A 'pumping' model for the spreading of computer viruses

Abstract

We present qualitative arguments concerning the probable infection pattern in a directed graph under the (weak or strong) influence of the outside world. This question is relevant for real computer viruses, which spread by following the (logical) directed links formed by address lists. Our arguments build on previous work in two (seemingly unrelated) areas: epidemic spreading on undirected graphs, and eigenvectors of directed graphs as applied to Web page ranking. More specifically, we borrow a recently proven result (used to design a 'sink remedy' for Web link analysis) and use it to argue for a threshold effect: that the effects of the outside world will not appear in the pattern of infection until the strength of the influence of the outside world exceeds a finite threshold value. We briefly discuss possible tests of this prediction, and its implications. © Springer-Verlag Berlin Heidelberg 2007.