Our model uses daily standardized death data from ECDC for 11 European countries currently experiencing the COVID-19 pandemic: Austria, Belgium, Denmark, France, Germany, Italy, Norway, Spain, Sweden, Switzerland, and the United Kingdom. The center provides information on confirmed cases and deaths attributed to COVID-19. For population statistics, we use the United Nations Population Division’s age stratified census18.
We also index data regarding the nature and type of major non-pharmacological interventions. We have looked at government web pages from each country as well as official public health web pages to determine the latest advice or laws issued by government and public health authorities. We collected the following: school closure order; case-based measures; Public events are banned; encouraging social distancing; Closing decision and time of first and last intervention. A full list of the timing of these interventions and the sources we used are provided in Supplementary Notes, Supplementary Table 2.
With ECDC data, we rely on a unified data source compiled by ECDC, which includes several data sources every day, and constantly refines and updates the data using a comprehensive and systematic process. However, despite strict protocols, countries may differ in the details of the data they report to ECDC. For example, there is discrepancy in reporting (ie, community versus hospital) and time delays. Despite these issues, we use ECDC data to ensure as much consistency as possible across all countries.
A visual summary of our model is given in Extended Data Fig.3; Details are provided in the Supplementary Methods.
We fit our model with observed deaths according to ECDC data from 11 European countries. Typical mortality is reported by the distribution of infection to death (Supplementary Figure 1; derived from assumptions about time from infection to symptom onset and time from onset of symptoms to death), and population mean infection fatality ratio (adjusted for age structure and contact patterns for each country). , as discussed in Supplementary Methods, Supplementary Table 3).
Given these distributions and proportions, typical deaths are a function of the number of infections. The number of injuries similar to the product sR With a separate wrap for the previous infection. The individual components of this torsion sum are weighted by the generation time distribution (mean time from one person injured to the time another person was injured; Supplementary Figure 2). In our work, we approximate the generation time distribution using the sequential interval distribution. sR It is a function of the initial letter sR Pre-interventions and effect sizes of the interventions, where the interventions are modeled as multipart fixed functions.
Following the Bayesian hierarchy from the bottom up gives us a complete framework for knowing how interventions affect infection, which can lead to mortality. Figure 3. A diagram of our model is shown in Figure 3. To maximize the ability to monitor the impact of interventions on mortality, we fit our model jointly to all 11 European countries, and use partial aggregation of information between countries that includes both individuals and countries. Common influences on sR. Partial assembly acts as the last intervention, which is – in most cases – a closure. The effect of partial pooling can be seen in Supplementary Discussion 12, Supplementary Fig. 29. We chose a balanced a priori that encodes the a priori belief that interventions have an equal chance of having an effect or not, and ensured a uniform a priori presence on the combined effect of all interventions (Supplementary Fig. 3). We evaluate the impact of our previous Bayesian distribution options and evaluate our Bayesian background calibration to ensure that our results are statistically robust.
We perform comprehensive analyzes to validate the model’s validity and sensitivity. We validate our model by cross-validation over a 14-day period (Supplementary Discussion 1, Supplementary Table 1) and show the fit to the waiting samples in Supplementary Figures. 5-15. We check the convergence of the Monte Carlo samples from the Markov chain (Supplementary Fig. 4). We consider the sensitivity of our estimates to sR to the mean generation distribution (Supplementary Discussion 3, Supplementary Figs 16, 17). We further show that the selection of the generational distribution does not change our heterodox conclusions (Supplementary Fig. 18). Using univariate analyzes and uninformative antecedents, we find (Supplementary Fig. 19) that all effects on themselves reduce sR (Supplementary Discussion 4). We compared our model to a non-parametric Gaussian process model (Supplementary Discussion 5). To assess the impact of individual countries on outcomes, we perform a ‘leave one country out’ sensitivity analysis (Supplementary Discussion 6, Supplementary Figs 20, 21). To validate our starting values sR, we compare our model with the linear model of exponential growth (Supplementary Discussion 7, Supplementary Fig. 22). Instead of a combined analysis, we consider that our model fits individual countries (Supplementary Discussion 8, Supplementary Figs 23–26). We perform a sensitivity analysis with respect to the distribution from onset to death (Supplementary Discussion 9, Supplementary Fig. 27). We validate our probabilistic seeding scheme by cross-checking the sampling of significance (Supplementary Discussion 10). We consider a typical extension of the lack of consistent probability reports (Supplementary Discussion 11), and finding that sR It does not change substantially (Supplementary Fig. 28).
Our model differs from other methods (eg EpiEstim19) that uses the discrete regeneration equation. We use the regeneration equation as a latent process to model infection and propose a generation mechanism to correlate this infection with mortality data. Applying the regeneration equation directly to death data requires the imposition of a mechanism by which past deaths can cause future deaths (see, for example, ref. 20). In addition, to sRWe are able to use a functional relationship on which non-pharmacological interventions can have a direct impact sR.
More information about the research design is available in the Nature Research report summary linked to this paper.