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

• DOI: 10.1098/rsif.2014.1125
• Publication Date: 2014-11-19T10:14:43Z
• Authors: Q. Caudron; A. S. Mahmud; C. J. E. Metcalf; M. Gottfreðsson; C. Viboud; A. D. Cliff; B. T. Grenfell
• Keywords: Metapopulation; Epidemic model; Basic reproduction number; Susceptible individual; Predictability; Extinction (optical mineralogy)

A standard assumption in the modelling of epidemic dynamics is that population interest well mixed, and no clusters metapopulations exist. The well-known oft-used SIR model, arguably most important compartmental model theoretical epidemiology, assumes disease being modelled strongly immunizing, directly transmitted has a well-defined period infection, addition to these mixing assumptions. Childhood infections, such as measles, are prime examples diseases fit SIR-like mechanism. These infections have been studied for many systems with large, well-mixed populations endemic infection. Here, we consider setting where small isolated. infection driven by stochastic extinction-recolonization events, producing sudden short-lived epidemics before rapidly dying out from lack susceptible hosts. Using TSIR prevaccination measles incidence demographic data Bornholm, Faroe Islands four districts Iceland, between 1901 1965. datasets each countries suffer different levels heterogeneity sparsity. We explore potential prediction this model: given historical up-to-date information, knowing new just begun, can predict how large it will be? show that, despite significant seasonality cases, potentially severe at level, able estimate size upcoming epidemics, conditioned on first time step, within reasonable confidence. Our results implications possible control measures early stages populations.