  Halting a computer or biological virus outbreak requires a detailed
understanding of the timing of the interactions between susceptible and
infected individuals. While current spreading models assume that users interact
uniformly in time, following a Poisson process, a series of recent measurements
indicate that the inter-contact time distribution is heavy tailed,
corresponding to a temporally inhomogeneous bursty contact process. Here we
show that the non-Poisson nature of the contact dynamics results in prevalence
decay times significantly larger than predicted by the standard Poisson process
based models. Our predictions are in agreement with the detailed time resolved
prevalence data of computer viruses, which, according to virus bulletins, show
a decay time close to a year, in contrast with the one day decay predicted by
the standard Poisson process based models.
