{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T01:22:15Z","timestamp":1790212935677,"version":"4.1.0"},"reference-count":42,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T00:00:00Z","timestamp":1729123200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/P020720\/2"],"award-info":[{"award-number":["EP\/P020720\/2"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R018413\/2"],"award-info":[{"award-number":["EP\/R018413\/2"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC-2046"],"award-info":[{"award-number":["EXC-2046"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC-2046"],"award-info":[{"award-number":["EXC-2046"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","award":["MODUS-COVID"],"award-info":[{"award-number":["MODUS-COVID"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","award":["MODUS-COVID"],"award-info":[{"award-number":["MODUS-COVID"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["EP\/X038645\/1"],"award-info":[{"award-number":["EP\/X038645\/1"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100023913","name":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100023913","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method\u2019s learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available.<\/jats:p>","DOI":"10.1371\/journal.pone.0306704","type":"journal-article","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T17:31:33Z","timestamp":1729186293000},"page":"e0306704","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":9,"title":["Neural parameter calibration and uncertainty quantification for epidemic forecasting"],"prefix":"10.1371","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5644-4431","authenticated-orcid":true,"given":"Thomas","family":"Gaskin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5590-5726","authenticated-orcid":true,"given":"Tim","family":"Conrad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Grigorios A.","family":"Pavliotis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5232-2683","authenticated-orcid":true,"given":"Christof","family":"Sch\u00fctte","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,10,17]]},"reference":[{"key":"pone.0306704.ref001","doi-asserted-by":"crossref","DOI":"10.3389\/fpubh.2020.00230","article-title":"A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model","volume":"8","author":"JM Carcione","year":"2020","journal-title":"Frontiers in Public Health"},{"key":"pone.0306704.ref002","doi-asserted-by":"crossref","first-page":"100520","DOI":"10.1016\/j.epidem.2021.100520","article-title":"Communicating uncertainty in epidemic models","volume":"37","author":"R McCabe","year":"2021","journal-title":"Epidemics"},{"issue":"8","key":"pone.0306704.ref003","doi-asserted-by":"crossref","first-page":"100310","DOI":"10.1016\/j.patter.2021.100310","article-title":"Accounting for uncertainty during a pandemic","volume":"2","author":"J Zelner","year":"2021","journal-title":"Patterns"},{"key":"pone.0306704.ref004","first-page":"1","article-title":"Essai d\u2019une nouvelle analyse de la mortalit\u00e9 caus\u00e9e par la petite v\u00e9role, et des avantages de l\u2019inoculation pour la pr\u00e9venir","author":"D Bernoulli","year":"1760","journal-title":"Acad\u00e9mie Royale des Sciences"},{"issue":"772","key":"pone.0306704.ref005","first-page":"700","article-title":"A contribution to the mathematical theory of epidemics","volume":"115","author":"WO Kermack","year":"1927","journal-title":"Proceedings of the royal society of london Series A, Containing papers of a mathematical and physical character"},{"key":"pone.0306704.ref006","first-page":"111","article-title":"Stability of a stochastic SIR system","volume":"354","author":"E Tornatore","year":"2005","journal-title":"PhysA"},{"issue":"3","key":"pone.0306704.ref007","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1137\/10081856X","article-title":"A Stochastic Differential Equation SIS Epidemic Model","volume":"71","author":"A Gray","year":"2011","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"10","key":"pone.0306704.ref008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0259037","article-title":"Predicting the effects of COVID-19 related interventions in urban settings by combining activity-based modelling, agent-based simulation, and mobile phone data","volume":"16","author":"SA M\u00fcller","year":"2021","journal-title":"PLOS ONE"},{"issue":"7","key":"pone.0306704.ref009","first-page":"1","article-title":"Covasim: An agent-based model of COVID-19 dynamics and interventions","volume":"17","author":"CC Kerr","year":"2021","journal-title":"PLOS Computational Biology"},{"key":"pone.0306704.ref010","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-78911-6","volume-title":"Mathematical epidemiology","author":"F Brauer","year":"2008"},{"issue":"12","key":"pone.0306704.ref011","doi-asserted-by":"crossref","DOI":"10.1128\/JVI.02238-18","article-title":"Reconstruction of the genetic history and the current spread of HIV-1 subtype A in Germany","volume":"93","author":"K Hanke","year":"2019","journal-title":"J Virol"},{"key":"pone.0306704.ref012","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.prrv.2020.06.014","article-title":"Modelling insights into the COVID-19 pandemic","volume":"35","author":"MT Meehan","year":"2020","journal-title":"Paediatric Respiratory Reviews"},{"issue":"4","key":"pone.0306704.ref013","doi-asserted-by":"crossref","first-page":"e0249676","DOI":"10.1371\/journal.pone.0249676","article-title":"Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts","volume":"16","author":"H Wulkow","year":"2021","journal-title":"PLOS ONE"},{"issue":"7","key":"pone.0306704.ref014","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2216415120","article-title":"Neural parameter calibration for large-scale multi-agent models","volume":"120","author":"T Gaskin","year":"2023","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pone.0306704.ref015","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-12385-1","volume-title":"Handbook of uncertainty quantification","author":"R Ghanem","year":"2017"},{"issue":"2","key":"pone.0306704.ref016","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/S0377-2217(99)00228-3","article-title":"An application-oriented view of modeling uncertainty","volume":"122","author":"HJ Zimmermann","year":"2000","journal-title":"European Journal of operational research"},{"issue":"1-3","key":"pone.0306704.ref017","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.ress.2004.03.025","article-title":"An exploration of alternative approaches to the representation of uncertainty in model predictions","volume":"85","author":"JC Helton","year":"2004","journal-title":"Reliability Engineering & System Safety"},{"issue":"10","key":"pone.0306704.ref018","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1016\/j.apnum.2006.10.006","article-title":"Validated solutions of initial value problems for parametric ODEs","volume":"57","author":"Y Lin","year":"2007","journal-title":"Applied Numerical Mathematics"},{"key":"pone.0306704.ref019","first-page":"20","article-title":"General state space Markov chains and MCMC algorithms","volume":"1","author":"GO Roberts","year":"2004","journal-title":"Probability Surveys [electronic only]"},{"issue":"1","key":"pone.0306704.ref020","first-page":"1593","article-title":"The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo","volume":"15","author":"MD Hoffman","year":"2014","journal-title":"J Mach Learn Res"},{"issue":"4","key":"pone.0306704.ref021","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2307\/3318418","article-title":"Exponential convergence of Langevin distributions and their discrete approximations","volume":"2","author":"GO Roberts","year":"1996","journal-title":"Bernoulli"},{"issue":"2","key":"pone.0306704.ref022","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1111\/j.1467-9868.2010.00765.x","article-title":"Riemann manifold Langevin and Hamiltonian Monte Carlo methods","volume":"73","author":"M Girolami","year":"2011","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"pone.0306704.ref023","doi-asserted-by":"crossref","unstructured":"Li C, Chen C, Carlson D, Carin L. Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence. AAAI\u201916. AAAI Press; 2016. p. 1788\u20131794.","DOI":"10.1609\/aaai.v30i1.10200"},{"issue":"6","key":"pone.0306704.ref024","doi-asserted-by":"crossref","first-page":"2100017","DOI":"10.1002\/mats.202100017","article-title":"Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples","volume":"30","author":"N Wulkow","year":"2021","journal-title":"Macromolecular Theory and Simulations"},{"key":"pone.0306704.ref025","doi-asserted-by":"crossref","first-page":"100368","DOI":"10.1016\/j.epidem.2019.100368","article-title":"Approximate Bayesian Computation for infectious disease modelling","volume":"29","author":"A Minter","year":"2019","journal-title":"Epidemics"},{"key":"pone.0306704.ref026","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.81916","article-title":"Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations","volume":"12","author":"K Sherratt","year":"2023","journal-title":"eLife"},{"issue":"1","key":"pone.0306704.ref027","doi-asserted-by":"crossref","first-page":"8637","DOI":"10.1038\/s41598-023-35580-z","article-title":"Dynamic calibration with approximate Bayesian computation for a microsimulation of disease spread","volume":"13","author":"M Asher","year":"2023","journal-title":"Scientific Reports"},{"issue":"4","key":"pone.0306704.ref028","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1093\/pnasnexus\/pgae063","article-title":"Inferring networks from time series: A neural approach","volume":"3","author":"T Gaskin","year":"2024","journal-title":"PNAS Nexus"},{"key":"pone.0306704.ref029","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1017\/S0962492910000061","article-title":"Inverse problems: A Bayesian perspective","volume":"19","author":"AM Stuart","year":"2010","journal-title":"Acta Numerica"},{"key":"pone.0306704.ref030","unstructured":"Kingma DP, Ba J. Adam: A Method for Stochastic Optimization. arXiv. 2014;1412.6980 [cs.LG]. https:\/\/doi.org\/10.48550\/ARXIV.1412.6980"},{"key":"pone.0306704.ref031","unstructured":"MODUS Covid. MATSim-Episim, Version 2020-November-12; 2020. https:\/\/covid-sim.info\/2020-11-12\/secondLockdown."},{"key":"pone.0306704.ref032","unstructured":"Robert Koch-Institut and Bundesamt f\u00fcr Kartographie und Geod\u00e4sie. Robert Koch-Institut: Fallzahlen in Deutschland; 2021. https:\/\/npgeo-corona-npgeo-de.hub.arcgis.com\/datasets\/6d78eb3b86ad4466a8e264aa2e32a2e4_0\/about."},{"key":"pone.0306704.ref033","unstructured":"ARD Tagesschau Online. Chronologie: Drei Jahre Pandemie; 2023. https:\/\/www.tagesschau.de\/inland\/gesellschaft\/corona-pandemie-rueckblick-101.html."},{"key":"pone.0306704.ref034","unstructured":"German Federal Health Ministry (Bundesministerium f\u00fcr Gesundheit). Coronavirus-Pandemie: Was geschah wann?; 2023. https:\/\/www.bundesgesundheitsministerium.de\/coronavirus\/chronik-coronavirus."},{"key":"pone.0306704.ref035","unstructured":"Statistik Berlin-Brandenbug. Schwerpunkt Corona; 2022. https:\/\/www.statistik-berlin-brandenburg.de\/corona."},{"key":"pone.0306704.ref036","unstructured":"Robert-Koch Institut. DIVI Intensivregister (Register of ICU bed occupancy); 2023. https:\/\/github.com\/robert-koch-institut\/Intensivkapazitaeten_und_COVID-19-Intensivbettenbelegung_in_Deutschland."},{"issue":"3","key":"pone.0306704.ref037","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1137\/19M1304891","article-title":"Affine Invariant Interacting Langevin Dynamics for Bayesian Inference","volume":"19","author":"A Garbuno-Inigo","year":"2020","journal-title":"SIAM Journal on Applied Dynamical Systems"},{"issue":"1","key":"pone.0306704.ref038","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1137\/19M1251655","article-title":"Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler","volume":"19","author":"A Garbuno-Inigo","year":"2020","journal-title":"SIAM J Appl Dyn Syst"},{"issue":"2","key":"pone.0306704.ref039","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1137\/19M1303162","article-title":"Fokker\u2013Planck Particle Systems for Bayesian Inference: Computational Approaches","volume":"9","author":"S Reich","year":"2021","journal-title":"SIAM\/ASA Journal on Uncertainty Quantification"},{"issue":"522","key":"pone.0306704.ref040","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1080\/01621459.2017.1294075","article-title":"The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method","volume":"113","author":"A Bouchard-C\u00f4t\u00e9","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"53","key":"pone.0306704.ref041","doi-asserted-by":"crossref","first-page":"2165","DOI":"10.21105\/joss.02165","article-title":"Utopia: A Comprehensive and Collaborative Modeling Framework for Complex and Evolving Systems","volume":"5","author":"L Riedel","year":"2020","journal-title":"Journal of Open Source Software"},{"issue":"52","key":"pone.0306704.ref042","doi-asserted-by":"crossref","first-page":"2316","DOI":"10.21105\/joss.02316","article-title":"dantro: a Python package for handling, transforming, and visualizing hierarchically structured data","volume":"5","author":"Y Sevinchan","year":"2020","journal-title":"Journal of Open Source Software"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0306704","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T18:16:15Z","timestamp":1745000175000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0306704"}},"subtitle":[],"editor":[{"given":"Viswanathan","family":"Arunachalam","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2024,10,17]]},"references-count":42,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10,17]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0306704","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,17]]}}}