministry of Health
- Convergence program of the European Regional Development Fund (ERDF)
- South African National Research Foundation
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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.
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