The effects of population heterogeneity on disease invasion

The incorporation of population heterogeneity is a central issue in theoretical biology, and it has received considerable attention in epidemiology recently. This paper presents general conclusions and interpretations about the effects of heterogeneity, with and without positive assortative mating, on the ability of a disease to establish itself. We show that the invasion of a disease into a population with random mixing is determined by an average of reproductive numbers for each subgroup, weighted by the total amount of mixing activity of the subgroup. In particular, if the mixing rate is constant across the population, invasion occurs if and only if the average reproductive number for the population exceeds 1. In the case of "preferred mixing," one can find a critical number for each subgroup such that invasion occurs if and only if a suitably defined average over subgroups exceeds 1.