一类具有垂直传染的传染病模型的稳定性  

Stability of an Epidemic Model with Vertical Transmission

作　　者：郝艳荣 赵春[1] HAO Yanrong;ZHAO Chun(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《应用数学》2024年第1期31-41,共11页Mathematica Applicata

基　　金：天津市高等学校创新团队培养计划资助项目(TD13-5078)。

摘　　要：基于动力系统的理论,讨论了一类具有垂直传染的传染病模型的稳定性.采用下一代矩阵法获得了基本再生数R0.当R0<1时,由Routh-Hurwitz判别法,得到了无病平衡点的局部渐近稳定性.通过构造Lyapunov函数,证明了系统在无病平衡点全局渐近稳定.当R0> 1时,地方病平衡点存在且唯一,借助Routh判据,得出了系统在地方病平衡点局部渐近稳定的条件,并通过构造Lyapunov函数,证明了系统在地方病平衡点全局渐近稳定.最后,用数值模拟验证了结论的合理性.Based on dynamical system theory,the stability of the epidemic model with vertical transmission is discussed.The basic reproduction number R0 is obtained by using the next-generation matrix method.When R0<1,the local asymptotic stability of the system at the disease-free equilibrium is obtained by the Routh–Hurwitz criterion,and the global asymptotic stability of the system at the disease-free equilibrium is proved by constructing Lyapunov function.When R0>1,the system exists a unique endemic equilibrium point.The conditions of the local asymptotic stability of the system at the endemic equilibrium point are obtained according to the Routh criterion,and by constructing Lyapunov function,it is proved that the system is globally asymptotically stable at the endemic equilibrium point.Finally,the rationality of the conclusion is verified by numerical simulation.

关 键 词：垂直传染 基本再生数 平衡点 稳定性 

分 类 号：O175[理学—数学]