{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T13:01:42Z","timestamp":1792155702274,"version":"4.4.0"},"reference-count":49,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T00:00:00Z","timestamp":1712448000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Infectious Disease Modelling"],"published-print":{"date-parts":[[2024,12]]},"DOI":"10.1016\/j.idm.2024.04.002","type":"journal-article","created":{"date-parts":[[2024,5,3]],"date-time":"2024-05-03T16:40:23Z","timestamp":1714754423000},"page":"1224-1249","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant parameters"],"prefix":"10.1016","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9320-6619","authenticated-orcid":false,"given":"Brandon","family":"Robinson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philippe","family":"Bisaillon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jodi D.","family":"Edwards","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5301-1796","authenticated-orcid":false,"given":"Tetyana","family":"Kendzerska","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6579-7127","authenticated-orcid":false,"given":"Mohammad","family":"Khalil","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dominique","family":"Poirel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abhijit","family":"Sarkar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib2","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0244474","article-title":"Tracking R of COVID-19: A new real-time estimation using the Kalman filter","volume":"16","author":"Arroyo-Marioli","year":"2021","journal-title":"PLoS One"},{"issue":"4","key":"10.1016\/j.idm.2024.04.002_bib3","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1061\/(ASCE)0733-9399(2002)128:4(380)","article-title":"Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation","volume":"128","author":"Beck","year":"2002","journal-title":"Journal of Engineering Mechanics"},{"key":"10.1016\/j.idm.2024.04.002_bib4","doi-asserted-by":"crossref","DOI":"10.1016\/j.jsv.2023.118106","article-title":"Robust bayesian state and parameter estimation framework for stochastic dynamical systems with combined time-varying and time-invariant parameters","volume":"575","author":"Bisaillon","year":"2024","journal-title":"Journal of Sound and Vibration"},{"issue":"3","key":"10.1016\/j.idm.2024.04.002_bib5","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1007\/s11071-015-2217-8","article-title":"Bayesian parameter estimation and model selection for strongly nonlinear dynamical systems","volume":"82","author":"Bisaillon","year":"2015","journal-title":"Nonlinear Dynamics"},{"key":"10.1016\/j.idm.2024.04.002_bib6","doi-asserted-by":"crossref","DOI":"10.1016\/j.jsv.2021.116418","article-title":"Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian inference","volume":"522","author":"Bisaillon","year":"2022","journal-title":"Journal of Sound and Vibration"},{"key":"10.1016\/j.idm.2024.04.002_bib7","first-page":"5","volume":"Vol. 2","author":"Bishop","year":"2006"},{"key":"10.1016\/j.idm.2024.04.002_bib8","volume":"Vol. 1945","author":"Brauer","year":"2008"},{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/02331880309257","article-title":"Bayesian filtering: From Kalman filters to particle filters, and beyond","volume":"182","author":"Chen","year":"2003","journal-title":"Statistics"},{"issue":"7","key":"10.1016\/j.idm.2024.04.002_bib10","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1061\/(ASCE)0733-9399(2007)133:7(816)","article-title":"Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging","volume":"133","author":"Ching","year":"2007","journal-title":"Journal of Engineering Mechanics"},{"key":"10.1016\/j.idm.2024.04.002_bib11","series-title":"Kalman filtering","author":"Chui","year":"2017"},{"key":"10.1016\/j.idm.2024.04.002_bib12","series-title":"Implications of heterogeneous SIR models for analyses of COVID-19. Technical report","author":"Ellison","year":"2020"},{"key":"10.1016\/j.idm.2024.04.002_bib13","series-title":"Data assimilation: The ensemble kalman filter","author":"Evensen","year":"2009"},{"issue":"3","key":"10.1016\/j.idm.2024.04.002_bib14","doi-asserted-by":"crossref","DOI":"10.3934\/fods.2021001","article-title":"An international initiative of predicting the SARS-CoV-2 pandemic using ensemble data assimilation","volume":"3","author":"Evensen","year":"2021","journal-title":"Foundations of Data Science"},{"key":"10.1016\/j.idm.2024.04.002_bib15","series-title":"A\u00a0simple SIR model with a large set of asymptomatic infectives","author":"Gaeta","year":"2020"},{"issue":"3","key":"10.1016\/j.idm.2024.04.002_bib16","doi-asserted-by":"crossref","DOI":"10.1126\/sciadv.abg5234","article-title":"Lack of practical identifiability may hamper reliable predictions in COVID-19 epidemic models","volume":"8","author":"Gallo","year":"2022","journal-title":"Science Advances"},{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib19","doi-asserted-by":"crossref","first-page":"4961","DOI":"10.1038\/s41467-020-18190-5","article-title":"The use of mobile phone data to inform analysis of COVID-19 pandemic epidemiology","volume":"11","author":"Grantz","year":"2020","journal-title":"Nature Communications"},{"issue":"4","key":"10.1016\/j.idm.2024.04.002_bib20","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1056\/NEJMp2016822","article-title":"Wrong but useful\u2014what COVID-19 epidemiologic models can and cannot tell us","volume":"383","author":"Holmdahl","year":"2020","journal-title":"New England Journal of Medicine"},{"key":"10.1016\/j.idm.2024.04.002_bib1","series-title":"Stochastic processes and filtering theory","author":"Jazwinski","year":"2007"},{"key":"10.1016\/j.idm.2024.04.002_bib21","author":"Jeffrey"},{"issue":"21\u201322","key":"10.1016\/j.idm.2024.04.002_bib22","doi-asserted-by":"crossref","first-page":"5067","DOI":"10.1016\/j.apm.2014.03.037","article-title":"Threshold behaviour of a stochastic SIR model","volume":"38","author":"Ji","year":"2014","journal-title":"Applied Mathematical Modelling"},{"issue":"9","key":"10.1016\/j.idm.2024.04.002_bib23","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1002\/jhm.12920","article-title":"Trends in all-cause mortality and inpatient and outpatient visits for ambulatory care sensitive conditions during the first year of the COVID-19 pandemic: A population-based study","volume":"17","author":"Kendzerska","year":"2022","journal-title":"Journal of Hospital Medicine"},{"issue":"15","key":"10.1016\/j.idm.2024.04.002_bib24","doi-asserted-by":"crossref","first-page":"3670","DOI":"10.1016\/j.jsv.2013.02.012","article-title":"Probabilistic parameter estimation of a fluttering aeroelastic system in the transitional Reynolds number regime","volume":"332","author":"Khalil","year":"2013","journal-title":"Journal of Sound and Vibration"},{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib25","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s11071-008-9349-z","article-title":"Nonlinear filters for chaotic oscillatory systems","volume":"55","author":"Khalil","year":"2009","journal-title":"Nonlinear Dynamics"},{"issue":"2","key":"10.1016\/j.idm.2024.04.002_bib26","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.jsv.2009.09.009","article-title":"Tracking noisy limit cycle oscillation with nonlinear filters","volume":"329","author":"Khalil","year":"2010","journal-title":"Journal of Sound and Vibration"},{"key":"10.1016\/j.idm.2024.04.002_bib27","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.jsv.2014.10.002","article-title":"The estimation of time-invariant parameters of noisy nonlinear oscillatory systems","volume":"344","author":"Khalil","year":"2015","journal-title":"Journal of Sound and Vibration"},{"issue":"11","key":"10.1016\/j.idm.2024.04.002_bib28","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1080\/10255842.2020.1759560","article-title":"Outbreak dynamics of COVID-19 in Europe and the effect of travel restrictions","volume":"23","author":"Linka","year":"2020","journal-title":"Computer Methods in Biomechanics and Biomedical Engineering"},{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib29","doi-asserted-by":"crossref","first-page":"5891","DOI":"10.1038\/s41598-022-09879-2","article-title":"Modeling time evolving COVID-19 uncertainties with density dependent asymptomatic infections and social reinforcement","volume":"12","author":"Liu","year":"2022","journal-title":"Scientific Reports"},{"key":"10.1016\/j.idm.2024.04.002_bib30","doi-asserted-by":"crossref","DOI":"10.1016\/j.compenvurbsys.2021.101710","article-title":"Associations between mobility and socio-economic indicators vary across the timeline of the COVID-19 pandemic","volume":"91","author":"Long","year":"2022","journal-title":"Computers, Environment and Urban Systems"},{"issue":"2269","key":"10.1016\/j.idm.2024.04.002_bib31","article-title":"Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties","volume":"479","author":"Mamis","year":"2023","journal-title":"Proceedings of the Royal Society A"},{"key":"10.1016\/j.idm.2024.04.002_bib32","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1007\/BF02846028","article-title":"Continuous markov processes and stochastic equations","volume":"4","author":"Maruyama","year":"1955","journal-title":"Rendiconti del Circolo Matematico di Palermo"},{"key":"10.1016\/j.idm.2024.04.002_bib33","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.arcontrol.2020.12.001","article-title":"Structural identifiability and observability of compartmental models of the COVID-19 pandemic","volume":"51","author":"Massonis","year":"2021","journal-title":"Annual Reviews in Control"},{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib34","doi-asserted-by":"crossref","first-page":"4725","DOI":"10.1038\/s41598-021-84055-6","article-title":"Inefficiency of SIR models in forecasting COVID-19 epidemic: A case study of isfahan","volume":"11","author":"Moein","year":"2021","journal-title":"Scientific Reports"},{"key":"10.1016\/j.idm.2024.04.002_bib35","article-title":"Estimation of undetected COVID-19 infections in India","author":"Mukhopadhyay","year":"2020","journal-title":"medRxiv"},{"key":"10.1016\/j.idm.2024.04.002_bib36","series-title":"Machine learning: A probabilistic perspective","author":"Murphy","year":"2012"},{"key":"10.1016\/j.idm.2024.04.002_bib37","first-page":"700","article-title":"A\u00a0contribution to the mathematical theory of epidemics","volume":"Vol. 115","author":"Ogilvy Kermack","year":"1927"},{"issue":"4","key":"10.1016\/j.idm.2024.04.002_bib38","doi-asserted-by":"crossref","first-page":"471","DOI":"10.3390\/epidemiologia2040033","article-title":"Data-driven deep-learning algorithm for asymptomatic COVID-19 model with varying mitigation measures and transmission rate","volume":"2","author":"Olumoyin","year":"2021","journal-title":"Epidemiologia"},{"key":"10.1016\/j.idm.2024.04.002_bib39","series-title":"Numerical solution of stochastic differential equations","first-page":"103","article-title":"Kloeden and eckhard platen. Stochastic differential equations","author":"Peter","year":"1992"},{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12879-020-05737-6","article-title":"Evaluation of undetected cases during the COVID-19 epidemic in Austria","volume":"21","author":"Rippinger","year":"2021","journal-title":"BMC Infectious Diseases"},{"issue":"3","key":"10.1016\/j.idm.2024.04.002_bib41","doi-asserted-by":"crossref","DOI":"10.1136\/bmjopen-2021-052681","article-title":"Comprehensive compartmental model and calibration algorithm for the study of clinical implications of the population-level spread of covid-19: A study protocol","volume":"12","author":"Robinson","year":"2022","journal-title":"BMJ Open"},{"key":"10.1016\/j.idm.2024.04.002_bib42","series-title":"Recursive Bayesian inference on stochastic differential equations","author":"S\u00e4rkk\u00e4","year":"2006"},{"key":"10.1016\/j.idm.2024.04.002_bib43","volume":"ume 3","author":"Shumway","year":"2000"},{"issue":"5","key":"10.1016\/j.idm.2024.04.002_bib44","doi-asserted-by":"crossref","first-page":"2714","DOI":"10.1007\/s10489-020-01948-1","article-title":"Kalman filter based short term prediction model for COVID-19 spread","volume":"51","author":"Singh","year":"2021","journal-title":"Applied Intelligence"},{"key":"10.1016\/j.idm.2024.04.002_bib45","doi-asserted-by":"crossref","DOI":"10.1016\/j.enbuild.2021.110948","article-title":"Modeling hospital energy and economic costs for COVID-19 infection control interventions","volume":"242","author":"Squire","year":"2021","journal-title":"Energy and Buildings"},{"key":"10.1016\/j.idm.2024.04.002_bib46","unstructured":"Statistics Canada. Census Profile, 2021 Census of Population. https:\/\/www12.statcan.gc.ca\/census-recensement\/2021\/dp-pd\/prof\/. Accessed: 2023-August-24."},{"key":"10.1016\/j.idm.2024.04.002_bib47","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2022.114772","article-title":"Analysis of COVID-19 in Japan with extended SEIR model and ensemble Kalman filter","volume":"419","author":"Sun","year":"2023","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"10.1016\/j.idm.2024.04.002_bib48","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.physa.2005.02.057","article-title":"Stability of a stochastic SIR system","volume":"354","author":"Tornatore","year":"2005","journal-title":"Physica A: Statistical Mechanics and Its Applications"},{"key":"10.1016\/j.idm.2024.04.002_bib49","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1007\/s00466-020-01911-4","article-title":"Dynamics identification and forecasting of COVID-19 by switching Kalman filters","volume":"66","author":"Zeng","year":"2020","journal-title":"Computational Mechanics"},{"issue":"1","key":"10.1016\/j.idm.2024.04.002_bib50","doi-asserted-by":"crossref","first-page":"8751","DOI":"10.1038\/s41598-022-12491-z","article-title":"Learning models for forecasting hospital resource utilization for COVID-19 patients in Canada","volume":"12","author":"Zhang","year":"2022","journal-title":"Scientific Reports"},{"issue":"8","key":"10.1016\/j.idm.2024.04.002_bib51","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1016\/j.aml.2013.03.013","article-title":"Stochastic SIR model with jumps","volume":"26","author":"Zhang","year":"2013","journal-title":"Applied Mathematics Letters"}],"container-title":["Infectious Disease Modelling"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S2468042724000563?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S2468042724000563?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T07:58:55Z","timestamp":1726819135000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S2468042724000563"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12]]},"references-count":49,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["S2468042724000563"],"URL":"https:\/\/doi.org\/10.1016\/j.idm.2024.04.002","relation":{},"ISSN":["2468-0427"],"issn-type":[{"value":"2468-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2024,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant parameters","name":"articletitle","label":"Article Title"},{"value":"Infectious Disease Modelling","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.idm.2024.04.002","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2024 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.","name":"copyright","label":"Copyright"}]}}