How re-infections and newborns can change the visible and hidden epidemic dynamics?

How re-infections and newborns can change the visible and hidden epidemic dynamics? | 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 How re-infections and newborns can change the visible and hidden epidemic dynamics? Igor Nesteruk This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6283381/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 A recently proposed model for visible and hidden epidemic dynamics has been generalized to account for the effects of re-infections and newborns. The set of five differential equations and initial conditions contain 13 unknown parameters. The analysis of the equilibrium points, the examples of numerical solutions and comparisons with dynamics of real epidemics are provided. It was shown that equilibriums exist when the influence of re-infections or newborns can be neglected. A stable quasi-equilibrium for the particular case of almost completely hidden epidemics was revealed. Numerical results and comparisons with the COVID-19 epidemic dynamics in Austria and South Korea showed that re-infections, newborns and hidden cases make epidemics endless. The newborns can cause repeating epidemic waves even without re-infections. In particular, numerical simulations of the pertussis epidemic in England in 2023 and 2024 demonstrated that the next epidemic peak is expected in 2031. The proposed model can be recommended for calculations and predictions of visible and hidden numbers of cases, infectious and removed patients. With the use of effective algorithms for parameter identification, the accuracy of method could be rather high. mathematical modeling of infection diseases SIR model hidden epidemic dynamics the COVIV-19 pandemic pertussis epidemic in England Full Text Additional Declarations No competing interests reported. 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-6283381","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":432449716,"identity":"fae6b23a-6233-4850-acc6-6408556ed6ee","order_by":0,"name":"Igor Nesteruk","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYBACNhhDgr2BgZl4LQdAWngOEKmFAa5FIoFILXzSzYc/f6i4lzhz5hvDzwUVNgz87d0J+B0mcyxN4sCZ4sTZ0jnG0jPOpDFInDm7Ab8WiRwzhoNtCYnzpHMMpHnbDjMYSOQS0pL/+cPBf0AtkmeMfxOpJYdB4mBDQuJsCR4zYm1JM5M4cyzBeGZPWpk1z5k0HoJ+kZ+R/PhDRU2C7Izjhzff5qmwkeNv78WvBQlwGIBIHmKVgwD7A1JUj4JRMApGwQgCAJuMRIBHzmZEAAAAAElFTkSuQmCC","orcid":"","institution":"National Academy of Sciences of Ukraine","correspondingAuthor":true,"prefix":"","firstName":"Igor","middleName":"","lastName":"Nesteruk","suffix":""}],"badges":[],"createdAt":"2025-03-22 11:38:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6283381/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6283381/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79484760,"identity":"568a75b2-0cf4-4198-ade3-6d057c8b65f8","added_by":"auto","created_at":"2025-03-29 08:38:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":495464,"visible":true,"origin":"","legend":"","description":"","filename":"simplest3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6283381/v1_covered_99cccea2-b1e7-4525-a77f-0525a5de5d43.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"How re-infections and newborns can change the visible and hidden epidemic dynamics?","fulltext":[],"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":true,"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":"mathematical modeling of infection diseases, SIR model, hidden epidemic dynamics, the COVIV-19 pandemic, pertussis epidemic in England","lastPublishedDoi":"10.21203/rs.3.rs-6283381/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6283381/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A recently proposed model for visible and hidden epidemic dynamics has been generalized to account for the effects of re-infections and newborns. 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