Global dynamics of a non-smooth SIV system with uncertain effective vaccine protection rate

Global dynamics of a non-smooth SIV system with uncertain effective vaccine protection rate | 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 Global dynamics of a non-smooth SIV system with uncertain effective vaccine protection rate Dongshu Wang, Shifan Luo, Wenxiu Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2479518/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Apr, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted 3 You are reading this latest preprint version Abstract We analyze a class of SIV system considering effective vaccine protection and protective measures, in which the effective vaccine protection rate is represented by a piecewise-smooth function. This piecewise function is composed of three segments. When the number of infected people exceeds a set threshold, the effective vaccine protection rate is increased based on the first paragraph. To further increase the effective vaccine protection rate to 1, we should take into account not only the influence of the number of infected people, but also the diagonal dividing line of the interaction between the number of infected people and that of vaccinated people. We analyze the global dynamical behavior of the SIV system using the discontinuous differential equation theory, Filippov convex method and other methods, and the theoretical results could provide recommendations for vaccination. Then, in order to achieve the best vaccine protection effect, we analyze the selection of the threshold and the two values of the vaccination effective protection rate using numerical simulation. Filippov system Global dynamics Stability Vaccine protection rate Threshold Full Text Cite Share Download PDF Status: Published Journal Publication published 01 Apr, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted Reviewers agreed at journal 02 Apr, 2023 Editor assigned by journal 22 Mar, 2023 First submitted to journal 07 Mar, 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-2479518","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":188478022,"identity":"fc9f6009-0c43-46bc-aa0a-9addc128021a","order_by":0,"name":"Dongshu Wang","email":"","orcid":"https://orcid.org/0000-0001-9207-1049","institution":"Huaqiao University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dongshu","middleName":"","lastName":"Wang","suffix":""},{"id":188478023,"identity":"74449466-6c2c-439f-827e-36e6afe9ff97","order_by":1,"name":"Shifan Luo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArElEQVRIiWNgGAWjYBACPhBRwcAgx8befoA4LWwg4gwDgzEfz5kE0rQkzpNwMCBSi0Ty4Q8Hau6kt0kwJDD8qNhGjJa0NIkDx57ltkk3HmDsOXObGC05Zswf2A7ntskcSGBmbCNOi/GHA/8Op7NJJBgQrcVA4mDb4QQStPA8S5M42HfYsA0YyAeJ8gs/OyjEvh2Wl29vP/jgRwURWlDAARLVj4JRMApGwSjABQBmXDt0UpMmCwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-2575-8243","institution":"Huaqiao University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Shifan","middleName":"","lastName":"Luo","suffix":""},{"id":188478024,"identity":"73641d51-840f-49d3-baac-f8b11a75fae5","order_by":2,"name":"Wenxiu Li","email":"","orcid":"","institution":"Zhejiang Sci-Tech University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wenxiu","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2023-01-15 03:52:46","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2479518/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2479518/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-024-09499-7","type":"published","date":"2024-04-01T15:00:38+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":54303635,"identity":"d0f11a3c-a50e-42b9-bf1a-345f89aac231","added_by":"auto","created_at":"2024-04-08 15:06:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1808258,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2479518/v1_covered_9f413615-ad76-4a51-8ce3-8b92327bc02f.pdf"}],"financialInterests":"","formattedTitle":"Global dynamics of a non-smooth SIV system with uncertain effective vaccine protection rate","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":true,"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":"Filippov system, Global dynamics, Stability, Vaccine protection rate, Threshold","lastPublishedDoi":"10.21203/rs.3.rs-2479518/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2479518/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We analyze a class of SIV system considering effective vaccine protection and protective measures, in which the effective vaccine protection rate is represented by a piecewise-smooth function. 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