{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:20:47Z","timestamp":1772173247279,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1011757","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T00:00:00Z","timestamp":1704758400000}}],"reference-count":34,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    The most common reported epidemic time series in epidemiological surveillance are the daily or weekly incidence of new cases, the hospital admission count, the ICU admission count, and the death toll, which played such a prominent role in the struggle to monitor the Covid-19 pandemic. We show that pairs of such curves are related to each other by a generalized renewal equation depending on a smooth time varying delay and a smooth ratio generalizing the reproduction number. Such a functional relation is also explored for pairs of simultaneous curves measuring the same indicator in two neighboring countries. Given two such simultaneous time series, we develop, based on a signal processing approach, an efficient numerical method for computing their time varying delay and ratio curves, and we verify that its results are consistent. Indeed, they experimentally verify symmetry and transitivity requirements and we also show, using realistic simulated data, that the method faithfully recovers time delays and ratios. We discuss several real examples where the method seems to display interpretable time delays and ratios. The proposed method generalizes and unifies many recent related attempts to take advantage of the plurality of these health data across regions or countries and time, providing a better understanding of the relationship between them. An implementation of the method is publicly available at the\n                    <jats:italic>EpiInvert<\/jats:italic>\n                    CRAN package.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1011757","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T13:36:27Z","timestamp":1703684187000},"page":"e1011757","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":5,"title":["Time warping between main epidemic time series in epidemiological surveillance"],"prefix":"10.1371","volume":"19","author":[{"given":"Jean-David","family":"Morel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Michel","family":"Morel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6953-9587","authenticated-orcid":true,"given":"Luis","family":"Alvarez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2023,12,27]]},"reference":[{"issue":"5","key":"pcbi.1011757.ref001","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/S2468-2667(23)00079-8","article-title":"Changes in COVID-19-related mortality across key demographic and clinical subgroups in England from 2020 to 2022: a retrospective cohort study using the OpenSAFELY platform","volume":"8","author":"L Nab","year":"2023","journal-title":"The Lancet Public Health"},{"key":"pcbi.1011757.ref002","volume-title":"Solutions of ill-posed problems","author":"AN Tikhonov","year":"1977"},{"issue":"10","key":"pcbi.1011757.ref003","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0257978","article-title":"Understanding an evolving pandemic: An analysis of the clinical time delay distributions of COVID-19 in the United Kingdom","volume":"16","author":"T Ward","year":"2021","journal-title":"PLoS ONE"},{"key":"pcbi.1011757.ref004","doi-asserted-by":"crossref","first-page":"100087","DOI":"10.1016\/j.lanepe.2021.100087","article-title":"Evolution of outcomes for patients hospitalised during the first 9 months of the SARS-CoV-2 pandemic in France: A retrospective national surveillance data analysis","volume":"5","author":"N Lefrancq","year":"2021","journal-title":"Lancet Reg Health Eur"},{"issue":"5","key":"pcbi.1011757.ref005","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1007\/s00134-021-06388-0","article-title":"Evolving changes in mortality of 13,301 critically ill adult patients with COVID-19 over 8 months","volume":"47","author":"P Kurtz","year":"2021","journal-title":"Intensive Care Med"},{"issue":"4","key":"pcbi.1011757.ref006","doi-asserted-by":"crossref","DOI":"10.1001\/jamanetworkopen.2021.6556","article-title":"Mortality Among US Patients Hospitalized With SARS-CoV-2 Infection in 2020","volume":"4","author":"L Finelli","year":"2021","journal-title":"JAMA Netw Open"},{"key":"pcbi.1011757.ref007","doi-asserted-by":"crossref","first-page":"w30105","DOI":"10.4414\/SMW.2021.w30105","article-title":"Evolution of COVID-19 mortality over time: results from the Swiss hospital surveillance system (CH-SUR)","volume":"151","author":"M Roelens","year":"2021","journal-title":"Swiss Med Wkly"},{"key":"pcbi.1011757.ref008","doi-asserted-by":"crossref","first-page":"100243","DOI":"10.1016\/j.lanepe.2021.100243","article-title":"Mortality comparison between the first and second\/third waves among 3,795 critical COVID-19 patients with pneumonia admitted to the ICU: A multicentre retrospective cohort study","volume":"11","author":"R Carbonell","year":"2021","journal-title":"Lancet Reg Health Eur"},{"key":"pcbi.1011757.ref009","doi-asserted-by":"crossref","unstructured":"Keogh EJ, Pazzani MJ. 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