Dynamic analysis and optimal control of SOIMR rumor propagation model considering the effect of media reports and time delay

Dynamic analysis and optimal control of SOIMR rumor propagation model considering the effect of media reports and time delay | 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 Dynamic analysis and optimal control of SOIMR rumor propagation model considering the effect of media reports and time delay Ye-Hui Zhou, Hong-xing Yao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6451435/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 Media reports and opposite factors have an important impact on the spread of rumors. When rumors appear on social networks, the media in the relevant departments need time to react before they can make authoritative announcements. The effects of media coverage and time lag on the spread of rumors, as well as the impact of individual rebuttals on the spread of rumors, are considered. This paper proposes a SOIMR (Susceptibility-Opposite-Infection-Media-Remover) model with media coverage and time lag. Firstly, the basic regeneration number and the equilibrium point of the model are obtained. Then, the local asymptotic stability of the equilibrium point of the model is demonstrated. On this basis, the control strategy is further considered, and the optimal control problem of maximizing the scale and control cost of rumor propagation is proposed. Finally, the accuracy of the theoretical results and the influence of different parameters of the model are verified by numerical simulations, the greater the number of rumor opponents, the shorter the time lag of media reports, the greater the influence of media reports, and the more effective the suppression of rumors. Rumor propagation Media report Time delay Optimal control 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. 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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-6451435","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":445309146,"identity":"d6d3899c-04a4-44f5-87e0-d59febfe247a","order_by":0,"name":"Ye-Hui Zhou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYDACCTB5gIGNmbHxAZDFw0e8FvbmZgOQFjaitTDwHG8DswlqkZ/dfEyap+JOYp9EYlvl1xw7GTYG5oePbuDRwjjnWJo0z5lniW1ALbdltyUDHcZmbJyDRwuzRI6ZNG/bYYgWyW3MQC08bNL4tLCBtfyDaCmW3FZPWAsPWEsDUAvPwTbGj9sOE9YiIZGWbDnn2GHjNvbGZmnGbcd52JgJ+EV+RvLBG29qDsvOb2Z/+PHntmp7fvbmh4/xaQEBJh4ogxnMYCagHAQYf6AzRsEoGAWjYBQgAwBkFkVkqjcXJgAAAABJRU5ErkJggg==","orcid":"","institution":"Jiangsu University","correspondingAuthor":true,"prefix":"","firstName":"Ye-Hui","middleName":"","lastName":"Zhou","suffix":""},{"id":445309147,"identity":"ddaa8135-6f1a-4ee6-8206-bcb29c9bd424","order_by":1,"name":"Hong-xing Yao","email":"","orcid":"","institution":"Jiangsu University","correspondingAuthor":false,"prefix":"","firstName":"Hong-xing","middleName":"","lastName":"Yao","suffix":""}],"badges":[],"createdAt":"2025-04-15 06:23:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6451435/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6451435/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81264755,"identity":"e7da3804-e164-4030-80a1-44cfad72f1a0","added_by":"auto","created_at":"2025-04-24 07:17:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7010136,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6451435/v1_covered_b722fe93-4767-450f-900b-df0dc95a019f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamic analysis and optimal control of SOIMR rumor propagation model considering the effect of media reports and time delay","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":"Rumor propagation, Media report, Time delay, Optimal control","lastPublishedDoi":"10.21203/rs.3.rs-6451435/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6451435/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Media reports and opposite factors have an important impact on the spread of rumors. 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