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

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.