A stochastic worm model

Internet worm infection continues to be one of top security threats and has been widely used by botnets to recruit newbots. In order to defend against future worms, it is important to understand how worms propagate and how different scanning strategies affect worm propagation dynamics. In our study, we present a (stochastic) continuous-time Markov chain model for characterizing the propagation of Internet worms. The model is developed for uniform scanning worms, and further for local preference scanning worms and flash worms. Specifically, for uniform and local preference scanning worms, we are able to (1) provide a precise condition that determines whether the worm spread would eventually stop and (2) obtain the distribution of the total number of infected hosts. By using the same modeling approach, we reveal the underlying similarity and relationship between uniform scanning and local preference scanning worms. Finally, we validate the model by simulating the propagation of worms.