一类吸血鬼模型的稳定性分析  

Analysis of Stability for a Class of Virus Models with Latency

作　　者：刘璐菊[1] 魏明威[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《洛阳师范学院学报》2012年第2期42-45,共4页Journal of Luoyang Normal University

基　　金：国家自然科学基金项目(11101127;11101126;11001215);河南科技大学博士启动基金项目(09001535)

摘　　要：本文建立了一类吸血鬼数学模型,定义了模型的基本再生数,通过构造适当的Lyapunov函数来研究模型解的渐近性态.证明了当基本再生数小于1时,无病平衡点是全局渐近稳定的;当基本再生数大于1时,唯一的地方病平衡点是全局渐近稳定的.This paper discusses a class of virus model with latency.The basic reproduction number of the virus model is defined by applying the next generation matrix method.The asymptotic behavior of the solutions of the virus model is investigated by constructing proper Lyapunov functions.It is proved that if the basic reproduction number is lower than one,the unique disease-free equilibrium is globally asymptotically stable;if the basic reproduction number is above one,the disease-free equilibrium is unstable,the unique endemic equilibrium is globally asymptotically stable.

关 键 词：吸血鬼模型 平衡点 基本再生数 LYAPUNOV函数 全局渐近稳定 

分 类 号：O175[理学—数学]