Worm spreading with immunization: An interplay of spreading and immunity time scales

A model of epidemic spreading that is applicable to email worms, for instance, is studied analytically and numerically. It is built on mean-field percolation, and incorporates two time scales originating in spreading dynamics and immunization. A comparison to empirical data is provided. The long-time limit of the dynamics is governed by an exponential decay. We derive an analytic expression for the characteristic time of the decay, and find a good agreement with numerics. There is a similar decay also in empirical observations.