Age of infection epidemic models with heterogeneous mixing.

We extend the age of infection epidemic models to populations divided into an arbitrary number of subgroups and derive a set of final size relations if there are no disease deaths. If there are disease deaths, the final size relations are inequalities, but it is possible to obtain bounds for the epidemic size in terms of the final size for the corresponding model without disease deaths and the disease death rates. If the mixing is proportionate, we obtain an explicit expression for the reproduction number of the model. The heterogeneous mixing age of infection epidemic model is a unified form that includes general compartmental structures and arbitrary distributions of stay in compartments as well as heterogeneity of mixing.