中文摘要：

提出了网络蠕虫的随机传播模型。首先，基于马尔可夫链对于网络蠕虫进行了建模，并且讨论了模型的极限分布以及平稳分布的存在性。然后，讨论了网络蠕虫在传播初期灭绝的充要条件以及在传播后期灭绝的必要条件。最后，讨论了网络蠕虫的传播规模。仿真实验对于模型进行了验证，讨论了模型中传播参数，时间参数以及漏洞主机数等相关参数对于网络蠕虫传播的影响，并且与G-W模型进行了数据对比，说明了本模型的优势。

英文摘要：

A stochastic model of Internet worms is presented. Firstly, the propagation of worms is modeled based on Markov chain, The limit distribution and invariant distribution of the model is discussed, Then, necessary and sufficient conditions of the worm propagation in the initial stage and sufficient conditions of the worm propagation in the late stage are discussed. Finally, the scale of the worm propagation is discussed. The simulation validates the model. And the effect of propagation, time and vulnerable host parameter on the spread of worms is discussed. Furthermore, it is compared to the G-W model, and the advantage of it is illustrated.