一类离散型结核病模型的全局稳定性

Global stability of a discrete tuberculosis model

本文研究了一类离散型结核病模型.利用求再生矩阵谱半径的方法,计算得到模型的基本再生数R_0.运用差分方程相关理论,证明了模型解的正性和有界性.通过构造适当的Lyapunov函数,证明了R_0=1是决定疾病消失或者持续的阈值.当基本再生数R_0<1时,无病平衡点是全局渐近稳定的;当基本再生数R_0>1时,地方病平衡点是全局渐近稳定的.

In this paper,a discrete tuberculosis model is investigated.By means of calculating the next generation matrix＇s spectral radius,we derive the reproduction number Ro of the model.The solutions of the model are bounded and positive,which can be verified through the relation theory of the difference equation.It is proved that R0=1 is a threshold to determine the disease extincation or persistence.The disease-free equilibrium is global asymptotically stable when the reproduction number R0〈1.The endemic equilibrium is global asymptotically stable when the reproduction number R0〉1.