中文摘要：

提出并分析了一类具有饱和发生率的时滞SEIR传染病模型,定义了基本再生数R0。通过分析系统对应的特征方程,得到了无病平衡点P0和地方病平衡点P＊的局部渐近稳定性。进一步,通过比较原理和构造李雅普诺夫函数,得出：当R0〈1时,无病平衡点P0是全局渐近稳定的;当R0〉1时,地方病平衡点P＊是持久的。

英文摘要：

A delayed SEIR epidemic model with saturation incidence rate is proposed and analyzed,and the basic reproductive number R0 is defined. By analyzing the corresponding characteristic equations,the local stability of a disease-free equilibrium P0 and an endemic equilibrium P＊are discussed. Further,by the comparison principle and constructing Lyapunov functions,it is found that if R〈0 1,the disease free equilibrium P0 is globally asymptotically stable,and if R〉0 1,the endemic equilibrium P＊is permanent.