A novel Bayesian Spatio-Temporal model for the disease infection rate of COVID-19 cases in England

The Covid-19 pandemic has provided many modeling challenges to investigate, evaluate, and understand various novel unknown aspects of epidemic processes and public health intervention strategies. This paper develops a model for the disease infection rate that can describe the spatio-temporal variations of the disease dynamic when dealing with small areal units. Such a model must be flexible, realistic, and general enough to describe jointly the multiple areal processes in a time of rapid interventions and irregular government policies. We develop a joint Poisson Auto-Regression model that incorporates both temporal and spatial dependence to characterize the individual dynamics while borrowing information among adjacent areas. The dependence is captured by two sets of space-time random effects governing the process growth rate and baseline, but the specification is general enough to include the effect of covariates to explain changes in both terms. This provides a framework for evaluating local policy changes over the whole spatial and temporal domain of the study. Adopted in a fully Bayesian framework and implemented through a novel sparse-matrix representation in Stan, the model has been validated through a substantial simulation study. We apply the model on the weekly Covid-19 cases observed in the different local authority regions in England between May 2020 and March 2021. We consider two alternative sets of covariates: the level of local restrictions in place and the value of the \textit{Google Mobility Indices}. The model detects substantial spatial and temporal heterogeneity in the disease reproduction rate, possibly due to policy changes or other factors. The paper also formalizes various novel model based investigation methods for assessing aspects of disease epidemiology.