On the Spread of Viruses on the Internet - Berger, Noam; Borgs, Christian; Chayes, Jennifer; Saberi, Amin (Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithm (SODA), 2005)
We analyze the contact process on random graphs generated according to the preferential attachment scheme as a model for the spread of viruses in the Internet. We show that any virus with a positive rate of spread from a node to its neighbors has a non-vanishing chance of becoming epidemic. Quantitatively, we discover an interesting dichotomy: for a virus with effective spread rate ¸, if the infection starts at a typical vertex, then it develops into an epidemic with probability ¸£( log(1=¸) log log(1=¸) ); but on average the epidemic probability is ¸£(1)