一年龄结构乙肝传染病模型及稳定性  

Stability of an Age-Structured Infectious Disease Modelwith Hepatitis B

作　　者：王改霞 刘纪轩 李学志 WANG Gaixia;LIU Jixuan;LI Xuezhi(College of Mathematics and Statistics,Xinyang University,Xinyang 464000,China;Basic Department,Aeronautic Sergeant College of Air Force Engingeering University,Xinyang 464000,China;College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区：[1]信阳学院数学与统计学院,河南信阳464000 [2]空军工程大学航空机务士官学校基础部,河南信阳464000 [3]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《应用数学》2020年第3期699-706,共8页Mathematica Applicata

基　　金：国家自然科学基金(11271314);河南省科技创新人才计划项目(144200510021);河南省高等学校重点科研项目(17A110030)。

摘　　要：本文讨论一年龄结构的乙肝传染病模型,得到基本再生数ℜ0的表达式,证明当ℜ0<1时,无病平衡点局部渐近稳定且全局渐近稳定;当ℜ0>1时,存在唯一的地方病平衡点,并给出地方病平衡点的局部渐近稳定性条件,这些条件对于控制疾病的传播具有重要的理论及实际意义.An age structured hepatitis B infectious disease model is discussed,and the expression of basic reproductive numberℜ0 is obtained.It is proved that whenℜ0<1,the disease free equilibrium is locally asymptotically stable and globally asymptotically stable,and whenℜ0>1,there is an unique endemic equilibrium,and the local asymptotic stability conditions of endemic equilibrium are given.These conditions have important theoretical and practical signiifcance in controlling the spread of diseases.

关 键 词：年龄结构 潜伏类 基本再生数 

分 类 号：O175.12[理学—数学]