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

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 R-0, are obtained. It is shown that DFE is locally and also globally asymptotically stable if R-0 < 1. Furthermore, it is proven that EE is locally asymptotically stable when R-0 > 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. (C) 2018 Elsevier Ltd. All rights reserved.