Evidence for complex fixed points in pandemic data

Evidence for complex fixed points in pandemic data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Social Sciences - Article Evidence for complex fixed points in pandemic data Giacomo Cacciapaglia, Francesco Sannino This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-70238/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Epidemic data show the existence of a region of quasi-linear growth (strolling period) of infected cases extending in between waves. We demonstrate that this constitutes evidence for the existence of near time-scale invariance that is neatly encoded via complex fixed points in the epidemic Renormalisation Group approach. As a result we achieve a deeper understanding of multiple wave dynamics and its inter-wave strolling regime. Our results are tested and calibrated against the COVID-19 pandemic data. Because of the simplicity of our approach that is organised around symmetry principles our discovery amounts to a paradigm shift in the way epidemiological data are mathematically modelled. Statistical Epidemiology Epidemic data Strolling Period Multiple Wave Dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-70238","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Social Sciences - Article","associatedPublications":[],"authors":[{"id":2088628,"identity":"185d909d-4c5b-4264-aa2d-1bdf93a5d1ab","order_by":0,"name":"Giacomo Cacciapaglia","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-3426-1618","institution":"University of Lyon and CNRS IN2P3","correspondingAuthor":true,"prefix":"","firstName":"Giacomo","middleName":"","lastName":"Cacciapaglia","suffix":""},{"id":2088629,"identity":"03d1e72a-7a5f-42d5-a82a-b19169917431","order_by":1,"name":"Francesco Sannino","email":"","orcid":"","institution":"Centre of excellence for Particle Physics Phenomenology, CP3-Origins","correspondingAuthor":false,"prefix":"","firstName":"Francesco","middleName":"","lastName":"Sannino","suffix":""}],"badges":[],"createdAt":"2020-09-01 14:06:50","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-70238/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-70238/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":2327142,"identity":"17cc6221-ccc0-4618-9b20-ee6cfff0b56c","added_by":"auto","created_at":"2020-09-09 21:51:41","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":190148,"visible":true,"origin":"","legend":"Emergence of the strolling dynamics from the CeRG beta function. Left panel: illustration of the beta function (−|β(α)|) extended to the complex plane, i.e. considering a complex α. The red line represents the trajectory on the real plane, emerging from the real fixed point at α = 0 (red dot): the strolling emerges as the solution slows down when passing between the two complex fixed points (green dots). Right panel: a) beta functions and b) solutions for p = 0.65 and various choices for δ.","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-70238/v1/Figure1.png"},{"id":2327143,"identity":"5af1ca4b-2f0d-4b71-bba0-b95cb03688fd","added_by":"auto","created_at":"2020-09-09 21:51:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":110969,"visible":true,"origin":"","legend":"Fit of the CeRG solutions (red curves) compared to the total number of infected cases (blue dots) adjourned to the 28th of August. For comparison, in dashed green we show the eRG \frst wave \fts obtained in [19], which do not feature the strolling dynamics. The epidemiological data is from www.worldometer.info.\n","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-70238/v1/Figure2.png"},{"id":2327144,"identity":"bf3bbbc1-d72d-472e-9046-91e4e0469459","added_by":"auto","created_at":"2020-09-09 21:51:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":35779,"visible":true,"origin":"","legend":"Fit of the second wave model for France. The parameters we use to draw the red curve are: γ = 1.15, a = 1.6 · 105 = e11.98, ζ = 0.41, p = 0.75, p2 = 1.2. The epidemiological data is from www.worldometer.info.","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-70238/v1/Figure3.png"},{"id":2327145,"identity":"0970fba5-0c8a-493e-987b-e2b458c6006a","added_by":"auto","created_at":"2020-09-09 21:51:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":43719,"visible":true,"origin":"","legend":"Values of ∆tStrolling for p = 0.5, 0.6, 0.7, 0.8, 0.9 and 1.","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-70238/v1/Figure4.png"},{"id":13529496,"identity":"c6742249-641f-4e5e-9e7b-b528c71f110e","added_by":"auto","created_at":"2021-09-17 01:04:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1097137,"visible":true,"origin":"","legend":"Article File","description":"","filename":"natureComplexPandemicfinal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-70238/v1_covered.pdf"},{"id":2327147,"identity":"ad073c5d-08aa-485f-867e-a1d0e99ddaf2","added_by":"auto","created_at":"2020-09-09 21:51:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":992365,"visible":true,"origin":"","legend":"Article File","description":"","filename":"natureComplexPandemicfinal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-70238/v1_stamped.pdf"},{"id":2327146,"identity":"39155f63-596d-46b0-b8e8-5a60e91e9be6","added_by":"auto","created_at":"2020-09-09 21:51:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":914726,"visible":true,"origin":"","legend":"Article File","description":"","filename":"natureComplexPandemicfinal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-70238/v1/natureComplexPandemicfinal.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Evidence for complex fixed points in pandemic data","fulltext":[{"header":"Full Text","content":"\u003cp\u003eThis preprint is available for \u003ca href='/article/rs-70238/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Epidemic data, Strolling Period, Multiple Wave Dynamics","lastPublishedDoi":"10.21203/rs.3.rs-70238/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-70238/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEpidemic data show the existence of a region of quasi-linear growth (strolling period) of infected cases extending in between waves. We demonstrate that this constitutes evidence for the existence of near time-scale invariance that is neatly encoded via complex fixed points in the epidemic Renormalisation Group approach. As a result we achieve a deeper understanding of multiple wave dynamics and its inter-wave strolling regime. Our results are tested and calibrated against the COVID-19 pandemic data. Because of the simplicity of our approach that is organised around symmetry principles our discovery amounts to a paradigm shift in the way epidemiological data are mathematically modelled.\u003c/p\u003e","manuscriptTitle":"Evidence for complex fixed points in pandemic data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2020-09-09 21:51:39","doi":"10.21203/rs.3.rs-70238/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f3a2f643-4e91-4872-a17e-91f12e21e8e6","owner":[],"postedDate":"September 9th, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":475458,"name":"Statistical Epidemiology"}],"tags":[],"updatedAt":"2020-09-09T21:51:39+00:00","versionOfRecord":[],"versionCreatedAt":"2020-09-09 21:51:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-70238","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-70238","identity":"rs-70238","version":["v1"]},"buildId":"J0_U0BvcaRcwD8yVFaRlm","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}