A Bayesian spatio-temporal Poisson auto-regressive model for the disease infection rate: application to COVID-19 cases in England

Abstract The COVID-19 pandemic provided new modelling challenges to investigate epidemic processes. This paper extends Poisson auto-regression to incorporate spatio-temporal dependence and characterize the local dynamics by borrowing information from adjacent areas. Adopted in a fully Bayesian framework and implemented through a novel sparse-matrix representation in Stan, the model has been validated through a simulation study. We use it to analyse the weekly COVID-19 cases in the English local authority districts and verify some of the epidemic-driving factors. The model detects substantial spatio-temporal heterogeneity and enables the formalization of novel model-based investigation methods for assessing additional aspects of disease epidemiology.