Using population based Kalman estimator to model COVID-19 epidemics in France: estimating the burden of SARS-CoV-2 and the effects of NPI.

Collin, A.; Hejblum, B.; Vignals, C.; Lehot, L.; Thiebaut, R.; Moireau, P.; Prague, M.

In response to the ongoing COVID-19 pandemics caused by SARS-CoV-2, governments are taking a wide range of non-pharmaceutical interventions (NPI). These measures include interventions as stringent as strict lockdown but also school closure, bars and restaurants closure, curfews and barrier gestures. Disentangling the effectiveness of each NPI is crucial to inform response to future outbreaks. To this end, we first develop a multi-level estimation of the French COVID-19 epidemic over a period of one year. We rely on a global extended Susceptible-Infectious-Recovered (SIR) mechanistic model of the infection including a dynamics over time for the transmission rate containing a Wiener process accounting for modeling error. Random effects are integrated by following an innovative population approach based on Kalman-type filter where the log-likelihood functional couples data across French regions. We then fit the estimated time-varying transmission rate using a regression model depending on NPI while accounting for the vaccination coverage, the apparition of variants of concern (VOC) and the seasonal weather conditions. We show that all NPI considered have an independent significant effect on the transmission rate. We additionally demonstrate a strong effect of weather condition, decreasing the transmission during the summer period, and also estimated an increased transmissibility of VOC.