一类具分布时滞的SEIRS传染病模型的阈值动力学分析  

Threshold Dynamical Behaviors for an SEIRS Epidemic Model with Distributed Delay

作　　者：彭源源 杨志春 PENG Yuanyuan;YANG Zhichun(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2020年第6期90-95,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11971081);重庆市教育委员会科技研究重大项目(No.KJZD-M202000502);重庆市研究生科研创新项目(No.CYS20242)。

摘　　要：【目的】研究一类具有一般非线性发生率、分布时滞和垂直传染的SEIRS传染病模型。【方法】利用时滞泛函微分方程的理论,证明了系统解的正定性和有界性。通过构造合适的Lyapunov泛函和运用LaSalle不变集原理,得到了平衡点全局渐近稳定性的阈值条件。【结果】给出模型基本再生数R0,当R0≤1时,无病平衡点是全局渐近稳定的;当R0>1时,存在一个唯一的地方病平衡点,并且它是全局渐近稳定的。【结论】在对发生率的非线性项进行适当的假设下,模型的全局动力学完全由基本再生数R0决定,分布时滞不会影响模型的全局动力学。[Purposes]An SEIRS epidemic model with general nonlinear incidence,distributed delay and vertical transmission is investigated.[Methods]Using the theory of delay functional differential equations,the existence of positive solutions and boundedness of the system are proved.By constructing suitable Lyapunov functionals and applying the LaSalle invariant set principle,the threshold conditions is obtained to determine the global asymptotical stability of the equilibrium points.[Findings]It obtain the basic reproduction number R0.The disease-free equilibrium point is globally asymptotically stable when R0≤1,while there is a unique endemic equilibrium point,which is globally asymptotically stable when R0>1.[Conclusions]Under appropriate assumptions about the nonlinear term of incidence,the global dynamics of the model is completely determined by the basic reproduction number R0.The distributed time delay will not affect the global dynamics of the model.

关 键 词：SEIRS传染病模型 非线性发生率 分布时滞 垂直传染 LYAPUNOV泛函 

分 类 号：O175[理学—数学]