一类具有标准发生率的SEIR传染病模型的稳定性分析  

Stability Analysis of a Class of SEIR Infectious Disease Models with Standard Incidence

作　　者：宫红艳 薛亚奎[1] GONG Hongyan;XUE Yakui(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2024年第4期448-454,共7页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11971278);山西省自然科学青年基金资助项目(201801D221040)。

摘　　要：根据肺结核(TB)的传播机理,建立了一类具有标准发生率的TB传染病SEIR模型,并讨论了该模型的稳定性。通过常数变易法和反证法证明了模型的正向不变集;利用下一代矩阵法计算得到模型的基本再生数R_(0);通过构造Lyapunov函数法证明了当R_(0)≤1时无病平衡点D_(0)是全局渐近稳定的;利用Hurwitz判据证明了当R_(0)>1时地方病平衡点D_(*)是局部渐近稳定的,且借助Li-Mulowney几何方法给出了地方病平衡点D*全局渐近稳定的条件;最后,通过数值模拟验证了所得结论的有效性.According to the transmission mechanism of tuberculosis(TB),a SEIR model of TB infectious disease with standard incidence was established,and the stability of the model was discussed.Through constant variation method and the reduction to absurdity,the prove the positive invariant sets of the model is proved;The basic regeneration number R_(0)of the model is calculated by the next generation matrix method,and it is proved that the disease-free equilibrium point D_(0)is globally asymptotically stable by constructing Lyapunov function method when R_(0)≤1.It is proved by Hurwitz criterion that the endemic equilibrium point D_(*)is locally asymptotically stable when R_(0)>1,and based on the Li-Mulowney geometric approach to determine the global stability,we obtain the conditions for global stability of the endemic equilibrium.Finally,the validity of the results is verified by numerical simulation.

关 键 词：肺结核 SEIR传染病模型 Hurwitz判据 Li-Mulowney几何方法 稳定性 

分 类 号：O175[理学—数学]