This paper analyses a discrete SEIS epidemic model derived from the continuous time model by using the for-ward Euler method,which is used the stability theory of the difference equations.Firstly,we give out that the positivity and boundedness of all solutions,and the existence of the equilibrium.Then,by the Jury criterion and the discrete Lyapunov function method,we prove that the disease free equilibrium P 0 is locally and globally asymptotically stable ifR 0 < 1.Final-ly,with the help of numerical simulations in MATLAB software,we discuss that the endemic equilibrium P 1 is likely glob-ally asymptotically stable if R 0 > 1.%运用差分方程的稳定性理论分析了一类离散时间的 SEIS 传染病模型，该模型是基于欧拉向前差分的方法，对连续时间的模型离散化得到的。首先，给出了模型所有解的正则性和有界性，以及模型平衡点的存在；其次，利用 Jury 判据和离散的 Lyapunov 函数法，证明了当 R 0<1时无病平衡点 P 0的局部和全局渐近稳定性；最后，借助 MATLAB 软件的数值模拟，讨论了当 R 0>1时地方病平衡点 P 1可能是全局渐近稳定的。
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