A note on metapopulation models

Metapopulation models are commonly used in ecology, evolution, and epidemiology. These models usually entail homogeneity assumptions within patches and study networks of migration between patches to generate insights into conservation of species, differentiation of populations, and persistence of infectious diseases. Here, focusing on infectious disease epidemiology, we take a complementary approach and study the effects of individual variation within patches while neglecting any form of disease transmission between patches. Consistently with previous work on single populations, we show how metapopulation models that neglect in-patch heterogeneity also underestimate basic reproduction numbers ($\mathcal{R}_{0}$) and the effort required to control or eliminate infectious diseases by uniform interventions. We then go beyond this confirmatory result and introduce a scheme to infer distributions of individual susceptibility or exposure to infection based on suitable stratifications of a population into patches. We apply the resulting metapopulation models to a simple case study of the COVID-19 pandemic.