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This paper addresses the limitation of coarse-scale measles transmission models by developing a method to create consistent, high-resolution models for open subcommunities. By framing subcommunity modeling as a constrained optimization problem, the approach allows for epidemiologically motivated approximations at the coarse population scale while preserving fine-grained dynamics. Applied to a pre-vaccination UK dataset, the models reveal intuitive seasonality and importation patterns, but highlight the critical influence of non-trivial case reporting probabilities on inferring transmission dynamics.
Subcommunity measles transmission models reveal that case reporting probabilities, not just transmission rates, are key to understanding cryptic spread versus transient elimination.
We're often in a situation where we have models of measles transmission that are stuck at a coarse population scale. This paper is about increasing their resolution or, said differently, creating consistent models for the population's subcommunities. We pay special attention to the fact that even if the full population is isolated, subcommunities are open to measles importations and related consequences of population movement. It turns out that the resolution issue can be productively framed as a constrained optimization problem, where the constraint is aggregation to the coarse model. That mathematical scaffolding allows us to make epidemiologically motivated approximations concentrated at the large population scale, where they're more valid, which leaves the estimates at the fine subcommunity scale atypically unstructured. We develop the idea in the context of the pre-vaccination-era 60 city UK dataset, building transmission models for all 60 cities. We find that they have intuitive seasonality, volatility, and importation elements, but that they depend on nontrivial dynamics in their case reporting probabilities. Potential interpretations of those surveillance processes are discussed in some detail, and we also describe how they influence inference on the balance between competing cryptic transmission and transient elimination dynamics.