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

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 R0>1R0>1, the system is permanent. By comparison arguments, it is shown that if R0<1R0<1, the disease free equilibrium is globally asymptotically stable. If R0>1R0>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.