Stochastic dual epidemic hypothesis model with Ornstein-Uhlenbeck process: Analysis and numerical simulations with SARS-CoV-2 variants

Stochastic dual epidemic hypothesis model with Ornstein-Uhlenbeck process: Analysis and numerical simulations with SARS-CoV-2 variants | 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 Stochastic dual epidemic hypothesis model with Ornstein-Uhlenbeck process: Analysis and numerical simulations with SARS-CoV-2 variants Zhenfeng Shi, Daqing Jiang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2669967/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Jun, 2024 Read the published version in Journal of Mathematical Analysis and Applications → Version 1 posted You are reading this latest preprint version Abstract As it is widely known, the spread of infectious diseases can result in significant socioeconomic consequences and pose a threat to public health. However, biologically plausible models that incorporate stochastic interference and dual epidemic hypotheses have received limited attention. This paper aims to bridge this gap by examining a stochastic dual epidemic hypothesis model that incorporates Ornstein-Uhlenbeck processes to perturb the nonlinear incidence rate. We provide a rigorous analysis of the model, first proving the existence and uniqueness of global solution. We also analyze sufficient conditions for the extinction or persistence of each disease. Additionally, we establish the existence of an ergodic stationary distribution and derive expressions for the normal distribution followed by the global solution around the endemic equilibrium. Finally, using several numerical experimental examples, we validate our theoretical results with the case of dual variants of SARS-CoV-2 that can simultaneously infect humans. This paper contributes to the understanding of stochastic dual epidemic hypotheses and provides a foundation for future research in this field. Double epidemic hypothesis Ornstein-Uhlenbeck process Extinction Stationary distribution Density function Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 30 Jun, 2024 Read the published version in Journal of Mathematical Analysis and Applications → 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. 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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-2669967","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":181952695,"identity":"525e4b9a-f5a2-41f2-9622-ca3d9ef9e90d","order_by":0,"name":"Zhenfeng Shi","email":"","orcid":"","institution":"Northeast Normal University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhenfeng","middleName":"","lastName":"Shi","suffix":""},{"id":181952696,"identity":"b3b6c979-921a-4113-b646-fadcf63221bd","order_by":1,"name":"Daqing Jiang","email":"data:image/png;base64,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","orcid":"","institution":"China University of Petroleum","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Daqing","middleName":"","lastName":"Jiang","suffix":""}],"badges":[],"createdAt":"2023-03-08 14:29:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2669967/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2669967/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1016/j.jmaa.2024.128232","type":"published","date":"2024-07-01T01:03:15+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":53126979,"identity":"c006b3bf-631f-473b-92f4-c1cda47df7e3","added_by":"auto","created_at":"2024-03-21 01:03:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":861223,"visible":true,"origin":"","legend":"","description":"","filename":"doubleSI1I2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2669967/v1_covered_55388f55-e575-4d1c-a2af-67c0c68ddfb3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Stochastic dual epidemic hypothesis model with Ornstein-Uhlenbeck process: Analysis and numerical simulations with SARS-CoV-2 variants","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Double epidemic hypothesis, Ornstein-Uhlenbeck process, Extinction, Stationary distribution, Density function","lastPublishedDoi":"10.21203/rs.3.rs-2669967/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2669967/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"As it is widely known, the spread of infectious diseases can result in significant socioeconomic consequences and pose a threat to public health. 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