Dynamics of an SIR epidemic model withstage structure and pulse vaccination

Abstract

Pulse vaccination is an important strategy to eradicate an infectious disease. In this paper, we investigate an SIR epidemic model with stage structure and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, we obtain the conditions for the global asymptotical stability of the infection-free periodic solution of the studied system. The permanent conditions of the investigated system are also given. The results indicate that a large pulse vaccination rate is a sufficient condition to eradicate the disease. It provides a reliable tactic basis for preventing the epidemic outbreak.