中文摘要：

讨论具有非线性发生率的SIQS流行病模型,定义了基本再生数R0,利用特征根法、函数分析法、线性化方法以及构造Liapunov函数法,对该模型的动力学特性进行分析.证明了当R0〈1时,无病平衡点P0是全局渐近稳定的;当R0〉1时,无病平衡点P0不稳定,但地方病平衡点P1是全局渐近稳定的.

英文摘要：

A SIQS epidemic model with nonlinear incidence rate is discussed. We have defined the reproductive num- ber R0. By using eigenvalue, function analysis, linearization and Liapunov function, the dynamic characteristics of this model are analyzed. It is proved that the disease free equilibrium point P0 is globally stable if R0〈1 ,and is un- stable if R0〉1, while the endemic equilibrium point P1 is globally stable if R0〉1.