title: Impact of non-Poissonian activity patterns on spreading processes.
abstract: 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 indicates that the intercontact 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 1 day decay predicted by the standard Poisson process based models.
authors.affiliation: The Simons Center for Systems Biology, Institute of Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA.
authors.forename: Alexei
authors.initials: A
authors.lastname: Vazquez
authors.forename: Balázs
authors.initials: B
authors.lastname: Rácz
authors.forename: András
authors.initials: A
authors.lastname: Lukács
authors.forename: Albert-László
authors.initials: AL
authors.lastname: Barabási
mesh_terms: D016494:Computer Security; D003198:Computer Simulation; D004812:Epidemiologic Methods; D015233:Models, Statistical; D008962:Models, Theoretical