Stability of a delayed SIRS epidemic model with a nonlinear incidence rate

In this paper, an SIRS epidemic model with a nonlinear incidence rate and a time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. By comparison arguments, it is proved that if the basic reproductive number R0<1R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>1R0>1, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the endemic equilibrium.