Chi Tran: Large graph limit and Volz' equations for an SIR epidemic spreading on a configuration model graph

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. This allows us to provide a rigorous proof of the equations obtained by Volz (2008) where the spread of the epidemics is summed up into 5 ordinary differential equations only.