PDE-Based Bayesian Hierarchical Modeling for Event Spread, with Application to COVID-19 Infection

We extended the Wikle's Bayesian hierarchical model based on a diffusion-reaction equation [Wikle, 2003] to investigate the COVID-19 spatio-temporal spread events across the USA from Mar 2020 to Feb 2022. Our model incorporated an advection term to account for the intra-state spread trend. We applied a Markov chain Monte Carlo (MCMC) method to obtain samples from the posterior distribution of the parameters. We implemented the approach via the collection of the COVID-19 infections across the states overtime from the New York Times. Our analysis shows that our approach can be robust to model misspecification to a certain extent and outperforms a few other approaches in the simulation settings. Our analysis results confirm that the diffusion rate is heterogeneous across the USA, and both the growth rate and the advection velocity are time-varying.