Global stability of a SIR epidemic model with nonlinear incidence rate and time delay

Abstract

In this paper, a SIR epidemic model with nonlinear incidence rate and time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease free equilibrium is discussed. It is proved that if the basic reproductive number R 0 > 1 , the system is permanent. By comparison arguments, it is shown that if R 0 < 1 , the disease free equilibrium is globally asymptotically stable. If R 0 > 1 , by means of an iteration technique and Lyapunov functional technique, respectively, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium.