title: Stochastic epidemic dynamics on extremely heterogeneous networks.
abstract: Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.
authors.affiliation: Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: César
authors.initials: C
authors.lastname: Parra-Rojas
authors.affiliation: School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Thomas
authors.initials: T
authors.lastname: House
authors.affiliation: Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Alan J
authors.initials: AJ
authors.lastname: McKane
mesh_terms: D003141:Communicable Diseases / Q000635:transmission; D004198:Disease Susceptibility; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008954:Models, Biological; D013269:Stochastic Processes; D013997:Time Factors