具有病例失踪的结核病模型的全局稳定性  

Global Stability of a TB model with Defaulters

作　　者：肖雪霞[1] 郭玉玲[1] 刘璐菊[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8期5-9,共5页Journal of Luoyang Normal University

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

摘　　要：建立了一类具有病例失踪的结核病数学模型,定义了模型的基本再生数R0,通过构造适当的Lyapunov函数证明了模型解的渐近性态.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.A class of TB mathematical model with defaulters was formulated in this paper. The basic reproduc- tion number Ro was defined and the asymptotic behavior of the solutions of the TB model was studied by constructing the proper Lyapunov functions. The result shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one- and the unique endemic equilibrium is globally asymptotically sta- ble if the basic reproduction number is greater than one.

关 键 词：病例失踪的结核病模型 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]