title: Equivalence between Non-Markovian and Markovian Dynamics in Epidemic Spreading Processes.
abstract: A general formalism is introduced to allow the steady state of non-Markovian processes on networks to be reduced to equivalent Markovian processes on the same substrates. The example of an epidemic spreading process is considered in detail, where all the non-Markovian aspects are shown to be captured within a single parameter, the effective infection rate. Remarkably, this result is independent of the topology of the underlying network, as demonstrated by numerical simulations on two-dimensional lattices and various types of random networks. Furthermore, an analytic approximation for the effective infection rate is introduced, which enables the calculation of the critical point and of the critical exponents for the non-Markovian dynamics.
authors.affiliation: Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.|Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain.
authors.forename: Michele
authors.initials: M
authors.lastname: Starnini
authors.affiliation: MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
authors.forename: James P
authors.initials: JP
authors.lastname: Gleeson
authors.affiliation: Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.|Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain.
authors.forename: Marián
authors.initials: M
authors.lastname: Boguñá