Qualitative analysis of malaria dynamics with nonlinear incidence function

Abstract

A compartmental model for the transmission dynamics of malaria with nonlinear incidence function is presented and rigorously analysed. An explicit formula for the threshold parameter, known as the basic reproduction number, is used to determine the stability of the diseasefree and endemic equilibria of the model. Using center manifold theory, the model is shown to exhibit a phenomenon of subcritical bifurcation whenever the threshold parameter crosses unity. Under specic conditions on the model parameters, the global dynamics of the model around the equilibria are explored using Lyapunov functions. For a threshold parameter less than unity, a globally asymptotically stable disease-free equilibrium is established while the endemic equilibrium is shown to be globally asymptotically stable at threshold parameter greater than unity. A sensitivity analysis is further carried out to investigate the impact of the model parameters on the transmission and spread of the disease.