一类病毒自发变异的SIR传染病模型稳定性分析  

Stability Analysis of a SIR Epidemic Model with Spontaneous Mutation of Virus

作　　者：高文哲 闫娟娟 GAO Wen-zhe;YAN Juan-juan(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《滨州学院学报》2022年第6期45-51,共7页Journal of Binzhou University

基　　金：国家自然科学基金项目(11561041)。

摘　　要：研究了病毒变异前疾病具有双线性发生率,病毒变异后疾病具有非线性发生率的SIR传染病模型。首先采用第二代生成矩阵法求得该模型的基本再生数并证明了各个平衡点的存在性。其次通过Hurwitz判别法得到该模型各个平衡点的局部渐近稳定性。然后借助Lyapunov函数、Lasalle不变集原理和Bendixson Dulac定理证明该模型各个平衡点全局渐近稳定的充分条件。最后通过数值模拟验证结果的正确性。A SIR epidemic model with bilinear incidence rate before virus mutation and nonlinear incidence rate after virus mutation is proposed.Firstly,the basic reproduction number in this model is found by using the next generation matrix method and the existence of equilibria are examined.Secondly,the local asymptotic stability of equilibria are carried out through the use of Hurwitz criterion.Then,the sufficient conditions for global asymptotic stability of equilibria are determined through suitable Lyapunov function,Lasalle invariant set principle and Bendixson-Dulac theorem.Finally,some numerical simulations are given to demonstrate the obtained results.

关 键 词：传染病模型 病毒变异 发生率 渐近稳定性 

分 类 号：O175[理学—数学]