Host heterogeneity and disease endemicity: a moment-based approach

This paper investigates the possibility of understanding the effects of host heterogeneity on disease levels through the use of moment approximations. The approach is to avoid assumptions about the distribution of mixing rates (or other parameters) in the population, by treating the low-order moments of the distribution as estimable parameters. This approach, while approximate, can greatly reduce the number of parameters needed to explore the effects of population heterogeneity on disease dynamics. This makes the approach useful for both inference and prediction, and also for gaining insight into the qualitative effects of heterogeneity on the spread of disease. This paper focuses on populations with variations in mixing rate and random mixing. It is shown that moment-based approximations can provide good quantitative estimates of disease dynamics, as well as aiding in qualitative under- standing, over a respectable range of parameters. It is hoped that this approach will provide a useful complement to more traditional box models of heterogeneity.