Stability of periodic solutions for an SIS model with pulse vaccination

Abstract

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 R 0 is defined. It is proved that the disease-free periodic solution is stable if R 0 < 1, and it is unstable if R 0 > 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.