Predictability in a highly stochastic system: final size of measles epidemics in small populations.

Abstract

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files. This article is open access.A standard assumption in the modelling of epidemic dynamics is that the population of interest is well mixed, and that no clusters of metapopulations exist. The well-known and oft-used SIR model, arguably the most important compartmental model in theoretical epidemiology, assumes that the disease being modelled is strongly immunizing, directly transmitted and has a well-defined period of infection, in addition to these population mixing assumptions. Childhood infections, such as measles, are prime examples of diseases that fit the SIR-like mechanism. These infections have been well studied for many systems with large, well-mixed populations with endemic infection. Here, we consider a setting where populations are small and isolated. The dynamics of infection are driven by stochastic extinction-recolonization events, producing large, sudden and short-lived epidemics before rapidly dying out from a lack of susceptible hosts. Using a TSIR model, we fit prevaccination measles incidence and demographic data in Bornholm, the Faroe Islands and four districts of Iceland, between 1901 and 1965. The datasets for each of these countries suffer from different levels of data heterogeneity and sparsity. We explore the potential for prediction of this model: given historical incidence data and up-to-date demographic information, and knowing that a new epidemic has just begun, can we predict how large it will be? We show that, despite a lack of significant seasonality in the incidence of measles cases, and potentially severe heterogeneity at the population level, we are able to estimate the size of upcoming epidemics, conditioned on the first time step, to within reasonable confidence. Our results have potential implications for possible control measures for the early stages of new epidemics in small populations.US Department of Homeland Security HSHQDC-12-C-00058 Eunice Kennedy Shriver National Institute of Child Health and Human Development 5R24HD047879 National Institutes of Health 5T32HD007163 Bill and Melinda Gates Foundation RAPIDD program of the Science and Technology Directorate, Department of Homeland Security Fogarty International Center, National Institutes of Healt