Finite horizon optimal control and invariant measure for a stochastic partial differential equation SIV epidemic model

Finite horizon optimal control and invariant measure for a stochastic partial differential equation SIV epidemic model | 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 Finite horizon optimal control and invariant measure for a stochastic partial differential equation SIV epidemic model Zong Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3341712/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract This paper mainly focuses on the finite horizon optimal control problems of a susceptible- infected-vaccinated(SIV) epidemic system governed by reaction-diffusion equations and Markov switching. Stochastic dynamic programming is employed to find the optimal vaccination effort and economic return for a stochastic reaction diffusion SIV epidemic model. To achieve this, a key step is to show the existence and uniqueness of invariant measure for the model. Then, we obtained the necessary and sufficient conditions for the near-optimal control. Furthermore, we give an algorithm to approximate the Hamilton-Jacobi-Bellman (HJB) equation. Finally, some numerical simulations are presented to confirm our analytic results. Stochastic SIV epidemic model Reaction diffusion Hamilton-Jacobi-Bellman equation Invariant measure Markov chain Full Text Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Reject after review 30 Nov, 2023 Reviewers agreed at journal 28 Oct, 2023 Editor assigned by journal 14 Sep, 2023 First submitted to journal 13 Sep, 2023 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-3341712","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":243716085,"identity":"d14d0031-fe6e-484d-b990-c71b3f21a4c6","order_by":0,"name":"Zong Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIiWNgGAWjYDADfvnDBw58+EGKFskZbIkHZ/aQosXgBo/xYQ42YlQeP3v45Y+KO3Ybbvd8OMzAwyDPL3aAgJYzeWkWEmeeJc+8c3bD4QILBsOZsxPwazE7kGNmYNh2OJnvQO6GwzN4GBIMbhPScv6NmUEiUAvDgZwHh3nYiNFyI8f4wcG2w3YCN3IYiNNif+ONGWPDmcMJkj3HDICBLEHYL5L9OcYff1Qctudnb3784cMPG3l+aQJagIBNAkgkNkA4EgSVgwDzB5ADiVI6CkbBKBgFIxMAAGmDT2nGz/GzAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-9938-0036","institution":"Qingdao University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Zong","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2023-09-10 09:23:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3341712/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3341712/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":45507232,"identity":"611845d0-a907-4376-944d-a63714439f8d","added_by":"auto","created_at":"2023-10-31 04:58:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1287185,"visible":true,"origin":"","legend":"","description":"","filename":"invariantSIV.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3341712/v1_covered_30b19e66-9193-4838-9a4d-514165252966.pdf"}],"financialInterests":"","formattedTitle":"Finite horizon optimal control and invariant measure for a stochastic partial differential equation SIV epidemic model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Stochastic SIV epidemic model, Reaction diffusion, Hamilton-Jacobi-Bellman equation, Invariant measure, Markov chain","lastPublishedDoi":"10.21203/rs.3.rs-3341712/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3341712/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper mainly focuses on the finite horizon optimal control problems of a susceptible- infected-vaccinated(SIV) epidemic system governed by reaction-diffusion equations and Markov switching. 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