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Patterns of measles infection in large urban populations have long been considered the paradigm of synchronized nonlinear dynamics. Indeed, recurrent epidemics appear approximately mass-action despite underlying heterogeneity. However, using a subset of rich, newly digitized mortality data (1897-1906), we challenge that proposition. We find that sub-regions of London exhibited a mixture of simultaneous annual and biennial dynamics, while the aggregate city-level dynamics appears firmly annual. Using a simple stochastic epidemic model and maximum-likelihood inference methods, we show that we can capture this observed variation in periodicity. We identify agreement between theory and data, indicating that both changes in periodicity and epidemic coupling between regions can follow relatively simple rules; in particular we find local variation in seasonality drives periodicity. Our analysis underlines that multiple attractors can coexist in a strongly mixed population and follow theoretical predictions.

Patterns of measles infection in large urban populations have long been considered the paradigm of synchronized nonlinear dynamics. Indeed, recurrent epidemics appear approximately mass-action despite underlying heterogeneity. However, using a subset of rich, newly digitized mortality data (1897–1906), we challenge that proposition. We find that sub-regions of London exhibited a mixture of simultaneous annual and biennial dynamics, while the aggregate city-level dynamics appears firmly annual. Using a simple stochastic epidemic model and maximum-likelihood inference methods, we show that we can capture this observed variation in periodicity. We identify agreement between theory and data, indicating that both changes in periodicity and epidemic coupling between regions can follow relatively simple rules; in particular we find local variation in seasonality drives periodicity. Our analysis underlines that multiple attractors can coexist in a strongly mixed population and follow theoretical predictions. [ABSTRACT FROM AUTHOR]

Data augmentation is required for the implementation of many Markov chain Monte Carlo (MCMC) algorithms. The inclusion of augmented data can often lead to conditional distributions from well-known probability distributions for some of the parameters in the model. In such cases, collapsing (integrating out parameters) has been shown to improve the performance of MCMC algorithms. We show how integrating out the infection rate parameter in epidemic models leads to efficient MCMC algorithms for two very different epidemic scenarios, final outcome data from a multitype SIR epidemic and longitudinal data from a spatial SI epidemic. The resulting MCMC algorithms give fresh insight into real-life epidemic data sets. [ABSTRACT FROM AUTHOR]