Bayesian state space modelling for COVID-19: with Tennessee and New York case studies.

We develop a Bayesian inferential framework for the spread of COVID-19 using mechanistic epidemiological models, such as SIR or SEIR, and allow the effective contact rate to vary in time. A novel aspect of our approach is the incorporation of a time-varying reporting rate accounting for the initial phase of the pandemic before testing was widely available. By varying both the reporting rate and the effective contact rate in time, our models can capture changes in the data induced by external influences, such as public health intervention measures, for example. We view COVID-19 incidence data as the observed measurements of a hidden Markov model, with latent space represented by the underlying epidemiological model, and employ a particle Markov chain Monte Carlo (PMCMC) sampling scheme for Bayesian inference. Parameter inference is performed via PMCMC on incidence data collated by the New York Times from the states of New York and Tennessee from March 1, 2020 through August 30, 2020. Lastly, we perform Bayesian model selection on the different formulations of the epidemiological models, make predictions from our fitted models, and validate our predictions against the true incidence data for the week between August 31, 2020 and September 7, 2020.