中文摘要：

文章研究了SI传染病模型的概率分布,将S（t）,I（t）看成随机过程中的生灭过程,发现当基本再生数R_0≤1时,无病平衡点（N,0）以概率1全局渐近稳定;当R0〉1时,地方病平衡点（μ/β,（Nβ-μ）/β）以概率1全局渐近稳定,和连续的确定性SI模型是一致的。

英文摘要：

In this paper, we investigate the probability distribution of SI epidemic model. Taking the S（t）, I（t） as the birth and death process in random process, we find that when the basic reproduction number R0≤1, the disease free equilibrium （N, 0） is globally asymptotically stable with probability one, when R0 〉 1, the endemic equilibrium （μ/β,（Nβ-μ）/β） is globally asymptotically stable with probability one, which is consistent with the continuous deterministic SI model.