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

作　　者：梁桂珍[1] 方慧文 王伟杰 LIANG Guizhen;FANG Huiwen;WANG Weijie(College of Mathematics and Statistics,Xinxiang University,Xinxiang 453003,China;College of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]新乡学院数学与统计学院,河南新乡453003 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《河南科技学院学报（自然科学版）》2021年第2期48-53,共6页Journal of Henan Institute of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金项目(11871238);河南省高等学校重点科研项目(20B110014);国家级大学生创新训练计划项目(202011071015)。

摘　　要：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.

关 键 词：传染病模型 LOGISTIC增长 病毒变异 全局稳定 

分 类 号：O175[理学—数学]