{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T01:04:40Z","timestamp":1791162280509,"version":"4.1.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010618","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T00:00:00Z","timestamp":1666224000000}}],"reference-count":45,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T00:00:00Z","timestamp":1665360000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"H2020 EpiPose","award":["101003688"],"award-info":[{"award-number":["101003688"]}]},{"name":"H2020 EpiPose","award":["101003688"],"award-info":[{"award-number":["101003688"]}]},{"name":"H2020 EpiPose","award":["101003688"],"award-info":[{"award-number":["101003688"]}]},{"name":"H2020 EpiPose","award":["101003688"],"award-info":[{"award-number":["101003688"]}]},{"name":"H2020 EpiPose","award":["101003688"],"award-info":[{"award-number":["101003688"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"\n In infectious disease epidemiology, the instantaneous reproduction number\n \n \n \n \n \n \n R<\/mml:mi>\n t<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is a time-varying parameter defined as the average number of secondary infections generated by an infected individual at time\n t<\/jats:italic>\n . It is therefore a crucial epidemiological statistic that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool (EpiLPS) for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible intervals of\n \n \n \n \n \n \n R<\/mml:mi>\n t<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of\n \n \n \n \n \n \n R<\/mml:mi>\n t<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n in only a few seconds; and (2) an approach based on a Markov chain Monte Carlo (MCMC) scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a negative binomial distribution to account for potential overdispersion in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a \u201cplug-in\u2019\u2019 estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of\n \n \n \n \n \n \n R<\/mml:mi>\n t<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and on the SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.\n <\/jats:p>","DOI":"10.1371\/journal.pcbi.1010618","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T13:53:27Z","timestamp":1665410007000},"page":"e1010618","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":47,"title":["EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4152-6159","authenticated-orcid":true,"given":"Oswaldo","family":"Gressani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1725-5627","authenticated-orcid":true,"given":"Jacco","family":"Wallinga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5230-6760","authenticated-orcid":true,"given":"Christian L.","family":"Althaus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1881-0637","authenticated-orcid":true,"given":"Niel","family":"Hens","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1878-9869","authenticated-orcid":true,"given":"Christel","family":"Faes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2022,10,10]]},"reference":[{"issue":"4","key":"pcbi.1010618.ref001","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1093\/aje\/kwaa211","article-title":"Statistical estimation of the reproductive number from case notification data","volume":"190","author":"LF White","year":"2021","journal-title":"American Journal of Epidemiology"},{"issue":"12","key":"pcbi.1010618.ref002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1008409","article-title":"Practical considerations for measuring the effective reproductive number, Rt","volume":"16","author":"KM Gostic","year":"2020","journal-title":"PloS Computational Biology"},{"issue":"9","key":"pcbi.1010618.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.1010618.ref004","unstructured":"Cori A. EpiEstim: estimate time varying reproduction numbers from epidemic curves (CRAN); 2021. Available from: https:\/\/cran.r-project.org\/web\/packages\/EpiEstim\/index.html."},{"issue":"9","key":"pcbi.1010618.ref005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1009347","article-title":"Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves","volume":"17","author":"KV Parag","year":"2021","journal-title":"PloS Computational Biology"},{"key":"pcbi.1010618.ref006","author":"S Abbott","year":"2020","journal-title":"EpiNow2: Estimate Real-Time Case Counts and Time-Varying Epidemiological Parameters"},{"issue":"7","key":"pcbi.1010618.ref007","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1002\/sim.6015","article-title":"On the estimation of the reproduction number based on misreported epidemic data","volume":"33","author":"A Azmon","year":"2014","journal-title":"Statistics in Medicine"},{"key":"pcbi.1010618.ref008","article-title":"An approximate Bayesian approach for estimation of the reproduction number under misreported epidemic data","author":"O Gressani","year":"2021","journal-title":"MedRxiv"},{"key":"pcbi.1010618.ref009","unstructured":"Pircalabelu E. 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