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 Fall 2019, public health confinement measures to contain the propagation of the pandemic are taken. Our method to estimate the reproductive 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 reproductive number and introduction of public health measures in a specific country, the infection dates are inferred from daily confirmed cases and death with the mean time between a case being declared as positive and its death estimated on 1430 cases at 10.7 days. The evolution of the reproductive rate 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 83.6 out of 100 to reduce the reproductive number below one and control the progression of the epidemic. 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 epidemic with a median time of 8 days. Our analysis reinforces the importance of having a fast response with a coherent and comprehensive set of confinement measures to control the epidemic. Only combinations of non-pharmaceutical interventions (NPIs) have shown to be effective.