具有一般发生率和潜伏期时滞的水痘传播动力学模型  

A Dynamic Model of Varicella Transmission withGeneral Incidence and Latency Time Delay

作　　者：胡巧 刘贤宁[1] HU Qiao;LIU Xianning(College of Mathematics and Statistic,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2023年第4期67-74,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12071382)。

摘　　要：建立并研究了一类具有一般发生率和潜伏期时滞的水痘传播动力学模型.首先,证明了模型解的非负性和有界性.其次,给出了模型的基本再生数R0,并证明了模型正平衡点的存在唯一性.再次,通过构造Lyapunov泛函,证明了无病平衡点及地方病平衡点的全局稳定性.最后通过数值模拟验证了:当R0<1时,无病平衡点E0全局渐近稳定;当R0>1时,地方病平衡点E*全局渐近稳定.In this paper,a kind of transmission dynamics model of varicella with general incidence and latency time delay is established and studied.Firstly,the nonnegativity and boundedness of the model solution are proved.Secondly,the basic reproduction number R 0 of the model is given,and the existence and uniqueness of the positive equilibrium of the model are proved.Thirdly,the global stability of disease-free equilibrium and endemic equilibrium are proved by constructing Lyapunov functionals.Finally,numerical simulations verify that the disease-free equilibrium E 0 is globally asymptotically stable when R 0<1 and the endemic equilibrium E*is globally asymptotically stable when R 0>1.

关 键 词：一般发生率 潜伏期时滞 水痘 基本再生数 全局稳定性 

分 类 号：O175[理学—数学]