An SIR-based Bayesian framework for COVID-19 infection estimation

Abstract

Estimating the COVID-19 infection fatality rate, inferring the latent incidence and predicting the future epidemic evolution are critical to public health surveillance, but often challenging due to limited data availability or quality. Recently, a Bayesian framework combining time series deconvolution of deaths with a parametric Susceptible–Infectious–Recovered (SIR) model was proposed by Irons and Raftery, 2021. We assess the parameter identifiability of the model using the profile likelihood approach and simulations, when only the time series of deaths and seroprevalence survey data are available. The robustness of the model to the more complex but also more realistic Susceptible–Exposed–Infectious–Recovered (SEIR)-based epidemics is evaluated through simulations; the influence of potential biases in the serosurveys on the inference is also investigated. We use a stationary first-order autoregressive prior to account for the variability of transmission rate over time. The results suggest that the model is relatively robust to SEIR-based epidemics, especially when the reproductive number is low, given sufficient information from serosurveys or priors. However, the lack of parameter identifiability under limited data availability cannot be neglected. We apply the model to infer the COVID-19 infections in Ontario and Quebec, Canada during the Omicron era.