{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T03:58:20Z","timestamp":1773287900997,"version":"3.50.1"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"vor","delay-in-days":290,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Toronto\u2019s Emerging and Pandemic Infections Consortium"},{"name":"Institute for Pandemics"},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,31]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We introduce a hierarchical Bayesian framework for reconstructing epidemic curves using under-reported case counts and wastewater data. Our approach models wastewater signals as differentiable Gaussian processes, enabling inference on their relative growth rates, which are used to define a wastewater-based reproduction rate. These estimates are incorporated into a binomially thinned Poisson autoregressive model for case counts using a modular inference strategy. We apply this framework to reconstruct the Covid-19 epidemic curve in Toronto, validating our model through out-of-sample forecasts and comparisons with independent serosurvey-based cumulative incidence estimates. We also apply the framework to New Zealand\u2019s Covid-19 data to reconstruct its epidemic curve and demonstrate improvements over an existing joint model for wastewater and case data. A key advantage of our framework, highlighted in this comparison, is that it does not rely on pre-specified constant parameters, allowing the model to better adapt to evolving pandemic conditions.<\/jats:p>","DOI":"10.1093\/biostatistics\/kxaf033","type":"journal-article","created":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T11:53:56Z","timestamp":1758628436000},"source":"Crossref","is-referenced-by-count":0,"title":["Wastewater-based reproduction rates for epidemic curve reconstruction"],"prefix":"10.1093","volume":"26","author":[{"given":"Emily","family":"Somerset","sequence":"first","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto , 700 University Avenue , Toronto, Ontario, M5G 1Z5,","place":["Canada"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Justin J","family":"Slater","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Guelph , 50 Stone Road East , Guelph, Ontario, N1G 2W1,","place":["Canada"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick E","family":"Brown","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto , 700 University Avenue , Toronto, Ontario, M5G 1Z5,","place":["Canada"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,10,17]]},"reference":[{"key":"2026031108182970200_kxaf033-B1","doi-asserted-by":"crossref","first-page":"e0249090","DOI":"10.1371\/journal.pone.0249090","article-title":"Magnitude of asymptomatic covid-19 cases throughout the course of infection: a systematic review and meta-analysis","volume":"16","author":"Alene","year":"2021","journal-title":"PloS One"},{"key":"2026031108182970200_kxaf033-B2","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1111\/jtsa.12728","article-title":"Count network autoregression","volume":"45","author":"Armillotta","year":"2024","journal-title":"J Time Series Anal"},{"key":"2026031108182970200_kxaf033-B3","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1111\/rssc.12284","article-title":"Stratified space\u2013time infectious disease modelling, with an application to hand, foot and mouth disease in China","volume":"67","author":"Bauer","year":"2018","journal-title":"J R Stat Soc Ser C Appl Stat"},{"key":"2026031108182970200_kxaf033-B4","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1111\/biom.13371","article-title":"A marginal moment matching approach for fitting endemic-epidemic models to underreported disease surveillance counts","volume":"77","author":"Bracher","year":"2021","journal-title":"Biometrics"},{"key":"2026031108182970200_kxaf033-B5","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1016\/j.ijforecast.2020.07.002","article-title":"Endemic-epidemic models with discrete-time serial interval distributions for infectious disease prediction","volume":"38","author":"Bracher","year":"2022","journal-title":"Int J Forecast"},{"key":"2026031108182970200_kxaf033-B6","doi-asserted-by":"crossref","first-page":"e89961. and","DOI":"10.7554\/eLife.89961","article-title":"Hybrid immunity from severe acute respiratory syndrome coronavirus 2 infection and vaccination in Canadian adults: a cohort study","volume":"13","author":"Brown","year":"2024","journal-title":"Elife"},{"key":"2026031108182970200_kxaf033-B7","first-page":"565","article-title":"Endemic-epidemic framework used in covid-19 modelling","volume":"18","author":"Dunbar","year":"2020","journal-title":"REVSTAT-Stat J"},{"key":"2026031108182970200_kxaf033-B8","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1191\/1471082X05st098oa","article-title":"A statistical framework for the analysis of multivariate infectious disease surveillance counts","volume":"5","author":"Held","year":"2005","journal-title":"Stat Modell"},{"key":"2026031108182970200_kxaf033-B9","doi-asserted-by":"crossref","first-page":"118032","DOI":"10.1016\/j.watres.2021.118032","article-title":"Sensitivity of wastewater-based epidemiology for detection of sars-cov-2 RNA in a low prevalence setting","volume":"211","author":"Hewitt Joanne Trowsdale","year":"2022","journal-title":"Water Res"},{"key":"2026031108182970200_kxaf033-B10","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1093\/jrsssc\/qlad011","article-title":"Faecal shedding models for sars-cov-2 RNA among hospitalised patients and implications for wastewater-based epidemiology","volume":"72","author":"Hoffmann","year":"2023","journal-title":"J R Stat Soc Ser C Appl Stat"},{"key":"2026031108182970200_kxaf033-B11","author":"Jacob","year":"2017"},{"key":"2026031108182970200_kxaf033-B12","doi-asserted-by":"crossref","first-page":"2300277","DOI":"10.2807\/1560-7917.ES.2024.29.8.2300277","article-title":"Wastewater-based reproduction numbers and projections of covid-19 cases in three areas in Japan, November 2021 to December 2022","volume":"29","author":"Miyazawa","year":"2024","journal-title":"Eurosurveillance"},{"key":"2026031108182970200_kxaf033-B13","doi-asserted-by":"crossref","first-page":"14384","DOI":"10.1038\/s41598-024-64864-1","article-title":"Estimating the covid-19 prevalence from wastewater","volume":"14","author":"Mohring","year":"2024","journal-title":"Sci Rep"},{"key":"2026031108182970200_kxaf033-B14","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s11222-014-9503-z","article-title":"Cuts in Bayesian graphical models","volume":"25","author":"Plummer","year":"2015","journal-title":"Stat Comput"},{"key":"2026031108182970200_kxaf033-B15","doi-asserted-by":"crossref","first-page":"e056229","DOI":"10.1136\/bmjopen-2021-056229","article-title":"Examining the association between reported covid-19 symptoms and testing for covid-19 in Canada: a cross-sectional survey","volume":"12","author":"Pongou","year":"2022","journal-title":"BMJ Open"},{"key":"2026031108182970200_kxaf033-B16","doi-asserted-by":"crossref","first-page":"154235","DOI":"10.1016\/j.scitotenv.2022.154235","article-title":"Model-based assessment of covid-19 epidemic dynamics by wastewater analysis","volume":"827","author":"Proverbio","year":"2022","journal-title":"Sci Total Environ"},{"key":"2026031108182970200_kxaf033-B17","author":"Public Health Agency of Canada","year":"2024"},{"key":"2026031108182970200_kxaf033-B18","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1038\/s41591-022-01816-0","article-title":"Infectious viral load in unvaccinated and vaccinated individuals infected with ancestral, Delta or omicron sars-cov-2","volume":"28","author":"Puhach","year":"2022","journal-title":"Nat Med"},{"key":"2026031108182970200_kxaf033-B19","first-page":"147","article-title":"Sars-cov-2 viral load and shedding kinetics","volume":"21","author":"Puhach","year":"2023","journal-title":"Nat Rev Microbiol"},{"key":"2026031108182970200_kxaf033-B20","doi-asserted-by":"crossref","first-page":"1561","DOI":"10.1080\/01621459.2021.2001339","article-title":"Regression models for understanding covid-19 epidemic dynamics with incomplete data","volume":"116","author":"Quick","year":"2021","journal-title":"J Am Stat Assoc"},{"key":"2026031108182970200_kxaf033-B21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/16-STS576","article-title":"Penalising model component complexity: a principled, practical approach to constructing priors","volume":"32","author":"Simpson","year":"2017","journal-title":"Statist Sci"},{"key":"2026031108182970200_kxaf033-B22","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1093\/biostatistics\/kxad003","article-title":"A Bayesian approach to estimating covid-19 incidence and infection fatality rates","volume":"25","author":"Slater","year":"2024","journal-title":"Biostatistics"},{"key":"2026031108182970200_kxaf033-B23","author":"Slater","year":"2025"},{"key":"2026031108182970200_kxaf033-B24","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1214\/24-AOAS1914","article-title":"Leveraging cellphone-derived mobility networks to assess covid-19 travel risk","volume":"19","author":"Slater","year":"2025","journal-title":"Ann Appl Stat"},{"key":"2026031108182970200_kxaf033-B25","first-page":"qlae073","author":"Somerset","year":"2024"},{"key":"2026031108182970200_kxaf033-B26","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1080\/10618600.2022.2099403","article-title":"Fast, scalable approximations to posterior distributions in extended latent gaussian models","volume":"32","author":"Stringer","year":"2023","journal-title":"J Comput Graphical Stat"},{"key":"2026031108182970200_kxaf033-B27","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1038\/s43856-024-00570-3","article-title":"Jointly estimating epidemiological dynamics of covid-19 from case and wastewater data in aotearoa New Zealand","volume":"4","author":"Watson","year":"2024","journal-title":"Commun Med (Lond)"},{"key":"2026031108182970200_kxaf033-B28","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1080\/10618600.2023.2289532","article-title":"Model-based smoothing with integrated Wiener processes and overlapping splines","volume":"33","author":"Zhang","year":"2024","journal-title":"J Comput Graphical Stat"}],"container-title":["Biostatistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biostatistics\/article-pdf\/26\/1\/kxaf033\/64740244\/kxaf033.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biostatistics\/article-pdf\/26\/1\/kxaf033\/64740244\/kxaf033.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:18:40Z","timestamp":1773231520000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biostatistics\/article\/doi\/10.1093\/biostatistics\/kxaf033\/8292786"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,31]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,12,31]]}},"URL":"https:\/\/doi.org\/10.1093\/biostatistics\/kxaf033","relation":{},"ISSN":["1468-4357"],"issn-type":[{"value":"1468-4357","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025]]},"published":{"date-parts":[[2024,12,31]]},"article-number":"kxaf033"}}