  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].
