A Bayesian hierarchical approach to account for reporting uncertainty, variants of concern and vaccination coverage when estimating the effects of non-pharmaceutical interventions on the spread of infectious diseases

Coronavirus disease (COVID-19) has highlighted both the shortcomings and value of modelling infectious diseases. Infectious disease models can serve as critical tools to predict the development of cases and associated healthcare demand and to determine the set of non-pharmaceutical interventions (NPI) that is most effective in slowing the spread of the infectious agent. Current approaches to estimate NPI effects typically focus on relatively short time periods and either on the number of reported cases, deaths, intensive care occupancy or hospital occupancy as a single indicator of disease transmission. In this work, we propose a Bayesian hierarchical model that integrates multiple outcomes and complementary sources of information in the estimation of the true and unknown number of infections while accounting for time-varying under-reporting and weekday-specific delays in reported cases and deaths, allowing us to estimate the number of infections on a daily basis rather than having to smooth the data. Using information from the entire course of the pandemic, we account for the spread of variants of concern, seasonality and vaccination coverage in the model. We implement a Markov Chain Monte Carlo algorithm to conduct Bayesian inference and estimate the effect of NPIs for 20 European countries. The approach shows good performance on simulated data and produces posterior predictions that show a good fit to reported cases, deaths, hospital and intensive care occupancy.