Large graph limit for a SIR process in a random network with heterogeneous connectivity
Jean-Stephane Dhersin, Mathematics (March 19, 2012)
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We consider a SIR epidemic model propagating on a random network generated by a configuration model, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemics 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 equations obtained by Volz.
This is a joint work with Laurent Decreusefond, Pascal Moyal and Viet Chi Tran