Global dynamics of an epidemic model with standard incidence rate and vaccination strategy

Abstract

We study an SIS epidemic model with a constant recruitment. The disease-related death is included in the model and total population size is variable. A vaccination program also affects both new members and susceptible individuals. Two equilibria of the model; the disease-free equilibrium (DFE) and the endemic equilibrium (EE), and the basic reproduction number R0, are obtained. It is shown that DFE is locally and also globally asymptotically stable if R0<1. Furthermore, it is proven that EE is locally asymptotically stable when R0>1. In addition, in this case some conditions for global asymptotic stability of EE are found by using Lyapunov’s direct method. Finally, some numerical simulations are presented to verify obtained theoretical results.