Bayesian investigation of SARS-CoV-2-related mortality in France

Abstract

<jats:p>The SARS-CoV-2 epidemic in France has focused a lot of attention as it has had one of the largest death tolls in Europe. It provides an opportunity to examine the effect of the lockdown and of other events on the dynamics of the epidemic. In particular, it has been suggested that municipal elections held just before lockdown was ordered may have helped spread the virus. In this manuscript we use Bayesian models of the number of deaths through time to study the epidemic in 13 regions of France. We found that the models accurately predict the number of deaths 2 to 3 weeks in advance, and recover estimates that are in agreement with recent models that rely on a different structure and different input data. In particular, the lockdown reduced the viral reproduction number by ≈ 80%. However, using a mixture model, we found that the lockdown had had different effectiveness depending on the region, and that it had been slightly more effective in decreasing the reproduction number in denser regions. The mixture model predicts that 2.08 (95% CI : 1.85-2.47) million people had been infected by May 11, and that there were 2567 (95% CI : 1781-5182) new infections on May 10. We found no evidence that the reproduction numbers differ between week-ends and week days, and no evidence that the reproduction numbers increased on the election day. Finally, we evaluated counterfactual scenarios showing that ordering the lockdown 1 to 7 days sooner would have resulted in 19% to 76% fewer deaths, but that ordering it 1 to 7 days later would have resulted in 21% to 266% more deaths. Overall, the predictions of the model indicate that holding the elections on March 15 did not have a detectable impact on the total number of deaths, unless it motivated a delay in imposing the lockdown.</jats:p>

Predicted effects of summer holidays and seasonality on the SARS-Cov-2 epidemic in France

“…Region wise proportions of S, E, I, R individuals on July 1 2020 were simulated using a Bayesian model of the French epidemic (Duchemin et al ., 2020). We chose to use the model without mixture between regions as it provided predictions that were very similar to the mixture model and was easier to fit and simulate.…”

“…To validate our implementation of the SEIR model, we ran it between March 1 2020 and June 1 2021 and compared the number of infectious individuals through time to the numbers obtained by running (Duchemin et al ., 2020)’s Bayesian model over the same time interval. The SEIR model was initialized with the parameter values that the Bayesian model has inferred for March 1 2020.…”

“…During the lockdown, one required a self-authorisation to leave home. The lockdown has successfully slowed down the spread of the epidemic, reducing the reproduction number R t from around 3 to less than 1 (Salje et al ., 2020; Sofonea et al ., 2020; Duchemin et al ., 2020). The lockdown was then lifted progressively.…”

“…1). These predictions are based on a Bayesian model that uses the number of SARS-CoV-2 related deaths through time to monitor the epidemic (Duchemin et al ., 2020). This model was found to have good accuracy and agreed with other models of the epidemic in France.…”

“…We implemented a compartmental Susceptible-Exposed-Infectious-Recovered/Removed (SEIR) model to simulate the infectious process, and complemented it with migrations between regions as gathered from (Direction Générale des Entreprises, 2018). We initialized the number of individuals in each compartment based on simulations from (Duchemin et al ., 2020)’s model. We first investigated how seasonality and reproduction numbers interact to determine the size and the timing of a second wave of infections in France.…”