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During 2020–2022, players and staff in the English Premier League in the United Kingdom were tested regularly for SARS-CoV-2 with the aim of creating a biosecure bubble for each team. We found that prevalence and reinfection estimates were consistent with those from other studies and with community infection trends.

Epidemiological delays are key quantities that inform public health policy and clinical practice. They are used as inputs for mathematical and statistical models, which in turn can guide control strategies. In recent work, we found that censoring, right truncation, and dynamical bias were rarely addressed correctly when estimating delays and that these biases were large enough to have knock-on impacts across a large number of use cases. Here, we formulate a checklist of best practices for estimating and reporting epidemiological delays. We also provide a flowchart to guide practitioners based on their data. Our examples are focused on the incubation period and serial interval due to their importance in outbreak response and modeling, but our recommendations are applicable to other delays. The recommendations, which are based on the literature and our experience estimating epidemiological delay distributions during outbreak responses, can help improve the robustness and utility of reported estimates and provide guidance for the evaluation of estimates for downstream use in transmission models or other analyses.

Abstract Background Defining healthcare facility catchment areas is a key step in predicting future healthcare demand in epidemic settings. Forecasts of hospitalisations can be informed by leading indicators measured at the community level. However, this relies on the definition of so-called catchment areas or the geographies whose populations make up the patients admitted to a given hospital, which are often not well-defined. Little work has been done to quantify the impact of hospital catchment area definitions on healthcare demand forecasting. Methods We made forecasts of local-level hospital admissions using a scaled convolution of local cases (as defined by the hospital catchment area) and delay distribution. Hospital catchment area definitions were derived from either simple heuristics (in which people are admitted to their nearest hospital or any nearby hospital) or historical admissions data (all emergency or elective admissions in 2019, or COVID-19 admissions), plus a marginal baseline definition based on the distribution of all hospital admissions. We evaluated predictive performance using each hospital catchment area definition using the weighted interval score and considered how this changed by the length of the predictive horizon, the date on which the forecast was made, and by location. We also considered the change, if any, in the relative performance of each definition in retrospective vs. real-time settings, or at different spatial scales. Results The choice of hospital catchment area definition affected the accuracy of hospital admission forecasts. The definition based on COVID-19 admissions data resulted in the most accurate forecasts at both a 7- and 14-day horizon and was one of the top two best-performing definitions across forecast dates and locations. The “nearby” heuristic also performed well, but less consistently than the COVID-19 data definition. The marginal distribution baseline, which did not include any spatial information, was the lowest-ranked definition. The relative performance of the definitions was larger when using case forecasts compared to future observed cases. All results were consistent across spatial scales of the catchment area definitions. Conclusions Using catchment area definitions derived from context-specific data can improve local-level hospital admission forecasts. Where context-specific data is not available, using catchment areas defined by carefully chosen heuristics is a sufficiently good substitute. There is clear value in understanding what drives local admissions patterns, and further research is needed to understand the impact of different catchment area definitions on forecast performance where case trends are more heterogeneous.

Background: Collaborative comparisons and combinations of epidemic models are used as policy-relevant evidence during epidemic outbreaks. In the process of collecting multiple model projections, such collaborations may gain or lose relevant information. Typically, modellers contribute a probabilistic summary at each time-step. We compared this to directly collecting simulated trajectories. We aimed to explore information on key epidemic quantities; ensemble uncertainty; and performance against data, investigating potential to continuously gain information from a single cross-sectional collection of model results. Methods: We compared projections from the European COVID-19 Scenario Modelling Hub. Five teams modelled incidence in Belgium, the Netherlands, and Spain. We compared July 2022 projections by incidence, peaks, and cumulative totals. We created a probabilistic ensemble drawn from all trajectories, and compared to ensembles from a median across each model’s quantiles, or a linear opinion pool. We measured the predictive accuracy of individual trajectories against observations, using this in a weighted ensemble. We repeated this sequentially against increasing weeks of observed data. We evaluated these ensembles to reflect performance with varying observed data. Results: By collecting modelled trajectories, we showed policy-relevant epidemic characteristics. Trajectories contained a right-skewed distribution well represented by an ensemble of trajectories or a linear opinion pool, but not models’ quantile intervals. Ensembles weighted by performance typically retained the range of plausible incidence over time, and in some cases narrowed this by excluding some epidemic shapes. Conclusions: We observed several information gains from collecting modelled trajectories rather than quantile distributions, including potential for continuously updated information from a single model collection. The value of information gains and losses may vary with each collaborative effort’s aims, depending on the needs of projection users. Understanding the differing information potential of methods to collect model projections can support the accuracy, sustainability, and communication of collaborative infectious disease modelling efforts.

Abstract Background Recurring COVID-19 waves highlight the need for tools able to quantify transmission risk, and identify geographical areas at risk of outbreaks. Local outbreak risk depends on complex immunity patterns resulting from previous infections, vaccination, waning and immune escape, alongside other factors (population density, social contact patterns). Immunity patterns are spatially and demographically heterogeneous, and are challenging to capture in country-level forecast models. Methods We used a spatiotemporal regression model to forecast subnational case and death counts and applied it to three EU countries as test cases: France, Czechia, and Italy. Cases in local regions arise from importations or local transmission. Our model produces age-stratified forecasts given age-stratified data, and links reported case counts to routinely collected covariates (e.g. test number, vaccine coverage). We assessed the predictive performance of our model up to four weeks ahead using proper scoring rules and compared it to the European COVID-19 Forecast Hub ensemble model. Using simulations, we evaluated the impact of variations in transmission on the forecasts. We developed an open-source RShiny App to visualise the forecasts and scenarios. Results At a national level, the median relative difference between our median weekly case forecasts and the data up to four weeks ahead was 25% (IQR: 12–50%) over the prediction period. The accuracy decreased as the forecast horizon increased (on average 24% increase in the median ranked probability score per added week), while the accuracy of death forecasts was more stable. Beyond two weeks, the model generated a narrow range of likely transmission dynamics. The median national case forecasts showed similar accuracy to forecasts from the European COVID-19 Forecast Hub ensemble model, but the prediction interval was narrower in our model. Generating forecasts under alternative transmission scenarios was therefore key to capturing the range of possible short-term transmission dynamics. Discussion Our model captures changes in local COVID-19 outbreak dynamics, and enables quantification of short-term transmission risk at a subnational level. The outputs of the model improve our ability to identify areas where outbreaks are most likely, and are available to a wide range of public health professionals through the Shiny App we developed.

Mathematical modelling has played an important role in offering informed advice during the COVID-19 pandemic. In England, a cross government and academia collaboration generated medium-term projections (MTPs) of possible epidemic trajectories over the future 4–6 weeks from a collection of epidemiological models. In this article, we outline this collaborative modelling approach and evaluate the accuracy of the combined and individual model projections against the data over the period November 2021–December 2022 when various Omicron subvariants were spreading across England. Using a number of statistical methods, we quantify the predictive performance of the model projections for both the combined and individual MTPs, by evaluating the point and probabilistic accuracy. Our results illustrate that the combined MTPs, produced from an ensemble of heterogeneous epidemiological models, were a closer fit to the data than the individual models during the periods of epidemic growth or decline, with the 90% confidence intervals widest around the epidemic peaks. We also show that the combined MTPs increase the robustness and reduce the biases associated with a single model projection. Learning from our experience of ensemble modelling during the COVID-19 epidemic, our findings highlight the importance of developing cross-institutional multi-model infectious disease hubs for future outbreak control.

Background In the past, two studies found ensembles of human judgement forecasts of COVID-19 to show predictive performance comparable to ensembles of computational models, at least when predicting case incidences. We present a follow-up to a study conducted in Germany and Poland and investigate a novel joint approach to combine human judgement and epidemiological modelling. Methods From May 24th to August 16th 2021, we elicited weekly one to four week ahead forecasts of cases and deaths from COVID-19 in the UK from a crowd of human forecasters. A median ensemble of all forecasts was submitted to the European Forecast Hub. Participants could use two distinct interfaces: in one, forecasters submitted a predictive distribution directly, in the other forecasters instead submitted a forecast of the effective reproduction number Rt . This was then used to forecast cases and deaths using simulation methods from the EpiNow2 R package. Forecasts were scored using the weighted interval score on the original forecasts, as well as after applying the natural logarithm to both forecasts and observations. Results The ensemble of human forecasters overall performed comparably to the official European Forecast Hub ensemble on both cases and deaths, although results were sensitive to changes in details of the evaluation. Rt forecasts performed comparably to direct forecasts on cases, but worse on deaths. Self-identified “experts” tended to be better calibrated than “non-experts” for cases, but not for deaths. Conclusions Human judgement forecasts and computational models can produce forecasts of similar quality for infectious disease such as COVID-19. The results of forecast evaluations can change depending on what metrics are chosen and judgement on what does or doesn't constitute a "good" forecast is dependent on the forecast consumer. Combinations of human and computational forecasts hold potential but present real-world challenges that need to be solved.

Background The COVID-19 pandemic both relied and placed significant burdens on the experts involved from research and public health sectors. The sustained high pressure of a pandemic on responders, such as healthcare workers, can lead to lasting psychological impacts including acute stress disorder, post-traumatic stress disorder, burnout, and moral injury, which can impact individual wellbeing and productivity. Methods As members of the infectious disease modelling community, we convened a reflective workshop to understand the professional and personal impacts of response work on our community and to propose recommendations for future epidemic responses. The attendees represented a range of career stages, institutions, and disciplines. This piece was collectively produced by those present at the session based on our collective experiences. Results Key issues we identified at the workshop were lack of institutional support, insecure contracts, unequal credit and recognition, and mental health impacts. Our recommendations include rewarding impactful work, fostering academia-public health collaboration, decreasing dependence on key individuals by developing teams, increasing transparency in decision-making, and implementing sustainable work practices. Conclusions Despite limitations in representation, this workshop provided valuable insights into the UK COVID-19 modelling experience and guidance for future public health crises. Recognising and addressing the issues highlighted is crucial, in our view, for ensuring the effectiveness of epidemic response work in the future.

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

Mathematical and statistical models can be used to make predictions of how epidemics may progress in the near future and form a central part of outbreak mitigation and control. Renewal equation based models allow inference of epidemiological parameters from historical data and forecast future epidemic dynamics without requiring complex mechanistic assumptions. However, these models typically ignore interaction between age groups, partly due to challenges in parameterising a time varying interaction matrix. Social contact data collected regularly during the COVID-19 epidemic provide a means to inform interaction between age groups in real-time. We developed an age-specific forecasting framework and applied it to two age-stratified time-series: incidence of SARS-CoV-2 infection, estimated from a national infection and antibody prevalence survey; and, reported cases according to the UK national COVID-19 dashboard. Jointly fitting our model to social contact data from the CoMix study, we inferred a time-varying next generation matrix which we used to project infections and cases in the four weeks following each of 29 forecast dates between October 2020 and November 2021. We evaluated the forecasts using proper scoring rules and compared performance with three other models with alternative data and specifications alongside two naive baseline models. Overall, incorporating age interaction improved forecasts of infections and the CoMix-data-informed model was the best performing model at time horizons between two and four weeks. However, this was not true when forecasting cases. We found that age group interaction was most important for predicting cases in children and older adults. The contact-data-informed models performed best during the winter months of 2020-2021, but performed comparatively poorly in other periods. We highlight challenges regarding the incorporation of contact data in forecasting and offer proposals as to how to extend and adapt our approach, which may lead to more successful forecasts in future.

Bracher et al. compare 15 forecasting models of COVID-19 cases and deaths in Germany and Poland between January and mid-April 2021. Many, though not all, models outperform a simple baseline model up to four weeks ahead, with ensemble methods showing very good relative performance.

Forecast evaluation is essential for the development of predictive epidemic models and can inform their use for public health decision-making. Common scores to evaluate epidemiological forecasts are the Continuous Ranked Probability Score (CRPS) and the Weighted Interval Score (WIS), which can be seen as measures of the absolute distance between the forecast distribution and the observation. However, applying these scores directly to predicted and observed incidence counts may not be the most appropriate due to the exponential nature of epidemic processes and the varying magnitudes of observed values across space and time. In this paper, we argue that transforming counts before applying scores such as the CRPS or WIS can effectively mitigate these difficulties and yield epidemiologically meaningful and easily interpretable results. Using the CRPS on log-transformed values as an example, we list three attractive properties: Firstly, it can be interpreted as a probabilistic version of a relative error. Secondly, it reflects how well models predicted the time-varying epidemic growth rate. And lastly, using arguments on variance-stabilizing transformations, it can be shown that under the assumption of a quadratic mean-variance relationship, the logarithmic transformation leads to expected CRPS values which are independent of the order of magnitude of the predicted quantity. Applying a transformation of log(x + 1) to data and forecasts from the European COVID-19 Forecast Hub, we find that it changes model rankings regardless of stratification by forecast date, location or target types. Situations in which models missed the beginning of upward swings are more strongly emphasised while failing to predict a downturn following a peak is less severely penalised when scoring transformed forecasts as opposed to untransformed ones. We conclude that appropriate transformations, of which the natural logarithm is only one particularly attractive option, should be considered when assessing the performance of different models in the context of infectious disease incidence.

Real-time surveillance is a crucial element in the response to infectious disease outbreaks. However, the interpretation of incidence data is often hampered by delays occurring at various stages of data gathering and reporting. As a result, recent values are biased downward, which obscures current trends. Statistical nowcasting techniques can be employed to correct these biases, allowing for accurate characterization of recent developments and thus enhancing situational awareness. In this paper, we present a preregistered real-time assessment of eight nowcasting approaches, applied by independent research teams to German 7-day hospitalization incidences during the COVID-19 pandemic. This indicator played an important role in the management of the outbreak in Germany and was linked to levels of non-pharmaceutical interventions via certain thresholds. Due to its definition, in which hospitalization counts are aggregated by the date of case report rather than admission, German hospitalization incidences are particularly affected by delays and can take several weeks or months to fully stabilize. For this study, all methods were applied from 22 November 2021 to 29 April 2022, with probabilistic nowcasts produced each day for the current and 28 preceding days. Nowcasts at the national, state, and age-group levels were collected in the form of quantiles in a public repository and displayed in a dashboard. Moreover, a mean and a median ensemble nowcast were generated. We find that overall, the compared methods were able to remove a large part of the biases introduced by delays. Most participating teams underestimated the importance of very long delays, though, resulting in nowcasts with a slight downward bias. The accompanying prediction intervals were also too narrow for almost all methods. Averaged over all nowcast horizons, the best performance was achieved by a model using case incidences as a covariate and taking into account longer delays than the other approaches. For the most recent days, which are often considered the most relevant in practice, a mean ensemble of the submitted nowcasts performed best. We conclude by providing some lessons learned on the definition of nowcasting targets and practical challenges.

Abstract Background SARS-CoV-2 is known to transmit in hospital settings, but the contribution of infections acquired in hospitals to the epidemic at a national scale is unknown. Methods We used comprehensive national English datasets to determine the number of COVID-19 patients with identified hospital-acquired infections (with symptom onset > 7 days after admission and before discharge) in acute English hospitals up to August 2020. As patients may leave the hospital prior to detection of infection or have rapid symptom onset, we combined measures of the length of stay and the incubation period distribution to estimate how many hospital-acquired infections may have been missed. We used simulations to estimate the total number (identified and unidentified) of symptomatic hospital-acquired infections, as well as infections due to onward community transmission from missed hospital-acquired infections, to 31st July 2020. Results In our dataset of hospitalised COVID-19 patients in acute English hospitals with a recorded symptom onset date (n = 65,028), 7% were classified as hospital-acquired. We estimated that only 30% (range across weeks and 200 simulations: 20–41%) of symptomatic hospital-acquired infections would be identified, with up to 15% (mean, 95% range over 200 simulations: 14.1–15.8%) of cases currently classified as community-acquired COVID-19 potentially linked to hospital transmission. We estimated that 26,600 (25,900 to 27,700) individuals acquired a symptomatic SARS-CoV-2 infection in an acute Trust in England before 31st July 2020, resulting in 15,900 (15,200–16,400) or 20.1% (19.2–20.7%) of all identified hospitalised COVID-19 cases. Conclusions Transmission of SARS-CoV-2 to hospitalised patients likely caused approximately a fifth of identified cases of hospitalised COVID-19 in the “first wave” in England, but less than 1% of all infections in England. Using time to symptom onset from admission for inpatients as a detection method likely misses a substantial proportion (> 60%) of hospital-acquired infections.

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 by a standardised source for 32 countries over the next 1–4 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 forecasts from 48 unique models. We evaluated 29 models’ forecast scores in comparison to the ensemble model. 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 83% of participating models’ forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models’ forecasts of deaths (N=763 predictions from 20 models). Across a 1–4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 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 2 weeks. Funding: AA, BH, BL, LWa, MMa, PP, SV funded by National Institutes of Health (NIH) Grant 1R01GM109718, NSF BIG DATA Grant IIS-1633028, NSF Grant No.: OAC-1916805, NSF Expeditions in Computing Grant CCF-1918656, CCF-1917819, NSF RAPID CNS-2028004, NSF RAPID OAC-2027541, US Centers for Disease Control and Prevention 75D30119C05935, a grant from Google, University of Virginia Strategic Investment Fund award number SIF160, Defense Threat Reduction Agency (DTRA) under Contract No. HDTRA1-19-D-0007, and respectively Virginia Dept of Health Grant VDH-21-501-0141, VDH-21-501-0143, VDH-21-501-0147, VDH-21-501-0145, VDH-21-501-0146, VDH-21-501-0142, VDH-21-501-0148. AF, AMa, GL funded by SMIGE - Modelli statistici inferenziali per governare l'epidemia, FISR 2020-Covid-19 I Fase, FISR2020IP-00156, Codice Progetto: PRJ-0695. AM, BK, FD, FR, JK, JN, JZ, KN, MG, MR, MS, RB funded by Ministry of Science and Higher Education of Poland with grant 28/WFSN/2021 to the University of Warsaw. BRe, CPe, JLAz funded by Ministerio de Sanidad/ISCIII. BT, PG funded by PERISCOPE European H2020 project, contract number 101016233. CP, DL, EA, MC, SA funded by European Commission - Directorate-General for Communications Networks, Content and Technology through the contract LC-01485746, and Ministerio de Ciencia, Innovacion y Universidades and FEDER, with the project PGC2018-095456-B-I00. DE., MGu funded by Spanish Ministry of Health / REACT-UE (FEDER). DO, GF, IMi, LC funded by Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20200700ER. DS, ELR, GG, NGR, NW, YW funded by National Institutes of General Medical Sciences (R35GM119582; the content is solely the responsibility of the authors and does not necessarily represent the official views of NIGMS or the National Institutes of Health). FB, FP funded by InPresa, Lombardy Region, Italy. HG, KS funded by European Centre for Disease Prevention and Control. IV funded by Agencia de Qualitat i Avaluacio Sanitaries de Catalunya (AQuAS) through contract 2021-021OE. JDe, SMo, VP funded by Netzwerk Universitatsmedizin (NUM) project egePan (01KX2021). JPB, SH, TH funded by Federal Ministry of Education and Research (BMBF; grant 05M18SIA). KH, MSc, YKh funded by Project SaxoCOV, funded by the German Free State of Saxony. Presentation of data, model results and simulations also funded by the NFDI4Health Task Force COVID-19 (https://www.nfdi4health.de/task-force-covid-19-2) within the framework of a DFG-project (LO-342/17-1). LP, VE funded by Mathematical and Statistical modelling project (MUNI/A/1615/2020), Online platform for real-time monitoring, analysis and management of epidemic situations (MUNI/11/02202001/2020); VE also supported by RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic: LM2018121), the CETOCOEN EXCELLENCE (CZ.02.1.01/0.0/0.0/17-043/0009632), RECETOX RI project (CZ.02.1.01/0.0/0.0/16-013/0001761). NIB funded by Health Protection Research Unit (grant code NIHR200908). SAb, SF funded by Wellcome Trust (210758/Z/18/Z).

Abstract Background Subnational heterogeneity in immunity to measles can create pockets of susceptibility and result in long-lasting outbreaks despite high levels of national vaccine coverage. The elimination status defined by the World Health Organization aims to identify countries where the virus is no longer circulating and can be verified after 36 months of interrupted transmission. However, since 2018, numerous countries have lost their elimination status soon after reaching it, showing that the indicators defining elimination may not be associated with lower risks of outbreaks. Methods We quantified the impact of local vaccine coverage and recent levels of incidence on the dynamics of measles in each French department between 2009 and 2018, using mathematical models based on the “Endemic-Epidemic” regression framework. After fitting the models using daily case counts, we simulated the effect of variations in the vaccine coverage and recent incidence on future transmission. Results High values of local vaccine coverage were associated with fewer imported cases and lower risks of local transmissions, but regions that had recently reported high levels of incidence were also at a lower risk of local transmission. This may be due to additional immunity accumulated during recent outbreaks. Therefore, the risk of local transmission was not lower in areas fulfilling the elimination criteria. A decrease of 3% in the 3-year average vaccine uptake led to a fivefold increase in the average annual number of cases in simulated outbreaks. Conclusions Local vaccine uptake was a reliable indicator of the intensity of transmission in France, even if it only describes yearly coverage in a given age group, and ignores population movements. Therefore, spatiotemporal variations in vaccine coverage, caused by disruptions in routine immunisation programmes, or lower trust in vaccines, can lead to large increases in both local and cross-regional transmission. The incidence indicator used to define the elimination status was not associated with a lower number of local transmissions in France, and may not illustrate the risks of imminent outbreaks. More detailed models of local immunity levels or subnational seroprevalence studies may yield better estimates of local risk of measles outbreaks.

Abstract Background Forecasting healthcare demand is essential in epidemic settings, both to inform situational awareness and facilitate resource planning. Ideally, forecasts should be robust across time and locations. During the COVID-19 pandemic in England, it is an ongoing concern that demand for hospital care for COVID-19 patients in England will exceed available resources. Methods We made weekly forecasts of daily COVID-19 hospital admissions for National Health Service (NHS) Trusts in England between August 2020 and April 2021 using three disease-agnostic forecasting models: a mean ensemble of autoregressive time series models, a linear regression model with 7-day-lagged local cases as a predictor, and a scaled convolution of local cases and a delay distribution. We compared their point and probabilistic accuracy to a mean-ensemble of them all and to a simple baseline model of no change from the last day of admissions. We measured predictive performance using the weighted interval score (WIS) and considered how this changed in different scenarios (the length of the predictive horizon, the date on which the forecast was made, and by location), as well as how much admissions forecasts improved when future cases were known. Results All models outperformed the baseline in the majority of scenarios. Forecasting accuracy varied by forecast date and location, depending on the trajectory of the outbreak, and all individual models had instances where they were the top- or bottom-ranked model. Forecasts produced by the mean-ensemble were both the most accurate and most consistently accurate forecasts amongst all the models considered. Forecasting accuracy was improved when using future observed, rather than forecast, cases, especially at longer forecast horizons. Conclusions Assuming no change in current admissions is rarely better than including at least a trend. Using confirmed COVID-19 cases as a predictor can improve admissions forecasts in some scenarios, but this is variable and depends on the ability to make consistently good case forecasts. However, ensemble forecasts can make forecasts that make consistently more accurate forecasts across time and locations. Given minimal requirements on data and computation, our admissions forecasting ensemble could be used to anticipate healthcare needs in future epidemic or pandemic settings.

Abstract Background Schools were closed in England on 4 January 2021 as part of increased national restrictions to curb transmission of SARS-CoV-2. The UK government reopened schools on 8 March. Although there was evidence of lower individual-level transmission risk amongst children compared to adults, the combined effects of this with increased contact rates in school settings and the resulting impact on the overall transmission rate in the population were not clear. Methods We measured social contacts of > 5000 participants weekly from March 2020, including periods when schools were both open and closed, amongst other restrictions. We combined these data with estimates of the susceptibility and infectiousness of children compared with adults to estimate the impact of reopening schools on the reproduction number. Results Our analysis indicates that reopening all schools under the same measures as previous periods that combined lockdown with face-to-face schooling would be likely to increase the reproduction number substantially. Assuming a baseline of 0.8, we estimated a likely increase to between 1.0 and 1.5 with the reopening of all schools or to between 0.9 and 1.2 reopening primary or secondary schools alone. Conclusion Our results suggest that reopening schools would likely halt the fall in cases observed between January and March 2021 and would risk a return to rising infections, but these estimates relied heavily on the latest estimates or reproduction number and the validity of the susceptibility and infectiousness profiles we used at the time of reopening.

Abstract Background Stratifying dengue risk within endemic countries is crucial for allocating limited control interventions. Current methods of monitoring dengue transmission intensity rely on potentially inaccurate incidence estimates. We investigated whether incidence or alternate metrics obtained from standard, or laboratory, surveillance operations represent accurate surrogate indicators of the burden of dengue and can be used to monitor the force of infection (FOI) across urban centres. Methods Among those who reported and resided in 13 cities across the Philippines, we collected epidemiological data from all dengue case reports between 2014 and 2017 (N 80,043) and additional laboratory data from a cross-section of sampled case reports (N 11,906) between 2014 and 2018. At the city level, we estimated the aggregated annual FOI from age-accumulated IgG among the non-dengue reporting population using catalytic modelling. We compared city-aggregated FOI estimates to aggregated incidence and the mean age of clinically and laboratory diagnosed dengue cases using Pearson’s Correlation coefficient and generated predicted FOI estimates using regression modelling. Results We observed spatial heterogeneity in the dengue average annual FOI across sampled cities, ranging from 0.054 [0.036–0.081] to 0.249 [0.223–0.279]. Compared to FOI estimates, the mean age of primary dengue infections had the strongest association (ρ −0.848, p value

Forecasts based on epidemiological modelling have played an important role in shaping public policy throughout the COVID-19 pandemic. This modelling combines knowledge about infectious disease dynamics with the subjective opinion of the researcher who develops and refines the model and often also adjusts model outputs. Developing a forecast model is difficult, resource- and time-consuming. It is therefore worth asking what modelling is able to add beyond the subjective opinion of the researcher alone. To investigate this, we analysed different real-time forecasts of cases of and deaths from COVID-19 in Germany and Poland over a 1-4 week horizon submitted to the German and Polish Forecast Hub. We compared crowd forecasts elicited from researchers and volunteers, against a) forecasts from two semi-mechanistic models based on common epidemiological assumptions and b) the ensemble of all other models submitted to the Forecast Hub. We found crowd forecasts, despite being overconfident, to outperform all other methods across all forecast horizons when forecasting cases (weighted interval score relative to the Hub ensemble 2 weeks ahead: 0.89). Forecasts based on computational models performed comparably better when predicting deaths (rel. WIS 1.26), suggesting that epidemiological modelling and human judgement can complement each other in important ways.

Dengue and Zika virus are closely related flaviviruses but can have contrasting transmission dynamics in the same populations. Here, the authors use a model combining serological, surveillance and viral sequence data to explain differences in transmission dynamics in Fiji.

Many countries have closed schools as part of their COVID-19 response. Here, the authors model SARS-CoV-2 transmission on a network of schools and households in England, and find that risk of transmission between schools is lower if primary schools are open than if secondary schools are open.

Vaccination uptake in the Federation of Bosnia and Herzegovina (FBiH), in Bosnia and Herzegovina, is suboptimal. This study aimed to (1) assess vaccination coverage, timeliness and drop-out for children born in 2015 and 2016 and compare these with official administrative coverage estimates, (2) identify associations between characteristics of children/caregivers and vaccination uptake. This was a cross-sectional study based on patient files for children 12–23 months (n = 1800) and 24–35 months (n = 1800). Methods were adapted from the World Health Organization cluster survey methodology. A two-stage stratified sampling procedure was conducted in urban and rural strata. A structured paper-based form was completed by a pediatrician/nurse from randomly selected primary care centers and patient files. Estimates were based on weighted analysis with a 95% confidence interval to account for the survey sampling design. Vaccination coverage was consistent with administrative coverage levels for BCG, DTP and MMR, and lower for HepB; all considerably lower than regional targets. Children in urban areas had lower vaccination uptake. An assumption that anti-vaccination sentiment prevails among caregivers was not confirmed; only 2% of children were not vaccinated at all, instead challenges related to delays and drop-out. An assumption of caregiver concerns for the MMR vaccine was confirmed with low uptake and delays. The FBiH has experienced vaccination schedule changes due to supply issues; findings confirmed that sustainability in supply and schedule is high priority. These data are new and provide important information for developing strategies to increase uptake.

The fraction of cases reported, known as 'reporting', is a key performance indicator in an outbreak response, and an essential factor to consider when modelling epidemics and assessing their impact on populations. Unfortunately, its estimation is inherently difficult, as it relates to the part of an epidemic which is, by definition, not observed. We introduce a simple statistical method for estimating reporting, initially developed for the response to Ebola in Eastern Democratic Republic of the Congo (DRC), 2018-2020. This approach uses transmission chain data typically gathered through case investigation and contact tracing, and uses the proportion of investigated cases with a known, reported infector as a proxy for reporting. Using simulated epidemics, we study how this method performs for different outbreak sizes and reporting levels. Results suggest that our method has low bias, reasonable precision, and despite sub-optimal coverage, usually provides estimates within close range (5-10%) of the true value. Being fast and simple, this method could be useful for estimating reporting in real-time in settings where person-to-person transmission is the main driver of the epidemic, and where case investigation is routinely performed as part of surveillance and contact tracing activities.

Background During the Coronavirus Disease 2019 (COVID-19) pandemic, the United Kingdom government imposed public health policies in England to reduce social contacts in hopes of curbing virus transmission. We conducted a repeated cross-sectional study to measure contact patterns weekly from March 2020 to March 2021 to estimate the impact of these policies, covering 3 national lockdowns interspersed by periods of less restrictive policies. Methods and findings The repeated cross-sectional survey data were collected using online surveys of representative samples of the UK population by age and gender. Survey participants were recruited by the online market research company Ipsos MORI through internet-based banner and social media ads and email campaigns. The participant data used for this analysis are restricted to those who reported living in England. We calculated the mean daily contacts reported using a (clustered) bootstrap and fitted a censored negative binomial model to estimate age-stratified contact matrices and estimate proportional changes to the basic reproduction number under controlled conditions using the change in contacts as a scaling factor. To put the findings in perspective, we discuss contact rates recorded throughout the year in terms of previously recorded rates from the POLYMOD study social contact study. The survey recorded 101,350 observations from 19,914 participants who reported 466,710 contacts over 53 weeks. We observed changes in social contact patterns in England over time and by participants’ age, personal risk factors, and perception of risk. The mean reported contacts for adults 18 to 59 years old ranged between 2.39 (95% confidence interval [CI] 2.20 to 2.60) contacts and 4.93 (95% CI 4.65 to 5.19) contacts during the study period. The mean contacts for school-age children (5 to 17 years old) ranged from 3.07 (95% CI 2.89 to 3.27) to 15.11 (95% CI 13.87 to 16.41). This demonstrates a sustained decrease in social contacts compared to a mean of 11.08 (95% CI 10.54 to 11.57) contacts per participant in all age groups combined as measured by the POLYMOD social contact study in 2005 to 2006. Contacts measured during periods of lockdowns were lower than in periods of eased social restrictions. The use of face coverings outside the home has remained high since the government mandated use in some settings in July 2020. The main limitations of this analysis are the potential for selection bias, as participants are recruited through internet-based campaigns, and recall bias, in which participants may under- or overreport the number of contacts they have made. Conclusions In this study, we observed that recorded contacts reduced dramatically compared to prepandemic levels (as measured in the POLYMOD study), with changes in reported contacts correlated with government interventions throughout the pandemic. Despite easing of restrictions in the summer of 2020, the mean number of reported contacts only returned to about half of that observed prepandemic at its highest recorded level. The CoMix survey provides a unique repeated cross-sectional data set for a full year in England, from the first day of the first lockdown, for use in statistical analyses and mathematical modelling of COVID-19 and other diseases. In a repeated cross-sectional study, Amy Gimma and colleagues study social contact patterns in the context of lockdown periods and government interventions in England during the first year of the COVID-19 pandemic. Author summary Why was this study done? Mathematical models can be used to better understand the transmission dynamics of Coronavirus Disease 2019 (COVID-19) and could be strengthened by empirical evidence of the number of social contacts made under pandemic conditions. We identified a need for real-time social contact data to inform outbreak models, as we expected social contact behaviour to change due to perceived risk and in response to government policies restricting social contact over the course of the pandemic. We launched the CoMix social contact and behavioural study on March 24, 2020 to capture the changes in social contacts, risk perception, and other behaviours, such as hand hygiene and the use of face coverings. What did the researchers do and find? During the most stringent lockdown in the UK, we found that the mean number of reported contacts in England was about 75% less than prepandemic measures for adults over the age of 17. Throughout the year, the mean number of contacts remained low—only reaching about 50% of the prepandemic levels, even during periods of relatively few policies remaining to restrict social activity. During each lockdown, contacts returned to similar levels as the first lockdown for adults, while the mean number of contacts for children depends on whether or not schools were open for in-person learning. What do these findings mean? Throughout the year, the UK government, which governs England, used the CoMix social contact data to monitor social contacts and as an early indication of changes to the basic reproduction number. While these data have been put to use in real time, both researchers and policymakers need to take into account some limitations of the CoMix study results, including the self-reporting of social contacts, which could lead to bias as a result of inaccurate memory or due to social pressure to report more or fewer contacts. These data will continue to be used by researchers and policymakers to monitor changes in social behaviour, to model transmission of COVID-19 and other diseases, and to make important policy decisions.

Abstract Background In dengue-endemic countries, targeting limited control interventions to populations at risk of severe disease could enable increased efficiency. Individuals who have had their first (primary) dengue infection are at risk of developing more severe secondary disease, thus could be targeted for disease prevention. Currently, there is no reliable algorithm for determining primary and post-primary (infection with more than one flavivirus) status from a single serum sample. In this study, we developed and validated an immune status algorithm using single acute serum samples from reporting patients and investigated dengue immuno-epidemiological patterns across the Philippines. Methods During 2015/2016, a cross-sectional sample of 10,137 dengue case reports provided serum for molecular (anti-DENV PCR) and serological (anti-DENV IgM/G capture ELISA) assay. Using mixture modelling, we re-assessed IgM/G seroprevalence and estimated functional, disease day-specific, IgG:IgM ratios that categorised the reporting population as negative, historical, primary and post-primary for dengue. We validated our algorithm against WHO gold standard criteria and investigated cross-reactivity with Zika by assaying a random subset for anti-ZIKV IgM and IgG. Lastly, using our algorithm, we explored immuno-epidemiological patterns of dengue across the Philippines. Results Our modelled IgM and IgG seroprevalence thresholds were lower than kit-provided thresholds. Individuals anti-DENV PCR+ or IgM+ were classified as active dengue infections (83.1%, 6998/8425). IgG− and IgG+ active dengue infections on disease days 1 and 2 were categorised as primary and post-primary, respectively, while those on disease days 3 to 5 with IgG:IgM ratios below and above 0.45 were classified as primary and post-primary, respectively. A significant proportion of post-primary dengue infections had elevated anti-ZIKV IgG inferring previous Zika exposure. Our algorithm achieved 90.5% serological agreement with WHO standard practice. Post-primary dengue infections were more likely to be older and present with severe symptoms. Finally, we identified a spatio-temporal cluster of primary dengue case reporting in northern Luzon during 2016. Conclusions Our dengue immune status algorithm can equip surveillance operations with the means to target dengue control efforts. The algorithm accurately identified primary dengue infections who are at risk of future severe disease.

Abstract Objective Establishing a social contact data sharing initiative and an interactive tool to assess mitigation strategies for COVID-19. Results We organized data sharing of published social contact surveys via online repositories and formatting guidelines. We analyzed this social contact data in terms of weighted social contact matrices, next generation matrices, relative incidence and R $$_{0}$$ 0 . We incorporated location-specific physical distancing measures (e.g. school closure or at work) and capture their effect on transmission dynamics. All methods have been implemented in an online application based on R Shiny and applied to COVID-19 with age-specific susceptibility and infectiousness. Using our online tool with the available social contact data, we illustrate that physical distancing could have a considerable impact on reducing transmission for COVID-19. The effect itself depends on assumptions made about disease-specific characteristics and the choice of intervention(s).

The distribution of the generation time (the interval between individuals becoming infected and transmitting the virus) characterises changes in the transmission risk during SARS-CoV-2 infections. Inferring the generation time distribution is essential to plan and assess public health measures. We previously developed a mechanistic approach for estimating the generation time, which provided an improved fit to data from the early months of the COVID-19 pandemic (December 2019-March 2020) compared to existing models (Hart et al., 2021). However, few estimates of the generation time exist based on data from later in the pandemic. Here, using data from a household study conducted from March to November 2020 in the UK, we provide updated estimates of the generation time. We considered both a commonly used approach in which the transmission risk is assumed to be independent of when symptoms develop, and our mechanistic model in which transmission and symptoms are linked explicitly. Assuming independent transmission and symptoms, we estimated a mean generation time (4.2 days, 95% credible interval 3.3–5.3 days) similar to previous estimates from other countries, but with a higher standard deviation (4.9 days, 3.0–8.3 days). Using our mechanistic approach, we estimated a longer mean generation time (5.9 days, 5.2–7.0 days) and a similar standard deviation (4.8 days, 4.0–6.3 days). As well as estimating the generation time using data from the entire study period, we also considered whether the generation time varied temporally. Both models suggest a shorter mean generation time in September-November 2020 compared to earlier months. Since the SARS-CoV-2 generation time appears to be changing, further data collection and analysis is necessary to continue to monitor ongoing transmission and inform future public health policy decisions.

Background Targeting interventions to areas that have recently experienced cases of disease is one strategy to contain outbreaks of infectious disease. Such case-area targeted interventions (CATI) have become an increasingly popular approach for dengue control but there is little evidence to suggest how precisely targeted or how recent cases need to be, to mount an effective response. The growing interest in the development of prophylactic and therapeutic drugs for dengue has also given new relevance for CATI strategies to interrupt transmission or deliver early treatment. Methods/Principal findings Here we develop a patch-based mathematical model of spatial dengue spread and fit it to spatiotemporal datasets from Singapore. Simulations from this model suggest CATI strategies could be effective, particularly if used in lower density areas. To maximise effectiveness, increasing the size of the radius around an index case should be prioritised even if it results in delays in the intervention being applied. This is partially because large intervention radii ensure individuals receive multiple and regular rounds of drug dosing or vector control, and thus boost overall coverage. Given equivalent efficacy, CATIs using prophylactic drugs are predicted to be more effective than adult mosquito-killing vector control methods and may even offer the possibility of interrupting individual chains of transmission if rapidly deployed. CATI strategies quickly lose their effectiveness if baseline transmission increases or case detection rates fall. Conclusions/Significance These results suggest CATI strategies can play an important role in dengue control but are likely to be most relevant for low transmission areas where high coverage of other non-reactive interventions already exists. Controlled field trials are needed to assess the field efficacy and practical constraints of large operational CATI strategies. Author summary In resource limited settings there is a pressing need for more efficient, more targeted ways of controlling transmission and preventing outbreaks. One option is to use case-area targeted interventions (CATI) that are focussed on areas that have recently reported disease cases. The effectiveness of such CATI strategies is highly dependent on how the disease spreads. Despite CATI strategies being widely used to control the vector-transmitted disease dengue, little evidence underpins its effectiveness. In this analysis we formulate a mathematical model designed to test the effectiveness of CATI strategies for dengue control in Singapore- a best case test scenario for the approach. Simulation from this model suggested CATI are likely to be effective for dengue, but need to have large (250m+) radii around index cases and may not be suitable in higher transmission areas. These results, when combined with limited field evidence of efficacy, suggest that CATI strategies are unlikely to be universally applicable dengue control tools. Only once high coverage with other (non-reactive) interventions has been achieved and comprehensive rapid disease surveillance has been established are CATI strategies likely to become efficient methods of disease control.

Reconstructing the history of individual transmission events between cases is key to understanding what factors facilitate the spread of an infectious disease. Since conducting extended contact-tracing investigations can be logistically challenging and costly, statistical inference methods have been developed to reconstruct transmission trees from onset dates and genetic sequences. However, these methods are not as effective if the mutation rate of the virus is very slow, or if sequencing data is sparse. We developed the package o2geosocial to combine variables from routinely collected surveillance data with a simple transmission process model. The model reconstructs transmission trees when full genetic sequences are unavailable, or uninformative. Our model incorporates the reported age-group, onset date, location and genotype of infected cases to infer probabilistic transmission trees. The package also includes functions to summarise and visualise the inferred cluster size distribution. The results generated by o2geosocial can highlight regions where importations repeatedly caused large outbreaks, which may indicate a higher regional susceptibility to infections. It can also be used to generate the individual number of secondary transmissions, and show the features associated with individuals involved in high transmission events. The package is available for download from the Comprehensive R Archive Network (CRAN) and GitHub.

Abstract Background Vaccination has reduced the global incidence of measles to the lowest rates in history. However, local interruption of measles virus transmission requires sustained high levels of population immunity that can be challenging to achieve and maintain. The herd immunity threshold for measles is typically stipulated at 90–95%. This figure does not easily translate into age-specific immunity levels required to interrupt transmission. Previous estimates of such levels were based on speculative contact patterns based on historical data from high-income countries. The aim of this study was to determine age-specific immunity levels that would ensure elimination of measles when taking into account empirically observed contact patterns. Methods We combined estimated immunity levels from serological data in 17 countries with studies of age-specific mixing patterns to derive contact-adjusted immunity levels. We then compared these to case data from the 10 years following the seroprevalence studies to establish a contact-adjusted immunity threshold for elimination. We lastly combined a range of hypothetical immunity profiles with contact data from a wide range of socioeconomic and demographic settings to determine whether they would be sufficient for elimination. Results We found that contact-adjusted immunity levels were able to predict whether countries would experience outbreaks in the decade following the serological studies in about 70% of countries. The corresponding threshold level of contact-adjusted immunity was found to be 93%, corresponding to an average basic reproduction number of approximately 14. Testing different scenarios of immunity with this threshold level using contact studies from around the world, we found that 95% immunity would have to be achieved by the age of five and maintained across older age groups to guarantee elimination. This reflects a greater level of immunity required in 5–9-year-olds than established previously. Conclusions The immunity levels we found necessary for measles elimination are higher than previous guidance. The importance of achieving high immunity levels in 5–9-year-olds presents both a challenge and an opportunity. While such high levels can be difficult to achieve, school entry provides an opportunity to ensure sufficient vaccination coverage. Combined with observations of contact patterns, further national and sub-national serological studies could serve to highlight key gaps in immunity that need to be filled in order to achieve national and regional measles elimination.

Abstract Background Between August and December 2017, more than 625,000 Rohingya from Myanmar fled into Bangladesh, settling in informal makeshift camps in Cox’s Bazar district and joining 212,000 Rohingya already present. In early November, a diphtheria outbreak hit the camps, with 440 reported cases during the first month. A rise in cases during early December led to a collaboration between teams from Médecins sans Frontières—who were running a provisional diphtheria treatment centre—and the London School of Hygiene and Tropical Medicine with the goal to use transmission dynamic models to forecast the potential scale of the outbreak and the resulting resource needs. Methods We first adjusted for delays between symptom onset and case presentation using the observed distribution of reporting delays from previously reported cases. We then fit a compartmental transmission model to the adjusted incidence stratified by age group and location. Model forecasts with a lead time of 2 weeks were issued on 12, 20, 26 and 30 December and communicated to decision-makers. Results The first forecast estimated that the outbreak would peak on 19 December in Balukhali camp with 303 (95% posterior predictive interval 122–599) cases and would continue to grow in Kutupalong camp, requiring a bed capacity of 316 (95% posterior predictive interval (PPI) 197–499). On 19 December, a total of 54 cases were reported, lower than forecasted. Subsequent forecasts were more accurate: on 20 December, we predicted a total of 912 cases (95% PPI 367–2183) and 136 (95% PPI 55–327) hospitalizations until the end of the year, with 616 cases actually reported during this period. Conclusions Real-time modelling enabled feedback of key information about the potential scale of the epidemic, resource needs and mechanisms of transmission to decision-makers at a time when this information was largely unknown. By 20 December, the model generated reliable forecasts and helped support decision-making on operational aspects of the outbreak response, such as hospital bed and staff needs, and with advocacy for control measures. Although modelling is only one component of the evidence base for decision-making in outbreak situations, suitable analysis and forecasting techniques can be used to gain insights into an ongoing outbreak.

Summary: Background: In most countries, contacts of confirmed COVID-19 cases are asked to quarantine for 14 days after exposure to limit asymptomatic onward transmission. While theoretically effective, this policy places a substantial social and economic burden on both the individual and wider society, which might result in low adherence and reduced policy effectiveness. We aimed to assess the merit of testing contacts to avert onward transmission and to replace or reduce the length of quarantine for uninfected contacts. Methods: We used an agent-based model to simulate the viral load dynamics of exposed contacts, and their potential for onward transmission in different quarantine and testing strategies. We compared the performance of quarantines of differing durations, testing with either PCR or lateral flow antigen (LFA) tests at the end of quarantine, and daily LFA testing without quarantine, against the current 14-day quarantine strategy. We also investigated the effect of contact tracing delays and adherence to both quarantine and self-isolation on the effectiveness of each strategy. Findings: Assuming moderate levels of adherence to quarantine and self-isolation, self-isolation on symptom onset alone can prevent 37% (95% uncertainty interval [UI] 12–56) of onward transmission potential from secondary cases. 14 days of post-exposure quarantine reduces transmission by 59% (95% UI 28–79). Quarantine with release after a negative PCR test 7 days after exposure might avert a similar proportion (54%, 95% UI 31–81; risk ratio [RR] 0·94, 95% UI 0·62–1·24) to that of the 14-day quarantine period, as would quarantine with a negative LFA test 7 days after exposure (50%, 95% UI 28–77; RR 0·88, 0·66–1·11) or daily testing without quarantine for 5 days after tracing (50%, 95% UI 23–81; RR 0·88, 0·60–1·43) if all tests are returned negative. A stronger effect might be possible if individuals isolate more strictly after a positive test and if contacts can be notified faster. Interpretation: Testing might allow for a substantial reduction in the length of, or replacement of, quarantine with a small excess in transmission risk. Decreasing test and trace delays and increasing adherence will further increase the effectiveness of these strategies. Further research is required to empirically evaluate the potential costs (increased transmission risk, false reassurance) and benefits (reduction in the burden of quarantine, increased adherence) of such strategies before adoption as policy. Funding: National Institute for Health Research, UK Research and Innovation, Wellcome Trust, EU Horizon 2021, and the Bill & Melinda Gates Foundation.

Introduction: Contact tracing has the potential to control outbreaks without the need for stringent physical distancing policies, e.g. civil lockdowns. Unlike forward contact tracing, backward contact tracing identifies the source of newly detected cases. This approach is particularly valuable when there is high individual-level variation in the number of secondary transmissions (overdispersion). Methods: By using a simple branching process model, we explored the potential of combining backward contact tracing with more conventional forward contact tracing for control of COVID-19. We estimated the typical size of clusters that can be reached by backward tracing and simulated the incremental effectiveness of combining backward tracing with conventional forward tracing. Results: Across ranges of parameter values consistent with dynamics of SARS-CoV-2, backward tracing is expected to identify a primary case generating 3-10 times more infections than a randomly chosen case, typically increasing the proportion of subsequent cases averted by a factor of 2-3. The estimated number of cases averted by backward tracing became greater with a higher degree of overdispersion. Conclusion: Backward contact tracing can be an effective tool for outbreak control, especially in the presence of overdispersion as is observed with SARS-CoV-2.

Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

The COVID-19 pandemic has motivated many open and collaborative analytical research projects with real-world impact. However, despite their value, such activities are generally overlooked by traditional academic metrics. Science is ultimately improved by analytical work, whether ensuring reproducible and well-documented code to accompany papers, developing and maintaining flexible tools, sharing and curating data, or disseminating analysis to wider audiences. To increase the impact and sustainability of modern science, it will be crucial to ensure these analytical activities-and the people who do them-are valued in academia.

Introduction: Contact tracing has the potential to control outbreaks without the need for stringent physical distancing policies, e.g. civil lockdowns. Unlike forward contact tracing, backward contact tracing identifies the source of newly detected cases. This approach is particularly valuable when there is high individual-level variation in the number of secondary transmissions (overdispersion). Methods: By using a simple branching process model, we explored the potential of combining backward contact tracing with more conventional forward contact tracing for control of COVID-19. We estimated the typical size of clusters that can be reached by backward tracing and simulated the incremental effectiveness of combining backward tracing with conventional forward tracing. Results: Across ranges of parameter values consistent with dynamics of SARS-CoV-2, backward tracing is expected to identify a primary case generating 3-10 times more infections than average, typically increasing the proportion of subsequent cases averted by a factor of 2-3. The estimated number of cases averted by backward tracing became greater with a higher degree of overdispersion. Conclusion: Backward contact tracing can be an effective tool for outbreak control, especially in the presence of overdispersion as was observed with SARS-CoV-2.

Summary: Background: The risk of severe COVID-19 if an individual becomes infected is known to be higher in older individuals and those with underlying health conditions. Understanding the number of individuals at increased risk of severe COVID-19 and how this varies between countries should inform the design of possible strategies to shield or vaccinate those at highest risk. Methods: We estimated the number of individuals at increased risk of severe disease (defined as those with at least one condition listed as “at increased risk of severe COVID-19” in current guidelines) by age (5-year age groups), sex, and country for 188 countries using prevalence data from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 and UN population estimates for 2020. The list of underlying conditions relevant to COVID-19 was determined by mapping the conditions listed in GBD 2017 to those listed in guidelines published by WHO and public health agencies in the UK and the USA. We analysed data from two large multimorbidity studies to determine appropriate adjustment factors for clustering and multimorbidity. To help interpretation of the degree of risk among those at increased risk, we also estimated the number of individuals at high risk (defined as those that would require hospital admission if infected) using age-specific infection–hospitalisation ratios for COVID-19 estimated for mainland China and making adjustments to reflect country-specific differences in the prevalence of underlying conditions and frailty. We assumed males were twice at likely as females to be at high risk. We also calculated the number of individuals without an underlying condition that could be considered at increased risk because of their age, using minimum ages from 50 to 70 years. We generated uncertainty intervals (UIs) for our estimates by running low and high scenarios using the lower and upper 95% confidence limits for country population size, disease prevalences, multimorbidity fractions, and infection–hospitalisation ratios, and plausible low and high estimates for the degree of clustering, informed by multimorbidity studies. Findings: We estimated that 1·7 billion (UI 1·0–2·4) people, comprising 22% (UI 15–28) of the global population, have at least one underlying condition that puts them at increased risk of severe COVID-19 if infected (ranging from 66% of those aged 70 years or older). We estimated that 349 million (186–787) people (4% [3–9] of the global population) are at high risk of severe COVID-19 and would require hospital admission if infected (ranging from

A key unknown for SARS-CoV-2 is how asymptomatic infections contribute to transmission. We used a transmission model with asymptomatic and presymptomatic states, calibrated to data on disease onset and test frequency from the Diamond Princess cruise ship outbreak, to quantify the contribution of asymptomatic infections to transmission. The model estimated that 74% (70–78%, 95% posterior interval) of infections proceeded asymptomatically. Despite intense testing, 53% (51–56%) of infections remained undetected, most of them asymptomatic. Asymptomatic individuals were the source for 69% (20–85%) of all infections. The data did not allow identification of the infectiousness of asymptomatic infections, however low ranges (0–25%) required a net reproduction number for individuals progressing through presymptomatic and symptomatic stages of at least 15. Asymptomatic SARS-CoV-2 infections may contribute substantially to transmission. Control measures, and models projecting their potential impact, need to look beyond the symptomatic cases if they are to understand and address ongoing transmission.

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R0, variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R0 and k (95% CrIs: R0 1.4-12; k 0.04-0.2); however, the upper bound of R0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R0, variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R0 and k (95% CrIs: R0 1.4-12; k 0.04-0.2); however, the upper bound of R0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

Summary: Background: Non-pharmaceutical interventions have been implemented to reduce transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in the UK. Projecting the size of an unmitigated epidemic and the potential effect of different control measures has been crucial to support evidence-based policy making during the early stages of the epidemic. This study assesses the potential impact of different control measures for mitigating the burden of COVID-19 in the UK. Methods: We used a stochastic age-structured transmission model to explore a range of intervention scenarios, tracking 66·4 million people aggregated to 186 county-level administrative units in England, Wales, Scotland, and Northern Ireland. The four base interventions modelled were school closures, physical distancing, shielding of people aged 70 years or older, and self-isolation of symptomatic cases. We also modelled the combination of these interventions, as well as a programme of intensive interventions with phased lockdown-type restrictions that substantially limited contacts outside of the home for repeated periods. We simulated different triggers for the introduction of interventions, and estimated the impact of varying adherence to interventions across counties. For each scenario, we projected estimated new cases over time, patients requiring inpatient and critical care (ie, admission to the intensive care units [ICU]) treatment, and deaths, and compared the effect of each intervention on the basic reproduction number, R0. Findings: We projected a median unmitigated burden of 23 million (95% prediction interval 13–30) clinical cases and 350 000 deaths (170 000–480 000) due to COVID-19 in the UK by December, 2021. We found that the four base interventions were each likely to decrease R0, but not sufficiently to prevent ICU demand from exceeding health service capacity. The combined intervention was more effective at reducing R0, but only lockdown periods were sufficient to bring R0 near or below 1; the most stringent lockdown scenario resulted in a projected 120 000 cases (46 000–700 000) and 50 000 deaths (9300–160 000). Intensive interventions with lockdown periods would need to be in place for a large proportion of the coming year to prevent health-care demand exceeding availability. Interpretation: The characteristics of SARS-CoV-2 mean that extreme measures are probably required to bring the epidemic under control and to prevent very large numbers of deaths and an excess of demand on hospital beds, especially those in ICUs. Funding: Medical Research Council.

Background: Concern about the health impact of novel coronavirus SARS-CoV-2 has resulted in widespread enforced reductions in people’s movement (“lockdowns”). However, there are increasing concerns about the severe economic and wider societal consequences of these measures. Some countries have begun to lift some of the rules on physical distancing in a stepwise manner, with differences in what these “exit strategies” entail and their timeframes. The aim of this work was to inform such exit strategies by exploring the types of indoor and outdoor settings where transmission of SARS-CoV-2 has been reported to occur and result in clusters of cases. Identifying potential settings that result in transmission clusters allows these to be kept under close surveillance and/or to remain closed as part of strategies that aim to avoid a resurgence in transmission following the lifting of lockdown measures. Methods: We performed a systematic review of available literature and media reports to find settings reported in peer reviewed articles and media with these characteristics. These sources are curated and made available in an editable online database. Results: We found many examples of SARS-CoV-2 clusters linked to a wide range of mostly indoor settings. Few reports came from schools, many from households, and an increasing number were reported in hospitals and elderly care settings across Europe. Conclusions: We identified possible places that are linked to clusters of COVID-19 cases and could be closely monitored and/or remain closed in the first instance following the progressive removal of lockdown restrictions. However, in part due to the limits in surveillance capacities in many settings, the gathering of information such as cluster sizes and attack rates is limited in several ways: inherent recall bias, biased media reporting and missing data.

Summary: Background: Isolation of cases and contact tracing is used to control outbreaks of infectious diseases, and has been used for coronavirus disease 2019 (COVID-19). Whether this strategy will achieve control depends on characteristics of both the pathogen and the response. Here we use a mathematical model to assess if isolation and contact tracing are able to control onwards transmission from imported cases of COVID-19. Methods: We developed a stochastic transmission model, parameterised to the COVID-19 outbreak. We used the model to quantify the potential effectiveness of contact tracing and isolation of cases at controlling a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-like pathogen. We considered scenarios that varied in the number of initial cases, the basic reproduction number (R0), the delay from symptom onset to isolation, the probability that contacts were traced, the proportion of transmission that occurred before symptom onset, and the proportion of subclinical infections. We assumed isolation prevented all further transmission in the model. Outbreaks were deemed controlled if transmission ended within 12 weeks or before 5000 cases in total. We measured the success of controlling outbreaks using isolation and contact tracing, and quantified the weekly maximum number of cases traced to measure feasibility of public health effort. Findings: Simulated outbreaks starting with five initial cases, an R0 of 1·5, and 0% transmission before symptom onset could be controlled even with low contact tracing probability; however, the probability of controlling an outbreak decreased with the number of initial cases, when R0 was 2·5 or 3·5 and with more transmission before symptom onset. Across different initial numbers of cases, the majority of scenarios with an R0 of 1·5 were controllable with less than 50% of contacts successfully traced. To control the majority of outbreaks, for R0 of 2·5 more than 70% of contacts had to be traced, and for an R0 of 3·5 more than 90% of contacts had to be traced. The delay between symptom onset and isolation had the largest role in determining whether an outbreak was controllable when R0 was 1·5. For R0 values of 2·5 or 3·5, if there were 40 initial cases, contact tracing and isolation were only potentially feasible when less than 1% of transmission occurred before symptom onset. Interpretation: In most scenarios, highly effective contact tracing and case isolation is enough to control a new outbreak of COVID-19 within 3 months. The probability of control decreases with long delays from symptom onset to isolation, fewer cases ascertained by contact tracing, and increasing transmission before symptoms. This model can be modified to reflect updated transmission characteristics and more specific definitions of outbreak control to assess the potential success of local response efforts. Funding: Wellcome Trust, Global Challenges Research Fund, and Health Data Research UK.

Background: Pre-symptomatic transmission can be a key determinant of the effectiveness of containment and mitigation strategies for infectious diseases, particularly if interventions rely on syndromic case finding. For COVID-19, infections in the absence of apparent symptoms have been reported frequently alongside circumstantial evidence for asymptomatic or pre-symptomatic transmission. We estimated the potential contribution of pre-symptomatic cases to COVID-19 transmission. Methods: Using the probability for symptom onset on a given day inferred from the incubation period, we attributed the serial interval reported from Shenzen, China, into likely pre-symptomatic and symptomatic transmission. We used the serial interval derived for cases isolated more than 6 days after symptom onset as the no active case finding scenario and the unrestricted serial interval as the active case finding scenario. We reported the estimate assuming no correlation between the incubation period and the serial interval alongside a range indicating alternative assumptions of positive and negative correlation. Results: We estimated that 23% (range accounting for correlation: 12 – 28%) of transmissions in Shenzen may have originated from pre-symptomatic infections. Through accelerated case isolation following symptom onset, this percentage increased to 46% (21 – 46%), implying that about 35% of secondary infections among symptomatic cases have been prevented. These results were robust to using reported incubation periods and serial intervals from other settings. Conclusions: Pre-symptomatic transmission may be essential to consider for containment and mitigation strategies for COVID-19.

We estimate the number of COVID-19 cases from newly reported deaths in a population without previous reports. Our results suggest that by the time a single death occurs, hundreds to thousands of cases are likely to be present in that population. This suggests containment via contact tracing will be challenging at this point, and other response strategies should be considered. Our approach is implemented in a publicly available, user-friendly, online tool.

Inference using mathematical models of infectious disease dynamics can be an invaluable tool for the interpretation and analysis of epidemiological data. However, researchers wishing to use this tool are faced with a choice of models and model types, simulation methods, inference methods and software packages. Given the multitude of options, it can be challenging to decide on the best approach. Here, we delineate the choices and trade-offs involved in deciding on an approach for inference, and discuss aspects that might inform this decision. We provide examples of inference with a dataset of influenza cases using the R packages pomp and rbi. Keywords: Inference, Infectious disease model, Bayesian, Frequentist, Model fitting