Large graph limit for an SIR process in random network with heterogeneous connectivity

We consider a SIR epidemic model propagating on a random network generated by 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 measurevalued 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 [27].