中文摘要：

本文借鉴保险上的方法来考虑这样一个传染病模型，即在一个区域中，初始有一定的传染病人，假设一方面病人不断增加，且传染率受当时病人数目的影响；另一方面病人减少（死亡或治愈）的发生频率及数目受一外界环境的影响，而外界环境假定为一有限状态的马氏过程。在这些假设下，我们得出初始状态为i时疾病灭绝的概率以及平稳状态下的疾病灭绝概率。

英文摘要：

In this paper,by using for reference methods of insurance theory, we consider such an infectious disease model, i.e. there are certain infection patients initially in one area, suppose on one hand, the patient is increasing constantly, and the infectious rate is affected by patient＇s figure at that time ; on the other hand, emergence frequency and figure of the patient reduces （death or cures ） are affected by an external environment, and the external environment assumes for a Markov processes with limited states, under these assumptions, we obtain the probability that disease become extinct when initial state is at the i and the probability that disease become extinct with steady states.