Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October–19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.

Background Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022. Methods We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported from a standardised source over the next one to four weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models’ predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models’ forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models’ past predictive performance. Results Over 52 weeks we collected and combined up to 28 forecast models for 32 countries. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 84% of participating models’ forecasts of incident cases (with a total N=862), and 92% of participating models’ forecasts of deaths (N=746). Across a one to four week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over four weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models. Conclusions Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than two weeks. Code and data availability All data and code are publicly available on Github: covid19-forecast-hub-europe/euro-hub-ensemble.

We study numerically the dynamics of elastic microfilaments which form closed loops and settle under gravity in a viscous fluid. We observe diversity of periodic and stationary sedimentation modes, dependent on flexibility and initial configuration.

Background: Short-term forecasts of infectious disease contribute to situational awareness and capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise forecasts’ predictive performance by combining independent models into an ensemble. Here we report the performance of ensemble predictions of COVID-19 cases and deaths across Europe from March 2021 to March 2022.Methods: We created the European COVID-19 Forecast Hub, an online open-access platform where modellers upload weekly forecasts for 32 countries with results publicly visualised and evaluated. We created a weekly ensemble forecast from the equally-weighted average across individual models' predictive quantiles. We measured forecast accuracy using a baseline and relative Weighted Interval Score (rWIS). We retrospectively explored ensemble methods, including weighting by past performance.Results: We collected weekly forecasts from 48 models, of which we evaluated 29 models alongside the ensemble model. The ensemble had a consistently strong performance across countries over time, performing better on rWIS than 91% of forecasts for deaths (N=763 predictions from 20 models), and 83% forecasts for cases (N=886 predictions from 23 models). Performance remained stable over a 4-week horizon for death forecasts but declined with longer horizons for cases. Among ensemble methods, the most influential choice came from using a median average instead of the mean, regardless of weighting component models.Conclusions: Our results support combining independent models into an ensemble forecast to improve epidemiological predictions, and suggest that median averages yield better performance than methods based on means. We highlight that forecast consumers should place more weight on incident death forecasts than case forecasts at horizons greater than two weeks.Funding: European Commission, Ministerio de Ciencia, Innovación y Universidades, FEDER; Agència de Qualitat i Avaluació Sanitàries de Catalunya; Netzwerk Universitätsmedizin; Health Protection Research Unit; Wellcome Trust; European Centre for Disease Prevention and Control; Ministry of Science and Higher Education of Poland; Federal Ministry of Education and Research; Los Alamos National Laboratory; German Free State of Saxony; NCBiR; FISR 2020 Covid-19 I Fase; Spanish Ministry of Health / REACT-UE (FEDER); National Institutes of General Medical Sciences; Ministerio de Sanidad/ISCIII; PERISCOPE European H2020; PERISCOPE European H2021; InPresa; National Institutes of Health, NSF, US Centers for Disease Control and Prevention, Google, University of Virginia, Defense Threat Reduction Agency.