SIR-type State Space Models with Piecewise Constant Transmission Rates

Abstract

The SARS-CoV-2 pandemic has seen multiple resurgences due to evolving virus variants, making it difficult to analyze these kinds of phenomena with classic epidemic models, and thus challenging decision makers to successfully counteract new infection waves in time. In this paper, we propose an epidemic model with the transmission rate between susceptible and infected individuals, β, being time varying and piecewise constant. At any point in time, β is linked to a latent variable that follows a Hidden Semi-Markov Model (HSMM). This HSMM-driven epidemic Model (HSMM-EM) structures the data into multiple regimes, which greatly enhances decision-making capabilities, while the limited number of continuous model parameter guarantees straightforward model interpretation. In a case study on COVID-19 numbers in the United Kingdom, reported fatalities as well as infections are used in the observation model specification to account for the uncertainty in either of the reporting methodologies. We show that this is preferable to using only fatalities based on Bayesian model choice derived from Particle MCMC (PMCMC) and Sequential Monte Carlo (SMC) runs.