{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:18:19Z","timestamp":1772173099859,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010434","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T00:00:00Z","timestamp":1663113600000}}],"reference-count":21,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T00:00:00Z","timestamp":1661990400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R35GM141821"],"award-info":[{"award-number":["R35GM141821"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>The reproductive number is an important metric that has been widely used to quantify the infectiousness of communicable diseases. The time-varying instantaneous reproductive number is useful for monitoring the real-time dynamics of a disease to inform policy making for disease control. Local estimation of this metric, for instance at a county or city level, allows for more targeted interventions to curb transmission. However, simultaneous estimation of local reproductive numbers must account for potential sources of heterogeneity in these time-varying quantities\u2014a key element of which is human mobility. We develop a statistical method that incorporates human mobility between multiple regions for estimating region-specific instantaneous reproductive numbers. The model also can account for exogenous cases imported from outside of the regions of interest. We propose two approaches to estimate the reproductive numbers, with mobility data used to adjust incidence in the first approach and to inform a formal priori distribution in the second (Bayesian) approach. Through a simulation study, we show that region-specific reproductive numbers can be well estimated if human mobility is reasonably well approximated by available data. We use this approach to estimate the instantaneous reproductive numbers of COVID-19 for 14 counties in Massachusetts using CDC case report data and the human mobility data collected by SafeGraph. We found that, accounting for mobility, our method produces estimates of reproductive numbers that are distinct across counties. In contrast, independent estimation of county-level reproductive numbers tends to produce similar values, as trends in county case-counts for the state are fairly concordant. These approaches can also be used to estimate any heterogeneity in transmission, for instance, age-dependent instantaneous reproductive number estimates. As people are more mobile and interact frequently in ways that permit transmission, it is important to account for this in the estimation of the reproductive number.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010434","type":"journal-article","created":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T14:01:17Z","timestamp":1662040877000},"page":"e1010434","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["Estimation of heterogeneous instantaneous reproduction numbers with application to characterize SARS-CoV-2 transmission in Massachusetts counties"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9424-7826","authenticated-orcid":true,"given":"Zhenwei","family":"Zhou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3376-626X","authenticated-orcid":true,"given":"Eric D.","family":"Kolaczyk","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8545-5212","authenticated-orcid":true,"given":"Robin N.","family":"Thompson","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0588-8235","authenticated-orcid":true,"given":"Laura F.","family":"White","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,9,1]]},"reference":[{"issue":"6","key":"pcbi.1010434.ref001","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1093\/aje\/kwh255","article-title":"Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures","volume":"160","author":"J Wallinga","year":"2004","journal-title":"American Journal of epidemiology"},{"issue":"8","key":"pcbi.1010434.ref002","doi-asserted-by":"crossref","first-page":"e758","DOI":"10.1371\/journal.pone.0000758","article-title":"Estimating individual and household reproduction numbers in an emerging epidemic","volume":"2","author":"C Fraser","year":"2007","journal-title":"PloS one"},{"issue":"9","key":"pcbi.1010434.ref003","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1093\/aje\/kwt133","article-title":"A new framework and software to estimate time-varying reproduction numbers during epidemics","volume":"178","author":"A Cori","year":"2013","journal-title":"American journal of epidemiology"},{"key":"pcbi.1010434.ref004","doi-asserted-by":"crossref","first-page":"100356","DOI":"10.1016\/j.epidem.2019.100356","article-title":"Improved inference of time-varying reproduction numbers during infectious disease outbreaks","volume":"29","author":"R Thompson","year":"2019","journal-title":"Epidemics"},{"key":"pcbi.1010434.ref005","doi-asserted-by":"crossref","first-page":"20210308","DOI":"10.1098\/rsta.2021.0308","article-title":"Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number","volume":"380","author":"R Creswell","year":"2022","journal-title":"Phil. Trans. Roy. Soc. A"},{"issue":"7","key":"pcbi.1010434.ref006","doi-asserted-by":"crossref","first-page":"e1009210","DOI":"10.1371\/journal.pcbi.1009210","article-title":"Bayesian back-calculation and nowcasting for line list data during the COVID-19 pandemic","volume":"17","author":"T Li","year":"2021","journal-title":"PLoS computational biology"},{"issue":"3","key":"pcbi.1010434.ref007","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1002\/bimj.202000112","article-title":"Nowcasting the COVID-19 pandemic in Bavaria","volume":"63","author":"F G\u00fcnther","year":"2021","journal-title":"Biometrical Journal"},{"key":"pcbi.1010434.ref008","doi-asserted-by":"crossref","unstructured":"Martinez de Salazar P, Lu F, Hay J, Gomez-Barroso D, Fernandez-Navarro P, Martinez E, et al. Near real-time surveillance of the SARS-CoV-2 epidemic with incomplete data. 2021;.","DOI":"10.1101\/2021.01.25.20230094"},{"key":"pcbi.1010434.ref009","article-title":"The impact of changes in diagnostic testing practices on estimates of COVID-19 transmission in the United States","author":"VE Pitzer","year":"2020","journal-title":"MedRxiv"},{"issue":"1","key":"pcbi.1010434.ref010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1476-072X-12-35","article-title":"Estimating the reproductive number in the presence of spatial heterogeneity of transmission patterns","volume":"12","author":"LF White","year":"2013","journal-title":"International journal of health geographics"},{"issue":"6526","key":"pcbi.1010434.ref011","article-title":"Transmission heterogeneities, kinetics, and controllability of SARS-CoV-2","volume":"371","author":"K Sun","year":"2021","journal-title":"Science"},{"issue":"1","key":"pcbi.1010434.ref012","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1073\/pnas.94.1.338","article-title":"Heterogeneities in the transmission of infectious agents: implications for the design of control programs","volume":"94","author":"ME Woolhouse","year":"1997","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"10","key":"pcbi.1010434.ref013","doi-asserted-by":"crossref","first-page":"3705","DOI":"10.3390\/ijerph17103705","article-title":"Evaluating transmission heterogeneity and super-spreading event of COVID-19 in a metropolis of China","volume":"17","author":"Y Zhang","year":"2020","journal-title":"International journal of environmental research and public health"},{"key":"pcbi.1010434.ref014","article-title":"Socioeconomic Disparities in Subway Use and COVID-19 Outcomes in New York City","author":"KTL Sy","year":"2020","journal-title":"American Journal of Epidemiology"},{"issue":"25","key":"pcbi.1010434.ref015","doi-asserted-by":"crossref","first-page":"E684","DOI":"10.1503\/cmaj.201112","article-title":"Understanding heterogeneity to inform the public health response to COVID-19 in Canada","volume":"192","author":"S Mishra","year":"2020","journal-title":"CMAJ"},{"key":"pcbi.1010434.ref016","unstructured":"CDC. Centers for Disease Control and Prevention, COVID-19 Response. COVID-19 Case Surveillance Data Access, Summary, and Limitations (version date: December 31, 2020); 2021. https:\/\/data.cdc.gov\/Case-Surveillance\/COVID-19-Case-Surveillance-Public-Use-Data\/vbim-akqf."},{"key":"pcbi.1010434.ref017","first-page":"1","article-title":"Multiscale Dynamic Human Mobility Flow Dataset in the U.S. during the COVID-19 Epidemic","author":"Y Kang","year":"2020","journal-title":"Scientific Data"},{"key":"pcbi.1010434.ref018","unstructured":"SafeGraph. The impact of coronavirus (COVID-19) on foot traffic; 2020. Available from: https:\/\/www.safegraph.com\/dashboard\/covid19-commercepatterns."},{"key":"pcbi.1010434.ref019","unstructured":"Mishra. On the derivation of the renewal equation from an age-dependent branching process: an epidemic modelling perspective. arXiv preprint arXiv:200616487. 2020;."},{"key":"pcbi.1010434.ref020","article-title":"Evolving epidemiology of novel coronavirus diseases 2019 and possible interruption of local transmission outside Hubei Province in China: a descriptive and modeling study","author":"J Zhang","year":"2020","journal-title":"MedRxiv"},{"issue":"3","key":"pcbi.1010434.ref021","doi-asserted-by":"crossref","first-page":"e74","DOI":"10.1371\/journal.pmed.0050074","article-title":"Social contacts and mixing patterns relevant to the spread of infectious diseases","volume":"5","author":"J Mossong","year":"2008","journal-title":"PLoS medicine"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1010434","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T00:00:00Z","timestamp":1663113600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010434","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T14:04:32Z","timestamp":1663164272000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010434"}},"subtitle":[],"editor":[{"given":"Joseph T.","family":"Wu","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,9,1]]},"references-count":21,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9,1]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1010434","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2021.12.02.21267164","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,1]]}}}