Correlations between stochastic endemic infection in multiple interacting subpopulations.

Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.