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'sspectral radius, we derive the reproduction number $R_0 $ of themodel. The solutions of the model are bounded and positive, whichcan be verified through the relation theory of the differenceequation. It is proved that $R_0 =1$ is a threshold to determine thedisease extincation or persistence. The disease-free equilibrium isglobal asymptotically stable when the reproduction number $R_0 <1$.The endemic equilibrium is global asymptotically stable when the reproduction number $R_0 >1$