Incorporating household structure and demography into models of endemic disease.

The spread of infectious diseases is intimately linked with the strength and type of contact between individuals. Multiple observational and modelling studies have highlighted the importance of two forms of social mixing: age structure, where the likelihood of interaction between two individuals is determined by their ages; and household structure, which recognizes the much stronger contacts and hence transmission potential within the family setting. Age structure has been ubiquitous in predictive models of both endemic and epidemic infections, in part due to the ease of assessing someone's age. By contrast, although household structure is potentially the dominant heterogeneity, it has received less attention, in part due to an absence of the necessary methodology. Here, we develop the modelling framework necessary to predict the behaviour of endemic infections (which necessitates capturing demographic processes) in populations that possess both household and age structure. We compare two childhood infections, with measles-like and mumps-like parameters, and two populations with UK-like and Kenya-like characteristics, which allows us to disentangle the impact of epidemiology and demography. For this high-dimensional model, we predict complex nonlinear dynamics, where the dynamics of within-household outbreaks are tempered by historical waves of infection and the immunity of older individuals.