一类具有Logistic增长和病毒变异的SEIR传染病模型的稳定性分析

Stability analysis of a SEIR epidemic model with logistic growth and virus mutation

建立一类具有Logistic增长和病毒变异的SEIR传染病模型,利用下一代矩阵的方法求得该模型的阈值R_(0).并且证明了当R_(0)<1时,利用Hurwitz判据得到该模型的无病平衡点的局部稳定性,当R_(0)>1时,通过构造适当的Lyapunov函数和LaSalle不变集原理来证明地方病平衡点的全局稳定性,并用对所得结果进行了数值模拟.

In this paper,a SEIR epidemic model with virus mutation and logistic growth is studied.The basic reproductive number R_(0)of the model is obtained by the next generation matrix method.When R_(0)<1 the global stability of the disease-free equilibrium is obtained based on methods of Lyapunov function and the Hurwitz criterion.Though the construction of proper Lyapunov functions and the principle of LaSalle Invariant set,the global stability of the endemic equilibrium point is proved when R_(0)>1.Finally,the results are verified by numerical simulation.