Large graph limit for an SIR process in random network with heterogeneous connectivity
Abstract
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz [Mathematical Biology 56 (2008) 293--310].
Cite
@article{arxiv.1007.3958,
title = {Large graph limit for an SIR process in random network with heterogeneous connectivity},
author = {Laurent Decreusefond and Jean-Stéphane Dhersin and Pascal Moyal and Viet Chi Tran},
journal= {arXiv preprint arXiv:1007.3958},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP773 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)