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On the spread of viruses on the internet

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 λ, if the infection starts at a typical vertex, then it develops into an epidemic with probability λΘ(log(1/λ)/log log(1/λ), but on average the epidemic probability is λΘ(1).