The effects of local homogeneity assumptions in metapopulation models of infectious disease

Computational models of infectious disease can be broadly categorized into two types: individual-based (Agent-based), or compartmental models. While compartmental models can be structured to separate distinct sectors of a population, they are conceptually distinct from individual-based models in which population structure emerges from micro-scale interactions. While the conceptual distinction is straightforward, a fair comparison of the approaches is difficult to achieve. Here, we carry out such a comparison by building a set of compartmental metapopulation models from an agent-based representation of a real population. By adjusting the compartmental model to approximately match the dynamics of the Agent-based model, we identify two key qualitative properties of the individual-based dynamics which are lost upon aggregation into metapopulations. These are (1) the local depletion of susceptibility to infection, and (2) decoupling of different regional groups due to correlation between commuting behaviors and contact rates. The first of these effects is a general consequence of aggregating small, closely connected groups (i.e., families) into larger homogeneous metapopulations. The second can be interpreted as a consequence of aggregating two distinct types of individuals: school children, who travel short distances but have many potentially infectious contacts, and adults, who travel further but tend to have fewer contacts capable of transmitting infection. Our results could be generalised to other types of correlations between the characteristics of individuals and the behaviors that distinguish them.