Bayesian inference for high-dimensional discrete-time epidemic models: spatial dynamics of the UK COVID-19 outbreak

In the event of a disease outbreak emergency, such as COVID-19, the ability to construct detailed stochastic models of infection spread is key to determining crucial policy-relevant metrics such as the reproduction number, true prevalence of infection, and the contribution of population characteristics to transmission. In particular, the interaction between space and human mobility is key to prioritising outbreak control resources to appropriate areas of the country. Model-based epidemiological intelligence must therefore be provided in a timely fashion so that resources can be adapted to a changing disease landscape quickly. The utility of these models is reliant on fast and accurate parameter inference, with the ability to account for large amount of censored data to ensure estimation is unbiased. Yet methods to fit detailed spatial epidemic models to national-level population sizes currently do not exist due to the difficulty of marginalising over the censored data. In this paper we develop a Bayesian data-augmentation method which operates on a stochastic spatial metapopulation SEIR state-transition model, using model-constrained Metropolis-Hastings samplers to improve the efficiency of an MCMC algorithm. Coupling this method with state-of-the-art GPU acceleration enabled us to provide nightly analyses of the UK COVID-19 outbreak, with timely information made available for disease nowcasting and forecasting purposes.