  Networks of contacts capable of spreading infectious diseases are often
observed to be highly heterogeneous, with the majority of individuals having
fewer contacts than the mean, and a significant minority having relatively very
many contacts. We derive a two-dimensional diffusion model for the full
temporal behavior of the stochastic susceptible-infectious-recovered (SIR)
model on such a network, by making use of a time-scale separation in the
deterministic limit of the dynamics. This low-dimensional process is an
accurate approximation to the full model in the limit of large populations,
even for cases when the time-scale separation is not too pronounced, provided
the maximum degree is not of the order of the population size.
