关键词: SIRS传染病模型, Lyapunov函数, 心理作用, 全局渐近稳定性

Abstract: According to the principle of epidemic dynamics, we established a class of SIRS epidemic model based on  psychology effect. The sufficient conditions for the global asymptotic stability of the model at the disease free equilibrium point and endemic disease equilibrium point  were obtained by constructing Lyapunov function, using the stability of ordinary differential equation and the theory of limit system, and then the results 
were verified  by numerical simulation. The  results of numerical simulation show that the positive influence of psychology effects can control the spread and prevalence of infectious diseases to a certain extent.

Key words: SIRS epidemic model, Lyapunov function, psychology effect, global asymptotic stability