一类具饱和发生率的时滞 SEIR 传染病模型的分析

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 R0 <1 ,the disease free equilibrium P0 is globally asymptotically stable,and ifR0 >1 ,the endemic equilibrium P* is permanent.%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。