Influence of Pro- and Anti-inflammatory Cytokines during Pathogenesis Atherosclerosis: A Dynamical Approach

Influence of Pro- and Anti-inflammatory Cytokines during Pathogenesis Atherosclerosis: A Dynamical Approach | 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 Influence of Pro- and Anti-inflammatory Cytokines during Pathogenesis Atherosclerosis: A Dynamical Approach Asish Adak, Arpita Devi, Praveen Kumar Gupta This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1798253/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 The role of anti-cytokines in atherosclerosis is to reduce the inflammation in the intima. In some situations, certain anti-inflammatory cytokines like TGF-beta and IL-6 have shown the characteristics like a pro-inflammatory cytokines, which are showing different nature. In this study, a dynamical atherosclerosis model is proposed in the form of reaction-diffusion equation with consideration of immune cells, pro-inflammatory cytokines and anti-inflammatory cytokines. The existence and uniqueness is discussed for reaction dynamical system. The three equilibrium points, non-inflammatory, chronic and coexistence, and their local stability are also determined for the model. Bellman and Cooke’s theorem is applied to illustrate the global stability at the coexistence equilibrium point. The effects of pro- and anti-inflammatory cytokines have discussed. The analytical and numerical studies evidently indicate that inflammation behaves differently when a certain amount of anti-inflammatory cytokines will behave like pro-inflammatory cytokines. The numerical simulations are demonstrated for different impact of reduction rate of macrophages due to presence of anti-inflammatory cytokines, inhibition time, and the portion of anti-inflammatory cytokines behaving like pro-inflammatory cytokines through graphically. Reaction-diffusion equation Immune Cells Pro and Anti inflammatory cytokines ox-LDL Bellman-Cooke’s Theorem 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-1798253","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":120450234,"identity":"dfb907fa-2802-479e-a78b-9163411ba17e","order_by":0,"name":"Asish Adak","email":"","orcid":"","institution":"National Institute of Technology Silchar","correspondingAuthor":false,"prefix":"","firstName":"Asish","middleName":"","lastName":"Adak","suffix":""},{"id":120450239,"identity":"e4c38e30-9f77-4e90-a9a9-d8a043dbd82b","order_by":1,"name":"Arpita Devi","email":"","orcid":"","institution":"National Institute of Technology Silchar","correspondingAuthor":false,"prefix":"","firstName":"Arpita","middleName":"","lastName":"Devi","suffix":""},{"id":120450241,"identity":"3cecd292-5b5d-4d56-9e52-8182aa8c1f71","order_by":2,"name":"Praveen Kumar Gupta","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYDACHhglAWR9ALLY2InSksDAwwPUwjgDpIWZSC0MIC3MYA4hLeY8x69JF/6wk7GX7j0mbfNrmzwfMwPjh485uLVY9vaUSc9ISObhkTmXJp3bd9uwjZmBWXLmNtxaDM7zpEnzJDAD/ZJjJp3bc5sRqIWNmZewlnqIFsue2/aEtZxtPwbUchiiheHH7USCWix7zjBbz0g7zsNz54yxZW/D7eQ2ZsZmvH4x50l/eLvAptqefXaP4Y0ff27bzm9vPvjhIz6HMfAYICKCsQ1MNuBWD9bC/gAp7v7gVTwKRsEoGAUjFAAAQM1Gryhmh0kAAAAASUVORK5CYII=","orcid":"","institution":"National Institute of Technology Silchar","correspondingAuthor":true,"prefix":"","firstName":"Praveen","middleName":"Kumar","lastName":"Gupta","suffix":""}],"badges":[],"createdAt":"2022-06-27 05:44:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1798253/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1798253/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":24111000,"identity":"cad615dc-8f1f-43b3-82ec-c8465af1ff06","added_by":"auto","created_at":"2022-07-20 20:13:25","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1106273,"visible":true,"origin":"","legend":"","description":"","filename":"Model27.06.2022Final.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1798253/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Influence of Pro- and Anti-inflammatory Cytokines during Pathogenesis Atherosclerosis: A Dynamical Approach","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1798253/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"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":"Reaction-diffusion equation, Immune Cells, Pro and Anti inflammatory cytokines, ox-LDL, Bellman-Cooke’s Theorem","lastPublishedDoi":"10.21203/rs.3.rs-1798253/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1798253/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe role of anti-cytokines in atherosclerosis is to reduce the inflammation in the intima. In some situations, certain anti-inflammatory cytokines like TGF-beta and IL-6 have shown the characteristics like a pro-inflammatory cytokines, which are showing different nature. In this study, a dynamical atherosclerosis model is proposed in the form of reaction-diffusion equation with consideration of immune cells, pro-inflammatory cytokines and anti-inflammatory cytokines. The existence and uniqueness is discussed for reaction dynamical system. The three equilibrium points, non-inflammatory, chronic and coexistence, and their local stability are also determined for the model. Bellman and Cooke\u0026rsquo;s theorem is applied to illustrate the global stability at the coexistence equilibrium point. The effects of pro- and anti-inflammatory cytokines have discussed. The analytical and numerical studies evidently indicate that inflammation behaves differently when a certain amount of anti-inflammatory cytokines will behave like pro-inflammatory cytokines. 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