On the spread of viruses on the internet

Abstract

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 de-O / I,,a(1/~),~ velops into an epidemic with probability A t ~ J, but on average the epidemic probability is A cO). 1