Heterogeneous mixing in epidemic models

We extend the relation between the basic reproduction number and the initial exponential growth rate of an epidemic to models with heterogeneous mixing, and show that an epidemic with heterogeneity of mixing may have a quite different epidemic size than an epidemic with homogeneous mixing and the same reproduction number and initial exponential growth rate. Determination of the final size of an epidemic if there is heterogeneous mixing requires additional data from the initial exponential growth stage of the epidemic.