一类具有饱和传染率的时滞传染病模型的全局稳定性  

Global stability of a delayed epidemic model with saturation infection

作　　者：李小玲[1] 梁欣 刘亚东 李栋梁[2] 胡广平[1] Li Xiao-ling Liang Xin Liu Ya-dong Li Dong-liang Hu Guang-ping(School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China College of Atmospheric Science, Nanjing University of Information Science and Technology, Nanjing 210044, China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044 [2]南京信息工程大学大气科学学院,南京210044

出　　处：《兰州大学学报（自然科学版）》2017年第5期691-695,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家重点基础研究发展计划(973计划)项目(2013CB956004);江苏省高校自然科学研究面上项目(15KJB110016);江苏省高校大学生实践创新训练计划项目(201510300049;201610300040)

摘　　要：研究了一类具有非线性饱和传染率和时滞效应的SEIR传染病模型,给出了用于判断疾病是否持续流行的基本再生数R_0.利用Lyapunov方法和LaSalle不变原理证明了当R_0≤1时,无病平衡点全局渐近稳定;当R_0>1时,疾病平衡点全局稳定.This paper was concerned with a mathematical model dealing with a delayed SEIR epidemic model with a saturation infection rate and a calculation method for the basic reproduction number R0 was given. Through constructing suitable Lyapunov functionals and using LaSalle invariant principle, we showed that the disease-free equilibrium was globally asymptotically stable if R0≤1 while the infected equilibrium was globally asymptotically stable if R01.

关 键 词：传染率 基本再生数 时滞 全局稳定性 

分 类 号：O231.2[理学—运筹学与控制论]