Stability of periodic solutions for an SIS model with pulse vaccination

Pulse vaccination is an important strategy for the elimination of infectious diseases. A mathematical SIS model with pulse vaccination is formulated in this paper. The dynamical behavior of the model is studied, and the basic reproductive number R0 is defined. It is proved that the disease-free periodic solution is stable if R0 < 1, and it is unstable if R0 > 1. The global stability of the disease-free periodic solution is studied and sufficient condition is obtained. The existence and stability of the endemic periodic solution are investigated analytically and numerically.