The κ-statistics approach to epidemiology

The κ-statistics approach to epidemiology | 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 Research Article The κ-statistics approach to epidemiology Giorgio Kaniadakis, Mauro M. Baldi, Thomas S. Deisboeck, Giulia Grisolia, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-35370/v2 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Nov, 2020 Read the published version in Scientific Reports → Version 2 posted You are reading this latest preprint version Show more versions Abstract A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced κ-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of κ-statistics in fitting empirical data. In this paper, we use κ-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived κ-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the κ-Weibull model has universal features. Thermodynamics and statistical mechanics Applied Statistics Epidemiology Plague Pandemics Epidemics κ-Statistics κ-deformed Weibull survival function Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Full Text Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the latest manuscript can be downloaded and accessed as a PDF. Cite Share Download PDF Status: Published Journal Publication published 16 Nov, 2020 Read the published version in Scientific Reports → Version 2 posted You are reading this latest preprint version Show more versions 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. 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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-35370","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":678953,"identity":"09e17284-d269-4e86-80bc-83af15dacfc8","order_by":1,"name":"Giorgio Kaniadakis","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0003-0379-4435","institution":"Dipartimento Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Giorgio","middleName":"","lastName":"Kaniadakis","suffix":""},{"id":678954,"identity":"4164ab19-4be9-4b69-bf51-662ac033932a","order_by":2,"name":"Mauro M. 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The theoretical curves are based on Eq. (2.20) and Eq.\n(2.11), respectively.","description":"","filename":"Pan11.png","url":"https://assets-eu.researchsquare.com/files/rs-35370/v2/fa91a4800e749163c18e425a.png"},{"id":3513286,"identity":"0c8b1308-a0b0-450f-8ad4-ffd1e41d6e73","added_by":"auto","created_at":"2020-11-11 15:37:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":132367,"visible":true,"origin":"","legend":"Theoretical (continuous curve) and empirical (dots) plots of the probability density function (top left), cumulative\ndistribution function (top right), quantile function (middle left), survival function (middle right), hazard function (bottom left)\nand cumulative hazard function (bottom right) versus time for the Covid-19 mortality data related to China 2020 epidemic.\nThe theoretical curves are based on Eq. (2.12), Eq. (2.11), Eq. (2.20), Eq. (2.7), Eq. (2.15) and Eq. (2.19) respectively.","description":"","filename":"Pan22.png","url":"https://assets-eu.researchsquare.com/files/rs-35370/v2/828d0021464a1db6d150cefc.png"},{"id":3513287,"identity":"dc3b1e50-6e9c-49b3-8813-b2fb8c0d9ced","added_by":"auto","created_at":"2020-11-11 15:37:23","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":159149,"visible":true,"origin":"","legend":"Theoretical (continuous curve) and empirical (dots) plots of the probability density function versus time for the Covid-19 mortality data related to Germany (top left), Italy (top right), Spain (bottom left) and United Kingdom (bottom right)\n2020 pandemic. The theoretical curves are based on Eq. (2.12).","description":"","filename":"Pan51.png","url":"https://assets-eu.researchsquare.com/files/rs-35370/v2/8bc4dc33f5c711cbf086c7eb.png"},{"id":3513288,"identity":"99ff8f4d-474e-4553-88fd-51a76890e96a","added_by":"auto","created_at":"2020-11-11 15:37:23","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":115829,"visible":true,"origin":"","legend":"Theoretical (continuous curve) and empirical (dots) plots of the cumulative distribution function versus time for the\nCovid-19 mortality data related to Germany (top left), Italy (top right), Spain (bottom left) and United Kingdom (bottom\nright) 2020 pandemic. The theoretical curves are based on Eq. (2.11).","description":"","filename":"Pan61.png","url":"https://assets-eu.researchsquare.com/files/rs-35370/v2/b542ce37c289fb18a34f008d.png"},{"id":3513289,"identity":"fdbd8a7b-ae64-4eb4-97f2-e6c07e512a31","added_by":"auto","created_at":"2020-11-11 15:37:23","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":93582,"visible":true,"origin":"","legend":"Theoretical (continuous curve) and empirical (dots) plots of the survival function versus time for the Covid-19 mortality\ndata related to Germany (top left), Italy (top right), Spain (bottom left) and United Kingdom (bottom right) 2020 pandemic.\nThe theoretical curves are based on Eq. (2.7).","description":"","filename":"Pan71.png","url":"https://assets-eu.researchsquare.com/files/rs-35370/v2/52412321fdac20819528fb15.png"},{"id":13554989,"identity":"ed4f7850-2a56-4847-9ed4-8dbf3dfc1e4c","added_by":"auto","created_at":"2021-09-17 02:43:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1114496,"visible":true,"origin":"","legend":"","description":"","filename":"articlerevtex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-35370/v2_covered.pdf"},{"id":13510272,"identity":"b04ccc2c-20d9-4712-8ea2-2819efd9d1a6","added_by":"auto","created_at":"2021-09-16 23:47:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":701426,"visible":true,"origin":"","legend":"","description":"","filename":"ArticleSR.pdf","url":"https://assets-eu.researchsquare.com/files/rs-35370/v1_covered.pdf"},{"id":3513291,"identity":"60ced62a-9fa7-47b1-b091-5c82a148a888","added_by":"auto","created_at":"2020-11-11 15:37:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":817276,"visible":true,"origin":"","legend":"","description":"","filename":"articlerevtex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-35370/v2_stamped.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eThe κ-statistics approach to epidemiology\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the latest manuscript can be downloaded and \u003ca href='/article/rs-35370/latest.pdf' target='_blank'\u003e accessed as a PDF.\u003c/a\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Plague, Pandemics, Epidemics, κ-Statistics, κ-deformed Weibull, survival function","lastPublishedDoi":"10.21203/rs.3.rs-35370/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-35370/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA great variety of complex physical, natural and artificial systems are governed by statistical distributions,\u0026nbsp;which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced κ-statistics framework predicts distribution functions with this feature. A growing number of applications\u0026nbsp;in different fields of investigation are beginning to prove the relevance and effectiveness of κ-statistics in fitting empirical data. In this paper, we use\u0026nbsp;κ-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived κ-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement\u0026nbsp;between theoretical predictions and empirical observations. For these countries\u0026nbsp;we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic\u0026nbsp;are successfully described by the same theoretical model, even though the two events\u0026nbsp;are caused by different diseases and they are separated by more than 600 years, is evidence that the κ-Weibull model has universal features.\u003c/p\u003e","manuscriptTitle":"The κ-statistics approach to epidemiology","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2020-11-11 15:37:22","doi":"10.21203/rs.3.rs-35370/v2","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}},{"code":1,"date":"2020-06-16 21:33:18","doi":"10.21203/rs.3.rs-35370/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":"17e875a6-91ec-434e-98b1-637a6e68e08e","owner":[],"postedDate":"November 11th, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":121689,"name":"Thermodynamics and statistical mechanics"},{"id":121690,"name":"Applied Statistics"},{"id":121691,"name":"Epidemiology"}],"tags":[],"updatedAt":"2021-07-22T02:38:41+00:00","versionOfRecord":{"articleIdentity":"rs-35370","link":"https://doi.org/10.1038/s41598-020-76673-3","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2020-11-17 02:38:41","publishedOnDateReadable":"November 17th, 2020"},"versionCreatedAt":"2020-11-11 15:37:22","video":"","vorDoi":"10.1038/s41598-020-76673-3","vorDoiUrl":"https://doi.org/10.1038/s41598-020-76673-3","workflowStages":[]},"version":"v2","identity":"rs-35370","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-35370","identity":"rs-35370","version":["v2"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}