Abstract
The transmission rate of a disease may vary across time and geographical regions. We introduce a new class of flexible spatio-temporal stochastic epidemic models amenable to scalable full Bayesian inference, focusing on more tractable computation than existing methodology. Drawing on ideass developed for Poisson data, we model the transmission rate of the epidemic model with a dynamic multiscale structure. This evolution process tracks changes in the transmission rate over time and across regions, and allowing practitioners to borrow information over time and space to stabilize the estimates of the transmission rate for regions with sparse reporting. Further, through the use of time-specific discount factors, we can capture both gradual and abrupt changes over time and between regions. We show the practicality of this process by developing a block Gibbs sampler relying on an efficient forward-filtering backward-sampling algorithm for the transmission rate under a discrete-time stochastic susceptible-exposed-infectious-removed model, enabling Bayesian posterior analysis for large outbreaks given incidence data via Markov chain Monte Carlo.