{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T18:10:59Z","timestamp":1773857459206,"version":"3.50.1"},"reference-count":42,"publisher":"AIP Publishing","issue":"10","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,10,1]]},"abstract":"<jats:p>Forecasting epidemic scenarios has been critical to many decision-makers in imposing various public health interventions. Despite progresses in determining the magnitude and timing of epidemics, epidemic peak time predictions for H1N1 and COVID-19 were inaccurate, with the peaks delayed with respect to predictions. Here, we show that infection and recovery rate fluctuations play a critical role in peak timing. Using a susceptible\u2013infected\u2013recovered model with daily fluctuations on control parameters, we show that infection counts follow a lognormal distribution at the beginning of an epidemic wave, similar to price distributions for financial assets. The epidemic peak time of the stochastic solution exhibits an inverse Gaussian probability distribution, fitting the spread of the epidemic peak times observed across Italian regions. We also show that, for a given basic reproduction number R0, the deterministic model anticipates the peak with respect to the most probable and average peak time of the stochastic model. The epidemic peak time distribution allows one for a robust estimation of the epidemic evolution. Considering these results, we believe that the parameters\u2019 dynamical fluctuations are paramount to accurately predict the epidemic peak time and should be introduced in epidemiological models.<\/jats:p>","DOI":"10.1063\/5.0067625","type":"journal-article","created":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T11:38:45Z","timestamp":1635248325000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Delayed epidemic peak caused by infection and recovery rate fluctuations"],"prefix":"10.1063","volume":"31","author":[{"given":"Maxence","family":"Arutkin","sequence":"first","affiliation":[{"name":"UMR CNRS 7083 Gulliver, ESPCI Paris 1 , 10 rue Vauquelin, 75005 Paris,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5001-5698","authenticated-orcid":false,"given":"Davide","family":"Faranda","sequence":"additional","affiliation":[{"name":"Laboratoire des Sciences du Climat et de l\u2019Environnement, CEA Saclay l\u2019Orme des Merisiers, UMR 8212 CEA-CNRS-UVSQ, Universit\u00e9 Paris-Saclay & IPSL 2 , 91191 Gif-sur-Yvette,","place":["France"]},{"name":"London Mathematical Laboratory 3 , 8 Margravine Gardens, London W6 8RH,","place":["United Kingdom"]},{"name":"LMD\/IPSL, Ecole Normale Superieure, PSL Research University 4 , 75005 Paris,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6096-0220","authenticated-orcid":false,"given":"Tommaso","family":"Alberti","sequence":"additional","affiliation":[{"name":"INAF-Istituto di Astrofisica e Planetologia Spaziali 5 , via del Fosso del Cavaliere 100, 00133 Rome,","place":["Italy"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9158-4467","authenticated-orcid":false,"given":"Alexandre","family":"Vall\u00e9e","sequence":"additional","affiliation":[{"name":"Department of Clinical Research and Innovation, Foch hospital 6 , 92150 Suresnes,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2021,10,26]]},"reference":[{"key":"2025100317170308900_c1","volume-title":"The Mathematical Theory of Infectious Diseases and its Applications","year":"1975"},{"key":"2025100317170308900_c2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1741-7015-10-165","article-title":"Real-time numerical forecast of global epidemic spreading: Case study of 2009 A\/H1N1pdm","volume":"10","year":"2012","journal-title":"BMC Med."},{"key":"2025100317170308900_c3","doi-asserted-by":"publisher","first-page":"e16591","DOI":"10.1371\/journal.pone.0016591","article-title":"Human mobility networks, travel restrictions, and the global spread of 2009 H1N1 pandemic","volume":"6","year":"2011","journal-title":"PLoS ONE"},{"key":"2025100317170308900_c4","doi-asserted-by":"publisher","first-page":"20120375","DOI":"10.1098\/rsta.2012.0375","article-title":"Network science","volume":"371","year":"2013","journal-title":"Philos. 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