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Bosse NI, Abbott S, Bracher J, van Leeuwen E, Cori A, Funk S. Human judgement forecasting of COVID-19 in the UK. Wellcome Open Res 2024; 8:416. [PMID: 38618198 PMCID: PMC11009611 DOI: 10.12688/wellcomeopenres.19380.2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/12/2024] [Indexed: 04/16/2024] Open
Abstract
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 R t. 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. R t 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.
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Affiliation(s)
- Nikos I. Bosse
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, WC1E 7HT, UK
- NIHR Health Protection Research Unit in Modelling & Health Economics, London, UK
| | - Sam Abbott
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, WC1E 7HT, UK
| | - Johannes Bracher
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies, Heidelberg, Germany
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Edwin van Leeuwen
- NIHR Health Protection Research Unit in Modelling & Health Economics, London, UK
- Modelling Economics Unit, UK Health Security Agency, London, UK
| | - Anne Cori
- MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, London, England, UK
| | - Sebastian Funk
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, WC1E 7HT, UK
- NIHR Health Protection Research Unit in Modelling & Health Economics, London, UK
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Bosse NI, Abbott S, Cori A, van Leeuwen E, Bracher J, Funk S. Scoring epidemiological forecasts on transformed scales. PLoS Comput Biol 2023; 19:e1011393. [PMID: 37643178 PMCID: PMC10495027 DOI: 10.1371/journal.pcbi.1011393] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Revised: 09/11/2023] [Accepted: 07/27/2023] [Indexed: 08/31/2023] Open
Abstract
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.
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Affiliation(s)
- Nikos I. Bosse
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases, London, United Kingdom
- NIHR Health Protection Research Unit in Modelling & Health Economics
| | - Sam Abbott
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases, London, United Kingdom
| | - Anne Cori
- MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, London, United Kingdom
| | - Edwin van Leeuwen
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- NIHR Health Protection Research Unit in Modelling & Health Economics
- Modelling & Economics Unit and NIHR Health Protection Research Unit in Modelling & Health Economics, UK Health Security Agency, London, United Kingdom
| | - Johannes Bracher
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology, Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies, Heidelberg, Germany
| | - Sebastian Funk
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases, London, United Kingdom
- NIHR Health Protection Research Unit in Modelling & Health Economics
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Sherratt K, Gruson H, Grah R, Johnson H, Niehus R, Prasse B, Sandmann F, Deuschel J, Wolffram D, Abbott S, Ullrich A, Gibson G, Ray EL, Reich NG, Sheldon D, Wang Y, Wattanachit N, Wang L, Trnka J, Obozinski G, Sun T, Thanou D, Pottier L, Krymova E, Meinke JH, Barbarossa MV, Leithäuser N, Mohring J, Schneider J, Włazło J, Fuhrmann J, Lange B, Rodiah I, Baccam P, Gurung H, Stage S, Suchoski B, Budzinski J, Walraven R, Villanueva I, Tucek V, Smid M, Zajíček M, Pérez Álvarez C, Reina B, Bosse NI, Meakin SR, Castro L, Fairchild G, Michaud I, Osthus D, Alaimo Di Loro P, Maruotti A, Eclerová V, Kraus A, Kraus D, Pribylova L, Dimitris B, Li ML, Saksham S, Dehning J, Mohr S, Priesemann V, Redlarski G, Bejar B, Ardenghi G, Parolini N, Ziarelli G, Bock W, Heyder S, Hotz T, Singh DE, Guzman-Merino M, Aznarte JL, Moriña D, Alonso S, Álvarez E, López D, Prats C, Burgard JP, Rodloff A, Zimmermann T, Kuhlmann A, Zibert J, Pennoni F, Divino F, Català M, Lovison G, Giudici P, Tarantino B, Bartolucci F, Jona Lasinio G, Mingione M, Farcomeni A, Srivastava A, Montero-Manso P, Adiga A, Hurt B, Lewis B, Marathe M, Porebski P, Venkatramanan S, Bartczuk RP, Dreger F, Gambin A, Gogolewski K, Gruziel-Słomka M, Krupa B, Moszyński A, Niedzielewski K, Nowosielski J, Radwan M, Rakowski F, Semeniuk M, Szczurek E, Zieliński J, Kisielewski J, Pabjan B, Kirsten H, Kheifetz Y, Scholz M, Biecek P, Bodych M, Filinski M, Idzikowski R, Krueger T, Ozanski T, Bracher J, Funk S. Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations. eLife 2023; 12:81916. [PMID: 37083521 DOI: 10.7554/elife.81916] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 02/20/2023] [Indexed: 04/22/2023] Open
Abstract
Background: Short-term forecasts of infectious disease contribute to situational awareness and capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise forecasts' predictive performance by combining independent models into an ensemble. Here we report the performance of ensemble predictions of COVID-19 cases and deaths across Europe from March 2021 to March 2022. Methods: We created the European COVID-19 Forecast Hub, an online open-access platform where modellers upload weekly forecasts for 32 countries with results publicly visualised and evaluated. We created a weekly ensemble forecast from the equally-weighted average across individual models' predictive quantiles. We measured forecast accuracy using a baseline and relative Weighted Interval Score (rWIS). We retrospectively explored ensemble methods, including weighting by past performance. Results: We collected weekly forecasts from 48 models, of which we evaluated 29 models alongside the ensemble model. The ensemble had a consistently strong performance across countries over time, performing better on rWIS than 91% of forecasts for deaths (N=763 predictions from 20 models), and 83% forecasts for cases (N=886 predictions from 23 models). Performance remained stable over a 4-week horizon for death forecasts but declined with longer horizons for cases. Among ensemble methods, the most influential choice came from using a median average instead of the mean, regardless of weighting component models. Conclusions: Our results support combining independent models into an ensemble forecast to improve epidemiological predictions, and suggest that median averages yield better performance than methods based on means. We highlight that forecast consumers should place more weight on incident death forecasts than case forecasts at horizons greater than two weeks. Funding: European Commission, Ministerio de Ciencia, Innovación y Universidades, FEDER; Agència de Qualitat i Avaluació Sanitàries de Catalunya; Netzwerk Universitätsmedizin; Health Protection Research Unit; Wellcome Trust; European Centre for Disease Prevention and Control; Ministry of Science and Higher Education of Poland; Federal Ministry of Education and Research; Los Alamos National Laboratory; German Free State of Saxony; NCBiR; FISR 2020 Covid-19 I Fase; Spanish Ministry of Health / REACT-UE (FEDER); National Institutes of General Medical Sciences; Ministerio de Sanidad/ISCIII; PERISCOPE European H2020; PERISCOPE European H2021; InPresa; National Institutes of Health, NSF, US Centers for Disease Control and Prevention, Google, University of Virginia, Defense Threat Reduction Agency.
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Affiliation(s)
- Katharine Sherratt
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Hugo Gruson
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Rok Grah
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Helen Johnson
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Rene Niehus
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Bastian Prasse
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Frank Sandmann
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | | | | | - Sam Abbott
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | | | - Graham Gibson
- University of Massachusetts Amherst, Amherst, United States
| | - Evan L Ray
- University of Massachusetts Amherst, Amherst, United States
| | | | - Daniel Sheldon
- University of Massachusetts Amherst, Amherst, United States
| | - Yijin Wang
- University of Massachusetts Amherst, Amherst, United States
| | | | - Lijing Wang
- Boston Children's Hospital, Boston, United States
| | - Jan Trnka
- Department of Biochemistry, Cell and Molecular Biology, Charles University, Prague, Czech Republic
| | | | - Tao Sun
- École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Dorina Thanou
- École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | | | | | | | | | - Neele Leithäuser
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | - Jan Mohring
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | - Johanna Schneider
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | - Jaroslaw Włazło
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | | | - Berit Lange
- Helmholtz Centre for Infection Research, Braunschweig, Germany
| | - Isti Rodiah
- Helmholtz Centre for Infection Research, Braunschweig, Germany
| | | | | | | | | | | | | | - Inmaculada Villanueva
- Institut d'Investigacions Biomediques August Pi i Sunyer, Universitat Pompeu Fabra, Barcelona, Spain
| | - Vit Tucek
- Institute of Computer Science, Prague, Czech Republic
| | - Martin Smid
- Institute of Information Theory and Automation, Prague, Czech Republic
| | - Milan Zajíček
- Institute of Information Theory and Automation, Prague, Czech Republic
| | | | | | - Nikos I Bosse
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Sophie R Meakin
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Lauren Castro
- Los Alamos National Laboratory, Los Alamos, United States
| | | | - Isaac Michaud
- Los Alamos National Laboratory, Los Alamos, United States
| | - Dave Osthus
- Los Alamos National Laboratory, Los Alamos, United States
| | | | | | | | | | | | | | | | | | - Soni Saksham
- Massachusetts Institute of Technology, Cambridge, United States
| | - Jonas Dehning
- Max-Planck-Institut fur Dynamik und Selbstorganisation, Göttingen, Germany
| | - Sebastian Mohr
- Max-Planck-Institut fur Dynamik und Selbstorganisation, Göttingen, Germany
| | - Viola Priesemann
- MPRG Priesemann, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | | | | | | | | | | | - Wolfgang Bock
- Technical University of Kaiserlautern, Kaiserslautern, Germany
| | | | - Thomas Hotz
- Technische Universitat Ilmenau, Ilmenau, Germany
| | | | | | - Jose L Aznarte
- Universidad Nacional de Educacion a Distancia, Madrid, Spain
| | | | - Sergio Alonso
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Enric Álvarez
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Daniel López
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Clara Prats
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Benjamin Hurt
- University of Virginia, Charlottesville, United States
| | - Bryan Lewis
- University of Virginia, Charlottesville, United States
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Marcin Bodych
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - Maciej Filinski
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | | | - Tyll Krueger
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - Tomasz Ozanski
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | | | - Sebastian Funk
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
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Bosse NI, Abbott S, Bracher J, Hain H, Quilty BJ, Jit M, van Leeuwen E, Cori A, Funk S. Comparing human and model-based forecasts of COVID-19 in Germany and Poland. PLoS Comput Biol 2022; 18:e1010405. [PMID: 36121848 PMCID: PMC9534421 DOI: 10.1371/journal.pcbi.1010405] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Revised: 10/05/2022] [Accepted: 07/18/2022] [Indexed: 11/19/2022] Open
Abstract
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.
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Affiliation(s)
- Nikos I. Bosse
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases (members of the CMMID COVID-19 working group are listed in S1 Acknowledgements), London, United Kingdom
| | - Sam Abbott
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases (members of the CMMID COVID-19 working group are listed in S1 Acknowledgements), London, United Kingdom
| | - Johannes Bracher
- Institute of Economic Theory and Statistics, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Habakuk Hain
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
| | - Billy J. Quilty
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases (members of the CMMID COVID-19 working group are listed in S1 Acknowledgements), London, United Kingdom
| | - Mark Jit
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases (members of the CMMID COVID-19 working group are listed in S1 Acknowledgements), London, United Kingdom
| | | | - Edwin van Leeuwen
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- UK Health Security Agency, London, United Kingdom
| | - Anne Cori
- MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, London, United Kingdom
| | - Sebastian Funk
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases (members of the CMMID COVID-19 working group are listed in S1 Acknowledgements), London, United Kingdom
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5
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Barnard RC, Davies NG, Jit M, Edmunds WJ, Leclerc QJ, Tully DC, Hodgson D, Pung R, Hellewell J, Koltai M, Simons D, Abbas K, Kucharski AJ, Procter SR, Sandmann FG, Pearson CAB, Prem K, Showering A, Meakin SR, O’Reilly K, McCarthy CV, Quaife M, Wong KLM, Jafari Y, Deol AK, Houben RMGJ, Diamond C, Jombart T, Villabona-Arenas CJ, Waites W, Eggo RM, Endo A, Gibbs HP, Klepac P, Williams J, Quilty BJ, Brady O, Emery JC, Atkins KE, Chapman LAC, Sherratt K, Abbott S, Bosse NI, Mee P, Funk S, Lei J, Liu Y, Flasche S, Rudge JW, Sun FY, Medley G, Russell TW, Gimma A, Hué S, Jarvis CI, Finch E, Clifford S, Jit M, Edmunds WJ. Modelling the medium-term dynamics of SARS-CoV-2 transmission in England in the Omicron era. Nat Commun 2022; 13:4879. [PMID: 35986002 PMCID: PMC9389516 DOI: 10.1038/s41467-022-32404-y] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 07/25/2022] [Indexed: 11/29/2022] Open
Abstract
England has experienced a heavy burden of COVID-19, with multiple waves of SARS-CoV-2 transmission since early 2020 and high infection levels following the emergence and spread of Omicron variants since late 2021. In response to rising Omicron cases, booster vaccinations were accelerated and offered to all adults in England. Using a model fitted to more than 2 years of epidemiological data, we project potential dynamics of SARS-CoV-2 infections, hospital admissions and deaths in England to December 2022. We consider key uncertainties including future behavioural change and waning immunity and assess the effectiveness of booster vaccinations in mitigating SARS-CoV-2 disease burden between October 2021 and December 2022. If no new variants emerge, SARS-CoV-2 transmission is expected to decline, with low levels remaining in the coming months. The extent to which projected SARS-CoV-2 transmission resurges later in 2022 depends largely on assumptions around waning immunity and to some extent, behaviour, and seasonality.
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Affiliation(s)
- Rosanna C. Barnard
- grid.8991.90000 0004 0425 469XCentre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK ,grid.8991.90000 0004 0425 469XDepartment of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK
| | - Nicholas G. Davies
- grid.8991.90000 0004 0425 469XCentre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK ,grid.8991.90000 0004 0425 469XDepartment of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK
| | | | - Mark Jit
- grid.8991.90000 0004 0425 469XCentre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK ,grid.8991.90000 0004 0425 469XDepartment of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK
| | - W. John Edmunds
- grid.8991.90000 0004 0425 469XCentre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK ,grid.8991.90000 0004 0425 469XDepartment of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT UK
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6
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McAndrew T, Majumder MS, Lover AA, Venkatramanan S, Bocchini P, Besiroglu T, Codi A, Braun D, Dempsey G, Abbott S, Chevalier S, Bosse NI, Cambeiro J. Early human judgment forecasts of human monkeypox, May 2022. Lancet Digit Health 2022; 4:e569-e571. [PMID: 35811294 PMCID: PMC9534486 DOI: 10.1016/s2589-7500(22)00127-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Revised: 06/20/2022] [Accepted: 06/27/2022] [Indexed: 01/25/2023]
Affiliation(s)
- Thomas McAndrew
- Department of Community and Population Health, College of Health, Lehigh University, Bethlehem, PA 18015, USA.
| | - Maimuna S Majumder
- Boston Children's Hospital, Boston, MA, USA; Harvard Medical School, Boston, MA, USA
| | - Andrew A Lover
- Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences, University of Massachusetts Amherst, Amherst, MA, USA
| | - Srini Venkatramanan
- Biocomplexity Institute and Initiative, University of Virginia, Charlottesville, VA, USA
| | - Paolo Bocchini
- Department of Civil and Environmental Engineering, P C Rossin College of Engineering and Applied Science, Lehigh University, Bethlehem, PA 18015, USA
| | - Tamay Besiroglu
- MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA, USA; Metaculus, Santa Cruz, CA, USA
| | - Allison Codi
- Department of Community and Population Health, College of Health, Lehigh University, Bethlehem, PA 18015, USA
| | - David Braun
- Department of Psychology, College of Arts and Sciences, Lehigh University, Bethlehem, PA 18015, USA
| | | | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, UK
| | | | - Nikos I Bosse
- Metaculus, Santa Cruz, CA, USA; Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, UK
| | - Juan Cambeiro
- Metaculus, Santa Cruz, CA, USA; Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY, USA
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Ray EL, Brooks LC, Bien J, Biggerstaff M, Bosse NI, Bracher J, Cramer EY, Funk S, Gerding A, Johansson MA, Rumack A, Wang Y, Zorn M, Tibshirani RJ, Reich NG. Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States. Int J Forecast 2022:S0169-2070(22)00096-6. [PMID: 35791416 PMCID: PMC9247236 DOI: 10.1016/j.ijforecast.2022.06.005] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The U.S. COVID-19 Forecast Hub aggregates forecasts of the short-term burden of COVID-19 in the United States from many contributing teams. We study methods for building an ensemble that combines forecasts from these teams. These experiments have informed the ensemble methods used by the Hub. To be most useful to policy makers, ensemble forecasts must have stable performance in the presence of two key characteristics of the component forecasts: (1) occasional misalignment with the reported data, and (2) instability in the relative performance of component forecasters over time. Our results indicate that in the presence of these challenges, an untrained and robust approach to ensembling using an equally weighted median of all component forecasts is a good choice to support public health decision makers. In settings where some contributing forecasters have a stable record of good performance, trained ensembles that give those forecasters higher weight can also be helpful.
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Affiliation(s)
- Evan L Ray
- School of Public Health and Health Sciences, University of Massachusetts Amherst, United States of America
| | - Logan C Brooks
- Machine Learning Department, Carnegie Mellon University, United States of America
| | - Jacob Bien
- Department of Data Sciences and Operations, University of Southern California, United States of America
| | - Matthew Biggerstaff
- COVID-19 Response, U.S. Centers for Disease Control and Prevention, United States of America
| | - Nikos I Bosse
- London School of Hygiene & Tropical Medicine, United Kingdom
| | - Johannes Bracher
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies, Germany
| | - Estee Y Cramer
- School of Public Health and Health Sciences, University of Massachusetts Amherst, United States of America
| | - Sebastian Funk
- London School of Hygiene & Tropical Medicine, United Kingdom
| | - Aaron Gerding
- School of Public Health and Health Sciences, University of Massachusetts Amherst, United States of America
| | - Michael A Johansson
- COVID-19 Response, U.S. Centers for Disease Control and Prevention, United States of America
| | - Aaron Rumack
- Machine Learning Department, Carnegie Mellon University, United States of America
| | - Yijin Wang
- School of Public Health and Health Sciences, University of Massachusetts Amherst, United States of America
| | - Martha Zorn
- School of Public Health and Health Sciences, University of Massachusetts Amherst, United States of America
| | - Ryan J Tibshirani
- Machine Learning Department, Carnegie Mellon University, United States of America
| | - Nicholas G Reich
- School of Public Health and Health Sciences, University of Massachusetts Amherst, United States of America
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Chen Y, Li N, Lourenço J, Wang L, Cazelles B, Dong L, Li B, Liu Y, Jit M, Bosse NI, Abbott S, Velayudhan R, Wilder-Smith A, Tian H, Brady OJ. Measuring the effects of COVID-19-related disruption on dengue transmission in southeast Asia and Latin America: a statistical modelling study. Lancet Infect Dis 2022; 22:657-667. [PMID: 35247320 PMCID: PMC8890758 DOI: 10.1016/s1473-3099(22)00025-1] [Citation(s) in RCA: 60] [Impact Index Per Article: 30.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Revised: 11/10/2021] [Accepted: 01/07/2022] [Indexed: 01/19/2023]
Abstract
BACKGROUND The COVID-19 pandemic has resulted in unprecedented disruption to society, which indirectly affects infectious disease dynamics. We aimed to assess the effects of COVID-19-related disruption on dengue, a major expanding acute public health threat, in southeast Asia and Latin America. METHODS We assembled data on monthly dengue incidence from WHO weekly reports, climatic data from ERA5, and population variables from WorldPop for 23 countries between January, 2014 and December, 2019 and fit a Bayesian regression model to explain and predict seasonal and multi-year dengue cycles. We compared model predictions with reported dengue data January to December, 2020, and assessed if deviations from projected incidence since March, 2020 are associated with specific public health and social measures (from the Oxford Coronavirus Government Response Tracer database) or human movement behaviours (as measured by Google mobility reports). FINDINGS We found a consistent, prolonged decline in dengue incidence across many dengue-endemic regions that began in March, 2020 (2·28 million cases in 2020 vs 4·08 million cases in 2019; a 44·1% decrease). We found a strong association between COVID-19-related disruption (as measured independently by public health and social measures and human movement behaviours) and reduced dengue risk, even after taking into account other drivers of dengue cycles including climatic and host immunity (relative risk 0·01-0·17, p<0·01). Measures related to the closure of schools and reduced time spent in non-residential areas had the strongest evidence of association with reduced dengue risk, but high collinearity between covariates made specific attribution challenging. Overall, we estimate that 0·72 million (95% CI 0·12-1·47) fewer dengue cases occurred in 2020 potentially attributable to COVID-19-related disruption. INTERPRETATION In most countries, COVID-19-related disruption led to historically low dengue incidence in 2020. Continuous monitoring of dengue incidence as COVID-19-related restrictions are relaxed will be important and could give new insights into transmission processes and intervention options. FUNDING National Key Research and Development Program of China and the Medical Research Council.
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Affiliation(s)
- Yuyang Chen
- State Key Laboratory of Remote Sensing Science, Center for Global Change and Public Health, College of Global Change and Earth System Science, Beijing Normal University, Beijing, China
| | - Naizhe Li
- State Key Laboratory of Remote Sensing Science, Center for Global Change and Public Health, College of Global Change and Earth System Science, Beijing Normal University, Beijing, China; MOE Key Laboratory for Biodiversity Science and Ecological Engineering, College of Life Sciences, Beijing Normal University, Beijing, China
| | - José Lourenço
- Biosystems and Integrative Sciences Institute, University of Lisbon, Lisbon, Portugal
| | - Lin Wang
- Department of Genetics, University of Cambridge, Cambridge, UK; Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, UMR2000, CNRS, Paris, France
| | - Bernard Cazelles
- Institut de Biologie de l'École Normale Supérieure UMR8197, Eco-Evolutionary Mathematics, École Normale Supérieure, Paris, France; Unité Mixte Internationnale 209, Mathematical and Computational Modeling of Complex Systems, Sorbonne Université, Paris, France
| | - Lu Dong
- MOE Key Laboratory for Biodiversity Science and Ecological Engineering, College of Life Sciences, Beijing Normal University, Beijing, China
| | - Bingying Li
- State Key Laboratory of Remote Sensing Science, Center for Global Change and Public Health, College of Global Change and Earth System Science, Beijing Normal University, Beijing, China
| | - Yang Liu
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, UK; Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene & Tropical Medicine, London, UK
| | - Mark Jit
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, UK; Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene & Tropical Medicine, London, UK
| | - Nikos I Bosse
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, UK; Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene & Tropical Medicine, London, UK
| | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, UK; Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene & Tropical Medicine, London, UK
| | - Raman Velayudhan
- Department of Control of Neglected Tropical Diseases, WHO, Geneva, Switzerland
| | - Annelies Wilder-Smith
- Department of Disease Control, London School of Hygiene & Tropical Medicine, London, UK; Heidelberg Institute of Global Health, University of Heidelberg, Heidelberg, Germany
| | - Huaiyu Tian
- State Key Laboratory of Remote Sensing Science, Center for Global Change and Public Health, College of Global Change and Earth System Science, Beijing Normal University, Beijing, China.
| | - Oliver J Brady
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, UK; Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene & Tropical Medicine, London, UK.
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9
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Cramer EY, Ray EL, Lopez VK, Bracher J, Brennen A, Castro Rivadeneira AJ, Gerding A, Gneiting T, House KH, Huang Y, Jayawardena D, Kanji AH, Khandelwal A, Le K, Mühlemann A, Niemi J, Shah A, Stark A, Wang Y, Wattanachit N, Zorn MW, Gu Y, Jain S, Bannur N, Deva A, Kulkarni M, Merugu S, Raval A, Shingi S, Tiwari A, White J, Abernethy NF, Woody S, Dahan M, Fox S, Gaither K, Lachmann M, Meyers LA, Scott JG, Tec M, Srivastava A, George GE, Cegan JC, Dettwiller ID, England WP, Farthing MW, Hunter RH, Lafferty B, Linkov I, Mayo ML, Parno MD, Rowland MA, Trump BD, Zhang-James Y, Chen S, Faraone SV, Hess J, Morley CP, Salekin A, Wang D, Corsetti SM, Baer TM, Eisenberg MC, Falb K, Huang Y, Martin ET, McCauley E, Myers RL, Schwarz T, Sheldon D, Gibson GC, Yu R, Gao L, Ma Y, Wu D, Yan X, Jin X, Wang YX, Chen Y, Guo L, Zhao Y, Gu Q, Chen J, Wang L, Xu P, Zhang W, Zou D, Biegel H, Lega J, McConnell S, Nagraj VP, Guertin SL, Hulme-Lowe C, Turner SD, Shi Y, Ban X, Walraven R, Hong QJ, Kong S, van de Walle A, Turtle JA, Ben-Nun M, Riley S, Riley P, Koyluoglu U, DesRoches D, Forli P, Hamory B, Kyriakides C, Leis H, Milliken J, Moloney M, Morgan J, Nirgudkar N, Ozcan G, Piwonka N, Ravi M, Schrader C, Shakhnovich E, Siegel D, Spatz R, Stiefeling C, Wilkinson B, Wong A, Cavany S, España G, Moore S, Oidtman R, Perkins A, Kraus D, Kraus A, Gao Z, Bian J, Cao W, Ferres JL, Li C, Liu TY, Xie X, Zhang S, Zheng S, Vespignani A, Chinazzi M, Davis JT, Mu K, Pastore y Piontti A, Xiong X, Zheng A, Baek J, Farias V, Georgescu A, Levi R, Sinha D, Wilde J, Perakis G, Bennouna MA, Nze-Ndong D, Singhvi D, Spantidakis I, Thayaparan L, Tsiourvas A, Sarker A, Jadbabaie A, Shah D, Della Penna N, Celi LA, Sundar S, Wolfinger R, Osthus D, Castro L, Fairchild G, Michaud I, Karlen D, Kinsey M, Mullany LC, Rainwater-Lovett K, Shin L, Tallaksen K, Wilson S, Lee EC, Dent J, Grantz KH, Hill AL, Kaminsky J, Kaminsky K, Keegan LT, Lauer SA, Lemaitre JC, Lessler J, Meredith HR, Perez-Saez J, Shah S, Smith CP, Truelove SA, Wills J, Marshall M, Gardner L, Nixon K, Burant JC, Wang L, Gao L, Gu Z, Kim M, Li X, Wang G, Wang Y, Yu S, Reiner RC, Barber R, Gakidou E, Hay SI, Lim S, Murray C, Pigott D, Gurung HL, Baccam P, Stage SA, Suchoski BT, Prakash BA, Adhikari B, Cui J, Rodríguez A, Tabassum A, Xie J, Keskinocak P, Asplund J, Baxter A, Oruc BE, Serban N, Arik SO, Dusenberry M, Epshteyn A, Kanal E, Le LT, Li CL, Pfister T, Sava D, Sinha R, Tsai T, Yoder N, Yoon J, Zhang L, Abbott S, Bosse NI, Funk S, Hellewell J, Meakin SR, Sherratt K, Zhou M, Kalantari R, Yamana TK, Pei S, Shaman J, Li ML, Bertsimas D, Lami OS, Soni S, Bouardi HT, Ayer T, Adee M, Chhatwal J, Dalgic OO, Ladd MA, Linas BP, Mueller P, Xiao J, Wang Y, Wang Q, Xie S, Zeng D, Green A, Bien J, Brooks L, Hu AJ, Jahja M, McDonald D, Narasimhan B, Politsch C, Rajanala S, Rumack A, Simon N, Tibshirani RJ, Tibshirani R, Ventura V, Wasserman L, O’Dea EB, Drake JM, Pagano R, Tran QT, Ho LST, Huynh H, Walker JW, Slayton RB, Johansson MA, Biggerstaff M, Reich NG. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States. Proc Natl Acad Sci U S A 2022; 119:e2113561119. [PMID: 35394862 PMCID: PMC9169655 DOI: 10.1073/pnas.2113561119] [Citation(s) in RCA: 87] [Impact Index Per Article: 43.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Accepted: 01/24/2022] [Indexed: 01/15/2023] Open
Abstract
Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks.
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Affiliation(s)
- Estee Y. Cramer
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Evan L. Ray
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Velma K. Lopez
- COVID-19 Response, Centers for Disease Control and Prevention; Atlanta, GA 30333
| | - Johannes Bracher
- Chair of Econometrics and Statistics, Karlsruhe Institute of Technology, 76185 Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies, 69118 Heidelberg, Germany
| | | | | | - Aaron Gerding
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Tilmann Gneiting
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies, 69118 Heidelberg, Germany
- Institute of Stochastics, Karlsruhe Institute of Technology, 69118 Karlsruhe, Germany
| | - Katie H. House
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Yuxin Huang
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Dasuni Jayawardena
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Abdul H. Kanji
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Ayush Khandelwal
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Khoa Le
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Anja Mühlemann
- Institute of Mathematical Statistics and Actuarial Science, University of Bern, CH-3012 Bern, Switzerland
| | - Jarad Niemi
- Department of Statistics, Iowa State University, Ames, IA 50011
| | - Apurv Shah
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Ariane Stark
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Yijin Wang
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Nutcha Wattanachit
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | - Martha W. Zorn
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
| | | | - Sansiddh Jain
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Nayana Bannur
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Ayush Deva
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Mihir Kulkarni
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Srujana Merugu
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Alpan Raval
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Siddhant Shingi
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Avtansh Tiwari
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | - Jerome White
- Wadhwani Institute of Artificial Intelligence, Andheri East, Mumbai, 400093, India
| | | | - Spencer Woody
- Department of Integrative Biology, University of Texas at Austin, Austin, TX 78712
| | - Maytal Dahan
- Texas Advanced Computing Center, Austin, TX 78758
| | - Spencer Fox
- Department of Integrative Biology, University of Texas at Austin, Austin, TX 78712
| | | | | | - Lauren Ancel Meyers
- Department of Integrative Biology, University of Texas at Austin, Austin, TX 78712
| | - James G. Scott
- Department of Information, Risk, and Operations Management, University of Texas at Austin, Austin, TX 78712
| | - Mauricio Tec
- Department of Statistics and Data Sciences, University of Texas at Austin, Austin, TX 78712
| | - Ajitesh Srivastava
- Ming Hsieh Department of Computer and Electrical Engineering, University of Southern California, Los Angeles, CA 90089
| | - Glover E. George
- US Army Engineer Research and Development Center, Vicksburg, MS 39180
| | - Jeffrey C. Cegan
- US Army Engineer Research and Development Center, Concord, MA 01742
| | - Ian D. Dettwiller
- US Army Engineer Research and Development Center, Vicksburg, MS 39180
| | | | | | - Robert H. Hunter
- US Army Engineer Research and Development Center, Vicksburg, MS 39180
| | - Brandon Lafferty
- US Army Engineer Research and Development Center, Vicksburg, MS 39180
| | - Igor Linkov
- US Army Engineer Research and Development Center, Concord, MA 01742
| | - Michael L. Mayo
- US Army Engineer Research and Development Center, Vicksburg, MS 39180
| | - Matthew D. Parno
- US Army Engineer Research and Development Center, Hanover, NH 03755
| | | | | | - Yanli Zhang-James
- Department of Psychiatry and Behavioral Sciences, State University of New York Upstate Medical University, Syracuse, NY 13210
| | - Samuel Chen
- School of Medicine, State University of New York Upstate Medical University, Syracuse, NY 13210
| | - Stephen V. Faraone
- Department of Psychiatry and Behavioral Sciences, State University of New York Upstate Medical University, Syracuse, NY 13210
| | - Jonathan Hess
- Department of Psychiatry and Behavioral Sciences, State University of New York Upstate Medical University, Syracuse, NY 13210
| | - Christopher P. Morley
- Department of Public Health & Preventive Medicine, State University of New York Upstate Medical University, Syracuse, NY 13210
| | - Asif Salekin
- Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13207
| | - Dongliang Wang
- Department of Public Health & Preventive Medicine, State University of New York Upstate Medical University, Syracuse, NY 13210
| | | | - Thomas M. Baer
- Department of Physics, Trinity University, San Antonio, TX 78212
| | - Marisa C. Eisenberg
- Department of Complex Systems, University of Michigan, Ann Arbor, MI 48109
- Department of Mathematics, University of Michigan, Ann Arbor, MI 48109
- School of Public Health, Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109
| | - Karl Falb
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109
| | - Yitao Huang
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109
| | - Emily T. Martin
- School of Public Health, Department of Epidemiology, University of Michigan, Ann Arbor, MI 48109
| | - Ella McCauley
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109
| | - Robert L. Myers
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109
| | - Tom Schwarz
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109
| | - Daniel Sheldon
- College of Information and Computer Sciences, University of Massachusetts, Amherst, MA 01003
| | - Graham Casey Gibson
- School of Public Health and Health Sciences, University of Massachusetts, Amherst, MA 01003
| | - Rose Yu
- Department of Computer Science and Engineering, University of California, San Diego, CA 92093
- Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115
| | - Liyao Gao
- Department of Statistics, University of Washington, Seattle, WA 98185
| | - Yian Ma
- Halıcıoğlu Data Science Institute, University of California, San Diego, CA 92093
| | - Dongxia Wu
- Department of Computer Science and Engineering, University of California, San Diego, CA 92093
| | - Xifeng Yan
- Department of Computer Science, University of California, Santa Barbara, CA 93106
| | - Xiaoyong Jin
- Department of Computer Science, University of California, Santa Barbara, CA 93106
| | - Yu-Xiang Wang
- Department of Computer Science, University of California, Santa Barbara, CA 93106
| | - YangQuan Chen
- Mechatronics, Embedded Systems and Automation Lab, Department of Mechanical Engineering, University of California, Merced, CA 95301
| | - Lihong Guo
- Jilin University, Changchun City, Jilin Province, 130012, People's Republic of China
| | - Yanting Zhao
- University of Science and Technology of China, Heifei, Anhui, 230027, People's Republic of China
| | - Quanquan Gu
- Department of Computer Science, University of California, Los Angeles, CA 90095
| | - Jinghui Chen
- Department of Computer Science, University of California, Los Angeles, CA 90095
| | - Lingxiao Wang
- Department of Computer Science, University of California, Los Angeles, CA 90095
| | - Pan Xu
- Department of Computer Science, University of California, Los Angeles, CA 90095
| | - Weitong Zhang
- Department of Computer Science, University of California, Los Angeles, CA 90095
| | - Difan Zou
- Department of Computer Science, University of California, Los Angeles, CA 90095
| | - Hannah Biegel
- Department of Mathematics, University of Arizona, Tucson, AZ 85721
| | - Joceline Lega
- Department of Mathematics, University of Arizona, Tucson, AZ 85721
| | | | - V. P. Nagraj
- Quality Assurance and Data Science, Signature Science, LLC, Charlottesville, VA 22911
| | - Stephanie L. Guertin
- Quality Assurance and Data Science, Signature Science, LLC, Charlottesville, VA 22911
| | | | - Stephen D. Turner
- Quality Assurance and Data Science, Signature Science, LLC, Charlottesville, VA 22911
| | - Yunfeng Shi
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY 12309
| | - Xuegang Ban
- Department of Civil and Environmental Engineering, University of Washington, Seattle, WA 98195
| | | | - Qi-Jun Hong
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287
- School of Engineering, Brown University, Providence, RI 02912
| | | | | | - James A. Turtle
- Infectious Disease Group, Predictive Science, Inc, San Diego, CA 92121
| | - Michal Ben-Nun
- Infectious Disease Group, Predictive Science, Inc, San Diego, CA 92121
| | - Steven Riley
- Medical Research Council Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College, W2 1PG London, United Kingdom
| | - Pete Riley
- Infectious Disease Group, Predictive Science, Inc, San Diego, CA 92121
| | | | | | - Pedro Forli
- Oliver Wyman Digital, Oliver Wyman, Sao Paolo, Brazil 04711-904
| | - Bruce Hamory
- Health & Life Sciences, Oliver Wyman, Boston, MA 02110
| | | | - Helen Leis
- Health & Life Sciences, Oliver Wyman, New York, NY 10036
| | - John Milliken
- Financial Services, Oliver Wyman, New York, NY 10036
| | | | - James Morgan
- Financial Services, Oliver Wyman, New York, NY 10036
| | | | - Gokce Ozcan
- Financial Services, Oliver Wyman, New York, NY 10036
| | - Noah Piwonka
- Health & Life Sciences, Oliver Wyman, New York, NY 10036
| | - Matt Ravi
- Core Consultant Group, Oliver Wyman, New York, NY 10036
| | - Chris Schrader
- Health & Life Sciences, Oliver Wyman, New York, NY 10036
| | | | - Daniel Siegel
- Financial Services, Oliver Wyman, New York, NY 10036
| | - Ryan Spatz
- Core Consultant Group, Oliver Wyman, New York, NY 10036
| | - Chris Stiefeling
- Financial Services, Oliver Wyman Digital, Toronto, ON, Canada M5J 0A1
| | | | | | - Sean Cavany
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556
| | - Guido España
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556
| | - Sean Moore
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556
| | - Rachel Oidtman
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556
- Department of Ecology and Evolution, University of Chicago, Chicago, IL 60637
| | - Alex Perkins
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556
| | - David Kraus
- Department of Mathematics and Statistics, Masaryk University, 61137 Brno, Czech Republic
| | - Andrea Kraus
- Department of Mathematics and Statistics, Masaryk University, 61137 Brno, Czech Republic
| | | | | | - Wei Cao
- Microsoft, Redmond, WA 98029
| | | | | | | | | | | | | | - Alessandro Vespignani
- Institute for Scientific Interchange Foundation, Turin, 10133, Italy
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115
| | - Matteo Chinazzi
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115
| | - Jessica T. Davis
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115
| | - Kunpeng Mu
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115
| | - Ana Pastore y Piontti
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115
| | - Xinyue Xiong
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115
| | - Andrew Zheng
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Jackie Baek
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Vivek Farias
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02142
| | - Andreea Georgescu
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Retsef Levi
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02142
| | - Deeksha Sinha
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Joshua Wilde
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | | | | | | | - Divya Singhvi
- Technology, Operations and Statistics (TOPS) group, Stern School of Business, New York University, New York, NY 10012
| | | | | | | | - Arnab Sarker
- Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Ali Jadbabaie
- Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Devavrat Shah
- Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Nicolas Della Penna
- Laboratory for Computational Physiology, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Leo A. Celi
- Laboratory for Computational Physiology, Massachusetts Institute of Technology, Cambridge, MA 02139
| | | | | | - Dave Osthus
- Statistical Sciences Group, Los Alamos National Laboratory, Los Alamos, NM 87545
| | - Lauren Castro
- Information Systems and Modeling Group, Los Alamos National Laboratory, Los Alamos, NM 87545
| | - Geoffrey Fairchild
- Information Systems and Modeling Group, Los Alamos National Laboratory, Los Alamos, NM 87545
| | - Isaac Michaud
- Statistical Sciences Group, Los Alamos National Laboratory, Los Alamos, NM 87545
| | - Dean Karlen
- Department of Physics and Astronomy, University of Victoria, Victoria, BC, V8W 2Y2, Canada
- Physical Sciences Division, TRIUMF, Vancouver, BC, V8W 2Y2, Canada
| | - Matt Kinsey
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723
| | - Luke C. Mullany
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723
| | | | - Lauren Shin
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723
| | | | - Shelby Wilson
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723
| | - Elizabeth C. Lee
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Juan Dent
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Kyra H. Grantz
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Alison L. Hill
- Institute for Computational Medicine, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21218
| | - Joshua Kaminsky
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | | | - Lindsay T. Keegan
- Division of Epidemiology, Department of Internal Medicine, University of Utah, Salt Lake City, UT 84108
| | - Stephen A. Lauer
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Joseph C. Lemaitre
- Laboratory of Ecohydrology, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Justin Lessler
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Hannah R. Meredith
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Javier Perez-Saez
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Sam Shah
- Unaffiliated, San Francisco, CA 94122
| | - Claire P. Smith
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
| | - Shaun A. Truelove
- Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21215
- International Vaccine Access Center, Johns Hopkins University, Baltimore, MD 21231
- Department of International Health, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21231
| | | | - Maximilian Marshall
- Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, MD 21218
| | - Lauren Gardner
- Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, MD 21218
| | - Kristen Nixon
- Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, MD 21218
| | | | - Lily Wang
- Department of Statistics, Iowa State University, Ames, IA 50011
| | - Lei Gao
- Department of Finance, Iowa State University, Ames, IA 50011
| | - Zhiling Gu
- Department of Statistics, Iowa State University, Ames, IA 50011
| | - Myungjin Kim
- Department of Statistics, Iowa State University, Ames, IA 50011
| | - Xinyi Li
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634
| | - Guannan Wang
- Department of Mathematics, College of William & Mary, Williamsburg, VA 23187
| | - Yueying Wang
- Department of Statistics, Iowa State University, Ames, IA 50011
| | - Shan Yu
- Department of Statistics, University of Virginia, Charlottesville, VA 22904
| | - Robert C. Reiner
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA 98195
| | - Ryan Barber
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA 98195
| | - Emmanuela Gakidou
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA 98195
| | - Simon I. Hay
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA 98195
| | - Steve Lim
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA 98195
| | - Chris Murray
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA 98195
| | - David Pigott
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA 98195
| | | | | | | | | | - B. Aditya Prakash
- College of Computing, Georgia Institute of Technology, Atlanta, GA 30308
| | - Bijaya Adhikari
- Department of Computer Science, University of Iowa, Iowa City, IA 52242
| | - Jiaming Cui
- College of Computing, Georgia Institute of Technology, Atlanta, GA 30308
| | | | - Anika Tabassum
- Department of Computer Science, Virginia Tech, Falls Church, VA 22043
| | - Jiajia Xie
- College of Computing, Georgia Institute of Technology, Atlanta, GA 30308
| | - Pinar Keskinocak
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332
| | - John Asplund
- Advanced Data Analytics, Metron, Inc., Reston, VA 20190
| | - Arden Baxter
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332
| | - Buse Eylul Oruc
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332
| | - Nicoleta Serban
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332
| | | | | | | | | | | | | | | | | | | | - Thomas Tsai
- Department of Health Policy and Management, Harvard University, Cambridge, MA 02138
| | | | | | | | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, WC1E 7HT London, United Kingdom
| | - Nikos I. Bosse
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, WC1E 7HT London, United Kingdom
| | - Sebastian Funk
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, WC1E 7HT London, United Kingdom
| | - Joel Hellewell
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, WC1E 7HT London, United Kingdom
| | - Sophie R. Meakin
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, WC1E 7HT London, United Kingdom
| | - Katharine Sherratt
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, WC1E 7HT London, United Kingdom
| | - Mingyuan Zhou
- McCombs School of Business, The University of Texas at Austin, Austin, TX 78712
| | - Rahi Kalantari
- Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712
| | - Teresa K. Yamana
- Department of Environmental Health Sciences, Columbia University, New York, NY 10032
| | - Sen Pei
- Department of Environmental Health Sciences, Columbia University, New York, NY 10032
| | - Jeffrey Shaman
- Department of Environmental Health Sciences, Columbia University, New York, NY 10032
| | - Michael L. Li
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Dimitris Bertsimas
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02142
| | - Omar Skali Lami
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Saksham Soni
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Hamza Tazi Bouardi
- Operations Research Center, Massachusetts Institute of Technology; Cambridge, MA 02139
| | - Turgay Ayer
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332
- Winship Cancer Institute, Emory University Medical School, Atlanta, GA 30322
| | - Madeline Adee
- Radiology-Institute for Technology Assessment, Massachusetts General Hospital, Boston, MA 02114
| | - Jagpreet Chhatwal
- Radiology-Institute for Technology Assessment, Massachusetts General Hospital, Boston, MA 02114
| | - Ozden O. Dalgic
- Health Economic Modeling, Value Analytics Labs, 34776 İstanbul, Turkey
| | - Mary A. Ladd
- Radiology-Institute for Technology Assessment, Massachusetts General Hospital, Boston, MA 02114
| | - Benjamin P. Linas
- Department of Medicine, Section of Infectious Diseases, Boston University School of Medicine, Boston, MA 02118
| | - Peter Mueller
- Radiology-Institute for Technology Assessment, Massachusetts General Hospital, Boston, MA 02114
| | - Jade Xiao
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332
| | - Yuanjia Wang
- Department of Biostatistics, Columbia University, New York, NY 10032
- Department of Psychiatry, Columbia University, New York, NY 10032
| | - Qinxia Wang
- Department of Biostatistics, Columbia University, New York, NY 10032
| | - Shanghong Xie
- Department of Biostatistics, Columbia University, New York, NY 10032
| | - Donglin Zeng
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599
| | - Alden Green
- Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Jacob Bien
- Marshall School of Business, Department of Data Sciences and Operations (DSO), University of Southern California, Los Angeles, CA 90089
| | - Logan Brooks
- Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Addison J. Hu
- Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Maria Jahja
- Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Daniel McDonald
- Department of Statistics, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada
| | - Balasubramanian Narasimhan
- Department of Biomedical Data Sciences, Stanford University, Stanford, CA 94305
- Department of Statistics, Stanford University, Stanford, CA 94305
| | - Collin Politsch
- Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Samyak Rajanala
- Department of Statistics, Stanford University, Stanford, CA 94305
| | - Aaron Rumack
- Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Noah Simon
- Department of Biostatistics, University of Washington, Seattle, WA 98195
| | - Ryan J. Tibshirani
- Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Rob Tibshirani
- Department of Statistics, Stanford University, Stanford, CA 94305
| | - Valerie Ventura
- Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Larry Wasserman
- Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213
| | - Eamon B. O’Dea
- Odum School of Ecology, University of Georgia, Athens, GA 30602
| | - John M. Drake
- Odum School of Ecology, University of Georgia, Athens, GA 30602
| | | | - Quoc T. Tran
- Catalog Data Science, Walmart Inc., Sunnyvale, CA 94085
| | - Lam Si Tung Ho
- Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 4R2, Canada
| | - Huong Huynh
- Virtual Power System Inc, Milpitas, CA 95035
| | - Jo W. Walker
- COVID-19 Response, Centers for Disease Control and Prevention; Atlanta, GA 30333
| | - Rachel B. Slayton
- COVID-19 Response, Centers for Disease Control and Prevention; Atlanta, GA 30333
| | - Michael A. Johansson
- COVID-19 Response, Centers for Disease Control and Prevention; Atlanta, GA 30333
| | - Matthew Biggerstaff
- COVID-19 Response, Centers for Disease Control and Prevention; Atlanta, GA 30333
| | - Nicholas G. Reich
- Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003
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10
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Gostic KM, McGough L, Baskerville EB, Abbott S, Joshi K, Tedijanto C, Kahn R, Niehus R, Hay JA, De Salazar PM, Hellewell J, Meakin S, Munday JD, Bosse NI, Sherrat K, Thompson RN, White LF, Huisman JS, Scire J, Bonhoeffer S, Stadler T, Wallinga J, Funk S, Lipsitch M, Cobey S. Correction: Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput Biol 2021; 17:e1009679. [PMID: 34879070 PMCID: PMC8654153 DOI: 10.1371/journal.pcbi.1009679] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
[This corrects the article DOI: 10.1371/journal.pcbi.1008409.].
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11
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Bracher J, Wolffram D, Deuschel J, Görgen K, Ketterer JL, Ullrich A, Abbott S, Barbarossa MV, Bertsimas D, Bhatia S, Bodych M, Bosse NI, Burgard JP, Castro L, Fairchild G, Fuhrmann J, Funk S, Gogolewski K, Gu Q, Heyder S, Hotz T, Kheifetz Y, Kirsten H, Krueger T, Krymova E, Li ML, Meinke JH, Michaud IJ, Niedzielewski K, Ożański T, Rakowski F, Scholz M, Soni S, Srivastava A, Zieliński J, Zou D, Gneiting T, Schienle M. A pre-registered short-term forecasting study of COVID-19 in Germany and Poland during the second wave. Nat Commun 2021; 12:5173. [PMID: 34453047 PMCID: PMC8397791 DOI: 10.1038/s41467-021-25207-0] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Accepted: 07/28/2021] [Indexed: 12/31/2022] Open
Abstract
Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October-19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.
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Affiliation(s)
- J Bracher
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany.
| | - D Wolffram
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
| | - J Deuschel
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - K Görgen
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - J L Ketterer
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - A Ullrich
- Robert Koch Institute (RKI), Berlin, Germany
| | - S Abbott
- London School of Hygiene and Tropical Medicine, London, UK
| | - M V Barbarossa
- Frankfurt Institute for Advanced Studies, Frankfurt, Germany
| | - D Bertsimas
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - S Bhatia
- MRC Centre for Global Infectious Disease Analysis, Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), Imperial College London, London, UK
| | - M Bodych
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - N I Bosse
- London School of Hygiene and Tropical Medicine, London, UK
| | - J P Burgard
- Economic and Social Statistics Department, University of Trier, Trier, Germany
| | - L Castro
- Information Systems and Modeling, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - G Fairchild
- Information Systems and Modeling, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - J Fuhrmann
- Frankfurt Institute for Advanced Studies, Frankfurt, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - S Funk
- London School of Hygiene and Tropical Medicine, London, UK
| | - K Gogolewski
- Institute of Informatics, University of Warsaw, Warsaw, Poland
| | - Q Gu
- Department of Computer Science, University of California, Los Angeles, CA, USA
| | - S Heyder
- Institute of Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
| | - T Hotz
- Institute of Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
| | - Y Kheifetz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - H Kirsten
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - T Krueger
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - E Krymova
- Swiss Data Science Center, ETH Zurich and EPFL, Lausanne, Switzerland
| | - M L Li
- Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - J H Meinke
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - I J Michaud
- Statistical Sciences Group, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - K Niedzielewski
- Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland
| | - T Ożański
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - F Rakowski
- Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland
| | - M Scholz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - S Soni
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - A Srivastava
- Ming Hsieh Department of Computer and Electrical Engineering, University of Southern California, Los Angeles, CA, USA
| | - J Zieliński
- Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland
| | - D Zou
- Department of Computer Science, University of California, Los Angeles, CA, USA
| | - T Gneiting
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
- Institute for Stochastics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - M Schienle
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
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12
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Munday JD, Sherratt K, Meakin S, Endo A, Pearson CAB, Hellewell J, Abbott S, Bosse NI, Atkins KE, Wallinga J, Edmunds WJ, van Hoek AJ, Funk S. Implications of the school-household network structure on SARS-CoV-2 transmission under school reopening strategies in England. Nat Commun 2021; 12:1942. [PMID: 33782396 PMCID: PMC8007691 DOI: 10.1038/s41467-021-22213-0] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 03/02/2021] [Indexed: 12/28/2022] Open
Abstract
In early 2020 many countries closed schools to mitigate the spread of SARS-CoV-2. Since then, governments have sought to relax the closures, engendering a need to understand associated risks. Using address records, we construct a network of schools in England connected through pupils who share households. We evaluate the risk of transmission between schools under different reopening scenarios. We show that whilst reopening select year-groups causes low risk of large-scale transmission, reopening secondary schools could result in outbreaks affecting up to 2.5 million households if unmitigated, highlighting the importance of careful monitoring and within-school infection control to avoid further school closures or other restrictions. 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.
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Affiliation(s)
- James D Munday
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK. .,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK.
| | - Katharine Sherratt
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Sophie Meakin
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Akira Endo
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Carl A B Pearson
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Joel Hellewell
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Nikos I Bosse
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | | | - Katherine E Atkins
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK.,Centre for Global Health, Usher Institute, College of Medicine and Veterinary Medicine, University of Edinburgh, Edinburgh, UK
| | - Jacco Wallinga
- National Institute for Public Health and the Environment (RIVM), Bilthoven, The Netherlands.,Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, The Netherlands
| | - W John Edmunds
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Albert Jan van Hoek
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK.,National Institute for Public Health and the Environment (RIVM), Bilthoven, The Netherlands
| | - Sebastian Funk
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
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13
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Abbott S, Hellewell J, Thompson RN, Sherratt K, Gibbs HP, Bosse NI, Munday JD, Meakin S, Doughty EL, Chun JY, Chan YWD, Finger F, Campbell P, Endo A, Pearson CAB, Gimma A, Russell T, Flasche S, Kucharski AJ, Eggo RM, Funk S. Estimating the time-varying reproduction number of SARS-CoV-2 using national and subnational case counts. Wellcome Open Res 2020. [DOI: 10.12688/wellcomeopenres.16006.2] [Citation(s) in RCA: 78] [Impact Index Per Article: 19.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Background: Assessing temporal variations in transmission in different countries is essential for monitoring the epidemic, evaluating the effectiveness of public health interventions and estimating the impact of changes in policy. Methods: We use case and death notification data to generate daily estimates of the time-varying reproduction number globally, regionally, nationally, and subnationally over a 12-week rolling window. Our modelling framework, based on open source tooling, accounts for uncertainty in reporting delays, so that the reproduction number is estimated based on underlying latent infections. Results: Estimates of the reproduction number, trajectories of infections, and forecasts are displayed on a dedicated website as both maps and time series, and made available to download in tabular form. Conclusions: This decision-support tool can be used to assess changes in virus transmission both globally, regionally, nationally, and subnationally. This allows public health officials and policymakers to track the progress of the outbreak in near real-time using an epidemiologically valid measure. As well as providing regular updates on our website, we also provide an open source tool-set so that our approach can be used directly by researchers and policymakers on confidential data-sets. We hope that our tool will be used to support decisions in countries worldwide throughout the ongoing COVID-19 pandemic.
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14
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Gostic KM, McGough L, Baskerville EB, Abbott S, Joshi K, Tedijanto C, Kahn R, Niehus R, Hay JA, De Salazar PM, Hellewell J, Meakin S, Munday JD, Bosse NI, Sherrat K, Thompson RN, White LF, Huisman JS, Scire J, Bonhoeffer S, Stadler T, Wallinga J, Funk S, Lipsitch M, Cobey S. Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput Biol 2020; 16:e1008409. [PMID: 33301457 PMCID: PMC7728287 DOI: 10.1371/journal.pcbi.1008409] [Citation(s) in RCA: 229] [Impact Index Per Article: 57.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
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.
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Affiliation(s)
- Katelyn M. Gostic
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
| | - Lauren McGough
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
| | - Edward B. Baskerville
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
| | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Keya Joshi
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Christine Tedijanto
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Rebecca Kahn
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Rene Niehus
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - James A. Hay
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Pablo M. De Salazar
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Joel Hellewell
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Sophie Meakin
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - James D. Munday
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Nikos I. Bosse
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Katharine Sherrat
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Robin N. Thompson
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Laura F. White
- Department of Biostatistics, Boston University School of Public Health, Boston, MA, United States of America
| | - Jana S. Huisman
- Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
| | - Jérémie Scire
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | | | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | - Jacco Wallinga
- Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, the Netherlands
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, the Netherlands
| | - Sebastian Funk
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Marc Lipsitch
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Sarah Cobey
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
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15
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Gostic KM, McGough L, Baskerville EB, Abbott S, Joshi K, Tedijanto C, Kahn R, Niehus R, Hay J, De Salazar PM, Hellewell J, Meakin S, Munday J, Bosse NI, Sherrat K, Thompson RN, White LF, Huisman JS, Scire J, Bonhoeffer S, Stadler T, Wallinga J, Funk S, Lipsitch M, Cobey S. Practical considerations for measuring the effective reproductive number, R t. medRxiv 2020:2020.06.18.20134858. [PMID: 32607522 PMCID: PMC7325187 DOI: 10.1101/2020.06.18.20134858] [Citation(s) in RCA: 50] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Estimation of the effective reproductive number, R t , is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using R t to assess the effectiveness of interventions and to inform policy. However, estimation of R t 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 R t , we recommend the approach of Cori et al. (2013), 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 (2004), 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 spread. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting R t 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 R t estimation.
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Affiliation(s)
- Katelyn M. Gostic
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
| | - Lauren McGough
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
| | | | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Keya Joshi
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Christine Tedijanto
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Rebecca Kahn
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Rene Niehus
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - James Hay
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Pablo M. De Salazar
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Joel Hellewell
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sophie Meakin
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - James Munday
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Nikos I. Bosse
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Katharine Sherrat
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Robin N. Thompson
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
- Mathematical Institute, University of Oxford, Oxford, UK
| | - Laura F. White
- Department of Biostatistics, Boston University School of Public Health, Boston, MA, USA
| | - Jana S. Huisman
- Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
| | - Jérémie Scire
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | | | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | - Jacco Wallinga
- Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, The Netherlands
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, The Netherlands
| | - Sebastian Funk
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Marc Lipsitch
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Sarah Cobey
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
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16
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Abbott S, Hellewell J, Thompson RN, Sherratt K, Gibbs HP, Bosse NI, Munday JD, Meakin S, Doughty EL, Chun JY, Chan YWD, Finger F, Campbell P, Endo A, Pearson CAB, Gimma A, Russell T, Flasche S, Kucharski AJ, Eggo RM, Funk S. Estimating the time-varying reproduction number of SARS-CoV-2 using national and subnational case counts. Wellcome Open Res 2020. [DOI: 10.12688/wellcomeopenres.16006.1] [Citation(s) in RCA: 122] [Impact Index Per Article: 30.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Background: Interventions are now in place worldwide to reduce transmission of the novel coronavirus. Assessing temporal variations in transmission in different countries is essential for evaluating the effectiveness of public health interventions and the impact of changes in policy. Methods: We use case notification data to generate daily estimates of the time-dependent reproduction number in different regions and countries. Our modelling framework, based on open source tooling, accounts for reporting delays, so that temporal variations in reproduction number estimates can be compared directly with the times at which interventions are implemented. Results: We provide three example uses of our framework. First, we demonstrate how the toolset displays temporal changes in the reproduction number. Second, we show how the framework can be used to reconstruct case counts by date of infection from case counts by date of notification, as well as to estimate the reproduction number. Third, we show how maps can be generated to clearly show if case numbers are likely to decrease or increase in different regions. Results are shown for regions and countries worldwide on our website (https://epiforecasts.io/covid/) and are updated daily. Our tooling is provided as an open-source R package to allow replication by others. Conclusions: This decision-support tool can be used to assess changes in virus transmission in different regions and countries worldwide. This allows policymakers to assess the effectiveness of current interventions, and will be useful for inferring whether or not transmission will increase when interventions are lifted. As well as providing daily updates on our website, we also provide adaptable computing code so that our approach can be used directly by researchers and policymakers on confidential datasets. We hope that our tool will be used to support decisions in countries worldwide throughout the ongoing COVID-19 pandemic.
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Jombart T, van Zandvoort K, Russell TW, Jarvis CI, Gimma A, Abbott S, Clifford S, Funk S, Gibbs H, Liu Y, Pearson CAB, Bosse NI, Eggo RM, Kucharski AJ, Edmunds WJ. Inferring the number of COVID-19 cases from recently reported deaths. Wellcome Open Res 2020; 5:78. [PMID: 32518842 PMCID: PMC7255910 DOI: 10.12688/wellcomeopenres.15786.1] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/30/2020] [Indexed: 01/14/2023] Open
Abstract
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.
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Affiliation(s)
- Thibaut Jombart
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
- UK Public Health Rapid Support Team, London, UK
- MRC Centre for Global Infectious Disease Analysis, Imperial College London, London, UK
| | - Kevin van Zandvoort
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Timothy W. Russell
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Christopher I. Jarvis
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Amy Gimma
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sam Abbott
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sam Clifford
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sebastian Funk
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Hamish Gibbs
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Yang Liu
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Carl A. B. Pearson
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
- South African Centre for Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch, South Africa
| | - Nikos I. Bosse
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Centre for the Mathematical Modelling of Infectious Diseases COVID-19 Working Group
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
- UK Public Health Rapid Support Team, London, UK
- MRC Centre for Global Infectious Disease Analysis, Imperial College London, London, UK
- South African Centre for Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch, South Africa
| | - Rosalind M. Eggo
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Adam J. Kucharski
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - W. John Edmunds
- Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
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18
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Hellewell J, Abbott S, Gimma A, Bosse NI, Jarvis CI, Russell TW, Munday JD, Kucharski AJ, Edmunds WJ, Funk S, Eggo RM. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob Health 2020; 8:e488-e496. [PMID: 32119825 DOI: 10.1101/2020.02.08.20021162] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2020] [Revised: 02/19/2020] [Accepted: 02/20/2020] [Indexed: 05/23/2023]
Abstract
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.
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Affiliation(s)
- Joel Hellewell
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sam Abbott
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Amy Gimma
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Nikos I Bosse
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Christopher I Jarvis
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Timothy W Russell
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - James D Munday
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Adam J Kucharski
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - W John Edmunds
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sebastian Funk
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Rosalind M Eggo
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK.
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19
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Hellewell J, Abbott S, Gimma A, Bosse NI, Jarvis CI, Russell TW, Munday JD, Kucharski AJ, Edmunds WJ, Funk S, Eggo RM. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob Health 2020; 8:e488-e496. [PMID: 32119825 PMCID: PMC7097845 DOI: 10.1016/s2214-109x(20)30074-7] [Citation(s) in RCA: 1353] [Impact Index Per Article: 338.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2020] [Revised: 02/19/2020] [Accepted: 02/20/2020] [Indexed: 02/02/2023]
Abstract
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.
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Affiliation(s)
- Joel Hellewell
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sam Abbott
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Amy Gimma
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Nikos I Bosse
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Christopher I Jarvis
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Timothy W Russell
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - James D Munday
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Adam J Kucharski
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - W John Edmunds
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sebastian Funk
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Rosalind M Eggo
- Centre for the Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK.
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Jombart T, van Zandvoort K, Russell TW, Jarvis CI, Gimma A, Abbott S, Clifford S, Funk S, Gibbs H, Liu Y, Pearson CAB, Bosse NI, Eggo RM, Kucharski AJ, Edmunds WJ. Inferring the number of COVID-19 cases from recently reported deaths. medRxiv 2020:2020.03.10.20033761. [PMID: 32511459 PMCID: PMC7239087 DOI: 10.1101/2020.03.10.20033761] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
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.
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Affiliation(s)
- Thibaut Jombart
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
- UK Public Health Rapid Support Team, London, United Kingdom
- MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, United Kingdom
| | - Kevin van Zandvoort
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Timothy W Russell
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Christopher I Jarvis
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Amy Gimma
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Sam Clifford
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Sebastian Funk
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Hamish Gibbs
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Yang Liu
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Carl A. B. Pearson
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
- South African Centre for Epidemiological Modelling and Analysis, Stellenbosch University, Republic of South Africa
| | - Nikos I Bosse
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | | | - Rosalind M Eggo
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - Adam J Kucharski
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
| | - W John Edmunds
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, Keppel Street, London. WC1E 7HT·
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