Global Stability Analysis of Malaria Model with Prophylactic Treatment

Abstract

In this paper, we present a mathematical model of the interaction between the human population and the vector (mosquito) population to study the stability of a malaria model in the presence of prophylactic treatment. The graph-theoretic method was used to obtain the basic reproduction number (R₀). We obtained the disease-free equilibrium for the model which is locally and globally asymptotically stable when the basic reproduction number is less than unity. Moreover, we showed that there exists a unique endemic equilibrium whenever R₀ > 1, and the Lyapunov function was used to establish that the endemic equilibrium is globally asymptotically stable whenever R₀ > 1. The simulations show that the presence of prophylactic treatment reduces the population of infectious individuals. Further numerical simulations carried out conformed with the analytic results.