title: Temporal percolation in activity-driven networks.
abstract: We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity-driven-network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework based on a mapping to hidden variables networks, we provide expressions for the percolation time Tp marking the onset of a giant connected component in the integrated network. In particular, we consider both the generating function formalism, valid for degree-uncorrelated networks, and the general case of networks with degree correlations. We discuss the different limits of the two approaches, indicating the parameter regions where the correlated threshold collapses onto the uncorrelated case. Our analytical predictions are confirmed by numerical simulations of the model. The temporal percolation concept can be fruitfully applied to study epidemic spreading on temporal networks. We show in particular how the susceptible-infected-removed model on an activity-driven network can be mapped to the percolation problem up to a time given by the spreading rate of the epidemic process. This mapping allows us to obtain additional information on this process, not available for previous approaches.
authors.affiliation: Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.
authors.forename: Michele
authors.initials: M
authors.lastname: Starnini
authors.affiliation: Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.
authors.forename: Romualdo
authors.initials: R
authors.lastname: Pastor-Satorras
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D015233:Models, Statistical; D018570:Risk Assessment / Q000379:methods; D012307:Risk Factors; D062211:Spatio-Temporal Analysis