Adaptive Time-Dependent Priors and Bayesian Inference to Evaluate SARS-CoV-2 Public Health Measures Validated on 31 Countries.

With the rapid spread of the SARS-CoV-2 virus since the end of 2019, public health confinement measures to contain the propagation of the pandemic have been implemented. Our method to estimate the reproduction number using Bayesian inference with time-dependent priors enhances previous approaches by considering a dynamic prior continuously updated as restrictive measures and comportments within the society evolve. In addition, to allow direct comparison between reproduction number and introduction of public health measures in a specific country, the infection dates are inferred from daily confirmed cases and confirmed death. The evolution of this reproduction number in combination with the stringency index is analyzed on 31 European countries. We show that most countries required tough state interventions with a stringency index equal to 79.6 out of 100 to reduce their reproduction number below one and control the progression of the pandemic. In addition, we show a direct correlation between the time taken to introduce restrictive measures and the time required to contain the spread of the pandemic with a median time of 8 days. This analysis is validated by comparing the excess deaths and the time taken to implement restrictive measures. Our analysis reinforces the importance of having a fast response with a coherent and comprehensive set of confinement measures to control the pandemic. Only restrictions or combinations of those have shown to effectively control the pandemic.