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

When both human and mosquito populations vary, forward bifurcation occurs if the basic reproduction number <italic>R</italic> ₀ is less than one in the absence of disease-induced death. When the disease-induced death rate is large enough, <italic>R</italic> 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.