Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate

Abstract

A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number R0. Specifically, it shows that the disease-free equilibrium E0 is globally asymptotically stable (GAS) for R0 < 1, and globally attractive (GA) for R0 = 1, while the endemic equilibrium E* is GAS and E0 is unstable for R0 > 1. Especially, to obtain the global stability of the equilibrium E* for R0 > 1, the weak persistence of the model is proved by some analysis techniques.