When is it better to use agent-based (AB) models, and when should differential equation (DE) models be used? Where DE models assume homogeneity and perfect mixing within compartments, AB models can capture heterogeneity in agent attributes and in the network of interactions among them. The costs and benefits of such disaggregation should guide the choice of model type. AB models may enhance realism but entail computational and cognitive costs that may limit sensitivity analysis and model scope. Using contagious disease as an example, we contrast the dynamics of AB models with those of the analogous mean-field DE model. We examine agent heterogeneity and the impact of different network topologies, including fully connected, random, Watts-Strogatz small world, scale-free, and lattice networks. Surprisingly, in many conditions differences between the DE and AB dynamics are not statistically significant for key metrics relevant to public health, including diffusion speed, peak load on health services infrastructure and total disease burden. We discuss implications for the choice between AB and DE models, level of aggregation, and model boundary. The results apply beyond epidemiology: from innovation adoption to financial panics, many important social phenomena involve analogous processes of diffusion and social contagion.

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