一类马氏环境中连续型传染病模型的灭绝概率

The Extinction Probability of a Class of Continuous Infectious Diseases Models in a Markovian Environment

这篇文章主要研究一类马氏环境中的连续型传染病模型,即假设疾病传染率和病人减少(死亡或治愈)的发生频率及数目都受一外在马氏过程的影响.在这些假设下,我们得出初始状态为i时疾病的灭绝概率满足的积分方程,并通过Laplace-变换的方法,给出了积分方程的解.进一步,当外在马氏环境为两个状态,并且每次病人减少的数目都服从指数分布时,给出了灭绝概率Laplace-变换的明确表达式.

In this paper, we investigate a class of continuous infectious diseases models in a markovian environment, i.e. the infectious rate, the occurrence frequency and the number of the patient reduce are all influenced by an external Markovian process. Under these assumptions, we obtain the integral equations of the extinction probability of disease when initial state is at i, and give the solution of integral equations by Laplace-transforms method. Furthermore, explicit formulas for extinction probability in two-state model are obtained when the number of every patient＇s reduction belongs to exponential distribution.