SIR dynamics in structured populations with heterogeneous connectivity
  Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by describing the exact dynamical behavior of epidemics as they occur in random networks. A system of nonlinear differential equations is presented which describes the behavior of epidemics spreading through random networks with arbitrary degree distributions. The degree distribution is observed to have significant impact on both the final size and time scale of epidemics. 
Erik Volz