On the global stability of the endemic state in an epidemic model with vaccination

This paper investigates an SIS epidemic model with variable population size including a vaccination program. Dynamics of the endemic equilibrium of the model are obtained, and it will be shown that this equilibrium exists and is locally asymptotically stable when R₀ > 1 . In this case, the disease uniformly persists, and moreover, using a geometric approach we conclude that the model is globally asymptotically stable under some conditions. Also, a numerical discussion is given to verify the theoretical results.