{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T17:13:05Z","timestamp":1790269985237,"version":"4.1.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Pandemics, like the 1918 Spanish Influenza and COVID-19, spread through regions of the World in subsequent waves. Here we propose a consistent picture of the wave pattern based on the epidemic Renormalisation Group (eRG) framework, which is guided by the global symmetries of the system under time rescaling. We show that the rate of spreading of the disease can be interpreted as a time-dilation symmetry, while the final stage of an epidemic episode corresponds to reaching a time scale-invariant state. We find that the endemic period between two waves is a sign of instability in the system, associated to near-breaking of the time scale-invariance. This phenomenon can be described in terms of an eRG model featuring complex fixed points. Our results demonstrate that the key to control the arrival of the next wave of a pandemic is in the strolling period in between waves, i.e. when the number of infections grows linearly. Thus, limiting the virus diffusion in this period is the most effective way to prevent or delay the arrival of the next wave. In this work we establish a new guiding principle for the formulation of mid-term governmental strategies to curb pandemics and avoid recurrent waves of infections, deleterious in terms of human life loss and economic damage.<\/jats:p>","DOI":"10.1038\/s41598-021-85875-2","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T07:04:44Z","timestamp":1616483084000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":80,"title":["Multiwave pandemic dynamics explained: how to tame the next wave of infectious diseases"],"prefix":"10.1038","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3426-1618","authenticated-orcid":false,"given":"Giacomo","family":"Cacciapaglia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Corentin","family":"Cot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Sannino","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"issue":"1","key":"85875_CR1","doi-asserted-by":"publisher","first-page":"69","DOI":"10.32776\/revbiomed.v17i1.440","volume":"17","author":"JK Taubenberger","year":"2006","unstructured":"Taubenberger, J. K. & Morens, D. M. 1918 influenza: The mother of all pandemics. Rev. Biomed. 17(1), 69\u201379 (2006).","journal-title":"Rev. Biomed."},{"key":"85875_CR2","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1098\/rspa.1927.0118","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack, W. O., McKendrick, A. & Walker, G. T. A contribution to the mathematical theory of epidemics. Proc. R. Soc. A 115, 700\u2013721. https:\/\/doi.org\/10.1098\/rspa.1927.0118 (1927).","journal-title":"Proc. R. Soc. A"},{"key":"85875_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.plrev.2015.07.006","volume":"15","author":"Z Wang","year":"2015","unstructured":"Wang, Z., Andrews, M. A., Wu, Z.-X., Wang, L. & Bauch, C. T. Coupled disease-behavior dynamics on complex networks: A review. Phys. Life Rev. 15, 1\u201329. https:\/\/doi.org\/10.1016\/j.plrev.2015.07.006 (2015).","journal-title":"Phys. Life Rev."},{"key":"85875_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2017.05.004","volume":"687","author":"M Perc","year":"2017","unstructured":"Perc, M. et al. Statistical physics of human cooperation. Phys. Rep. 687, 1\u201351. https:\/\/doi.org\/10.1016\/j.physrep.2017.05.004 (2017).","journal-title":"Phys. Rep."},{"key":"85875_CR5","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/j.amc.2018.03.050","volume":"332","author":"X-X Zhan","year":"2018","unstructured":"Zhan, X.-X. et al. Coupling dynamics of epidemic spreading and information diffusion on complex networks. Appl. Math. Comput. 332, 437\u2013448. https:\/\/doi.org\/10.1016\/j.amc.2018.03.050 (2018).","journal-title":"Appl. Math. Comput."},{"key":"85875_CR6","doi-asserted-by":"publisher","first-page":"144","DOI":"10.3389\/fphy.2020.00144","volume":"8","author":"M Della Morte","year":"2020","unstructured":"Della Morte, M., Orlando, D. & Sannino, F. Renormalization group approach to pandemics: The COVID-19 case. Front. Phys. 8, 144. https:\/\/doi.org\/10.3389\/fphy.2020.00144 (2020).","journal-title":"Front. Phys."},{"key":"85875_CR7","doi-asserted-by":"publisher","first-page":"15828","DOI":"10.1038\/s41598-020-72175-4","volume":"10","author":"G Cacciapaglia","year":"2020","unstructured":"Cacciapaglia, G. & Sannino, F. Interplay of social distancing and border restrictions for pandemics via the epidemic Renormalisation Group framework. Sci. Rep. 10, 15828. https:\/\/doi.org\/10.1038\/s41598-020-72175-4 (2020).","journal-title":"Sci. Rep."},{"key":"85875_CR8","doi-asserted-by":"publisher","unstructured":"Cacciapaglia, G. & Sannino, F. Evidence for complex fixed points in pandemic data. https:\/\/doi.org\/10.21203\/rs.3.rs-70238\/v1 (2020).","DOI":"10.21203\/rs.3.rs-70238\/v1"},{"key":"85875_CR9","doi-asserted-by":"publisher","first-page":"127","DOI":"10.3389\/fphy.2020.00127","volume":"8","author":"M Perc","year":"2020","unstructured":"Perc, M., Gori\u0161ek Miksi\u0107, N., Slavinec, M. & Sto\u017eer, A. Forecasting COVID-19. Front. Phys. 8, 127. https:\/\/doi.org\/10.3389\/fphy.2020.00127 (2020).","journal-title":"Front. Phys."},{"key":"85875_CR10","doi-asserted-by":"publisher","first-page":"200780","DOI":"10.1098\/rsos.200780","volume":"7","author":"M-G H\u00e2ncean","year":"2020","unstructured":"H\u00e2ncean, M.-G., Perc, M. & Juergen, L. Early spread of COVID-19 in Romania: Imported cases from Italy and human-to-human transmission networks. R. Soc. Open sci. 7, 200780. https:\/\/doi.org\/10.1098\/rsos.200780 (2020).","journal-title":"R. Soc. 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Lancet Public Health 5(5), E261\u2013E270. https:\/\/doi.org\/10.1016\/S2468-2667(20)30073-6 (2020).","journal-title":"Lancet Public Health"},{"key":"85875_CR18","doi-asserted-by":"publisher","first-page":"13764","DOI":"10.1038\/s41598-020-70631-9","volume":"10","author":"A Scala","year":"2020","unstructured":"Scala, A. et al. Time, space and social interactions: Exit mechanisms for the COVID-19 epidemics. Sci. Rep. 10, 13764. https:\/\/doi.org\/10.1038\/s41598-020-70631-9 (2020).","journal-title":"Sci. Rep."},{"key":"85875_CR19","doi-asserted-by":"publisher","first-page":"4150","DOI":"10.1038\/s41598-021-83441-4","volume":"11","author":"G Cacciapaglia","year":"2020","unstructured":"Cacciapaglia, G., Cot, C. & Sannino, F. Mining Google and Apple mobility data: Temporal anatomy for COVID-19 social distancing. Sci. Rep. 11, 4150. https:\/\/doi.org\/10.1038\/s41598-021-83441-4 (2020).","journal-title":"Sci. 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You better watch out: US COVID-19 wave dynamics versus vaccination strategy (2020)."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-85875-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-85875-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-85875-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,3]],"date-time":"2022-12-03T00:52:09Z","timestamp":1670028729000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-85875-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,23]]},"references-count":22,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["85875"],"URL":"https:\/\/doi.org\/10.1038\/s41598-021-85875-2","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,23]]},"assertion":[{"value":"21 December 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests. All data used in this work are obtained from open-source repositories: Ourworldindata.org, Worldometer.info, Citypopulation.de, Data.gouv.fr, Toyokeizai.net.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"6638"}}