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.