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BackgroundShort-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. MethodsWe 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. ResultsOver 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. ConclusionsOur 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 availabilityAll data and code are publicly available on Github: covid19-forecast-hub-europe/euro-hub-ensemble.
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SO_SCPLOWUMMARYC_SCPLOWO_ST_ABSBackgroundC_ST_ABSEvidence is accumulating that the effectiveness of covid-19 vaccines against infection wanes, reaching relatively low values after 6 months. Published studies demonstrating this effect based their findings on a limited range of vaccines or subset of populations, and did not include booster vaccine doses or immunity obtained due to covid-19 infection. Here we evaluate effectiveness of covid-19 vaccines, booster doses or previous infection against covid-19 infection, hospital admission or death for the whole population in the Czech Republic. MethodsData used in this study cover the whole population of the Czech Republic reported as infected and/or vaccinated between the first detected case on March 1, 2020 and November 20, 2021 (for reinfections), or December 26, 2020 and November 20, 2021 (for vaccinations), including hospital admissions and deaths. Vaccinations by all vaccines approved in the EU were included in this study. Anonymous, individual-level data including dates of vaccination, infection, hospital admission and death were provided by the the Institute of Health Information and Statistics of the Czech Republic. The risks of reinfection, breakthrough infection after vaccination, hospital admission and death were calculated using hazard ratios from a Cox regression adjusted for sex, age, vaccine type and vaccination status. FindingsThe vaccine effectiveness against any PCR-confirmed infection declined from 87% (95% CI 86-87) at 0-2 months after the second dose to 53% (95% CI 52-54) at 7-8 months for Comirnaty, from 90% (95% CI 89-91) at 0-2 monthsto 65% (95% CI 63-67) at 7-8 months for Spikevax, and from 83% (95% CI 80-85) at 0-2 months to 55% at (95% CI 54-56) 5-6 months for the Vaxzevria. For Janssen Covid-19 Vaccine we found no significant decline but the estimates are less certain. The vaccine effectiveness against hospital admissions and deaths decayed at a significantly lower rate with about 15%, resp. 10% decline during the first 6-8 months. The administration of a booster dose returns the protection to or above the estimates in the first two months after dose 2. In unvaccinated but previously SARS-CoV-2-positive individuals the protection against PCR-confirmed SARS-CoV-2 infection declined from close to 97% (95% CI 97-97) after 2 months through 90% at 6 months down to 72% (95% CI 65-78) at 18 months. InterpretationOur results confirm the waning of vaccination-induced immunity against infection and a smaller decline in the protection against hospital admission and death. A booster dose is shown to restore the vaccine effectiveness back to the levels seen soon after the completion of the basic vaccination schedule. The post-infection immunity decreases over time, too. FundingNo external funding was used to conduct this study. RO_SCPLOWESEARCHC_SCPLOWO_SCPCAP C_SCPCAPO_SCPLOWINC_SCPLOWO_SCPCAP C_SCPCAPO_SCPLOWCONTEXTC_SCPLOWO_ST_ABSEvidence before this studyC_ST_ABSAccumulating evidence from several countries indicates that the effectiveness of covid-19 vaccines against infection declines in time, from about 80-90% shortly after completing the vaccination to about 50-60% and even less after 6 months. Published studies also suggest a significant boosting in vaccine effectiveness against infection about one week after the third vaccine dose. However, these observations come from different and often limited data sets. Moreover, the existing studies do not compare the decline in vaccine effectiveness with a decline in infection-based immunity in unvaccinated individuals. Added value of this studyIn our study, we bring together data on infections, vaccinations (including booster doses), hospital admissions and deaths to estimate how the protection due to vaccination or previous SARS-CoV-2 infection declines with time, for the whole population of the Czech Republic. Our findings show an overall decrease in vaccine effectiveness over time and a large increase after the administration of a booster dose. At the same time we show a fairly stable and high post-infection immunity over the study period. We hope this evidence will contribute to a better understanding of the changing impact of vaccines and previous infection in complex, real-world environments, which is crucial for the development of more effective and more easily communicated public health policies. Implications of all the available evidenceOur results strongly support a timely and widespread application of booster vaccine doses since their application appears to restore the vaccine-induced protection to the levels attained soon after completing the original vaccination scheme, including the high protection against mild disease or asymptomatic infection.
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PurposeIt is unclear how much opening of schools during Covid-19 pandemic contributes to new SARS-CoV-2 infections among children. We investigated the impact of school opening with various mitigation measures (masks, rotations, mass testing) on growth rate of new cases in child cohorts ranging from kindergartens to upper secondary in Czechia, a country heavily hit by Covid-19, since April 2020 to June 2021. MethodsOur primary method is comparison of the reported infections in age cohorts corresponding to school grades undergoing different regimes. When there is no opportunity for such a comparison, we estimate corresponding coefficients from a regression model. In both the cases, we assume that district-level infections in particular cohorts depend on the school attendance and the external environment in dependence on the current overall risk contact reduction. ResultsThe estimates of in-cohort growth rates were significantly higher for normally opened schools compared to closed schools. When prevalence is comparable in the cohorts and general population, and no further measures are applied, the in-cohort growth reduction for closed kindergartens is 29% (SE=11%); primary: 19% (7%); lower secondary: 39% (6%); upper secondary: 47% (6%). For secondary education, mitigation measures reduce school-related growth 2-6 times. ConclusionConsidering more infectious SARS-CoV-2 variants and the long covid risk, mitigation measures in schools, especially in secondary levels, should be implemented for the next school year. Some infections, however, are inevitable, even in kindergartens (where mitigation measures are difficult to implement) and primary schools (where they may not work due to low adherence).
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There are many epidemiological models at hand to cope with the present pandemic; it is, however, difficult to calibrate these models when data are noisy, partial or observed only indirectly. It is also difficult to distinguish relevant data from noise, and to distinguish the impact of individual determinants of the epidemic. In mathematical statistics, the tools to handle all of these phenomena exist; however, they are seldom used for epidemiological models. The goal of this paper is to start filling this gap by proposing a general stochastic epidemiological model, which we call SEIR Filter. Technically our model is a heterogeneous partially observable vector autoregression model, in which we are able to express closed form formulas for the distribution of compartments and observations, so both maximum likelihood and least square estimators are analytically tractable. We give conditions for vanishing, explosion and stationary behaviour of the epidemic and we are able to express a closed form formula for reproduction number. Finally, we present several examples of the models application. We construct an estimate age-cohort model of the COVID-19 pandemic in the Czech Republic. To demonstrate the strengths of the model, we employ it to analyse and compare three vaccination scenarios.
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Running across the globe for more than a year, the COVID-19 pandemic keeps demonstrating its strength. Despite a lot of understanding, uncertainty regarding the efficiency of interventions still persists. We developed an age-structured epidemic model parameterized with sociological data for the Czech Republic and found that (1) delaying the spring 2020 lockdown by four days produced twice as many confirmed cases by the end of the lockdown period, (2) personal protective measures such as face masks appear more effective than just a reduction of social contacts, (3) only sheltering the elderly is by no means effective, and (4) leaving schools open is a risky strategy. Despite the onset of vaccination, an evidence-based choice and timing of non-pharmaceutical interventions still remains the most important weapon against the COVID-19 pandemic. One sentence summaryWe address several issues regarding COVID-19 interventions that still elicit controversy and pursue ignorance
