THE SIQRS EPIDEMIC MODEL OF IMPULSIVE VACCINATION WITH CONSTANT INPUT AND SATURATION INCIDENCE RATE
具常数输入及饱和发生率的脉冲接种SIQRS传染病模型

This paper deals with the SIQRS epidemic model of impulsive vaccination with constant input and saturation incidence rate, and the threshold value $R_{0}=1$ is obtained at which disease is eliminated. It is proved that when $R_{0}<1$, the disease-free periodic solution is globally asymptotically stable, and that when $R_{0}>1$, the system is uniformly persistent.