The influence of virus suppression and delayed immunity mediation on an HIV model with virus-to-cell and cell-to-cell infections

The influence of virus suppression and delayed immunity mediation on an HIV model with virus-to-cell and cell-to-cell infections | 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 The influence of virus suppression and delayed immunity mediation on an HIV model with virus-to-cell and cell-to-cell infections Bing Song, Hao Wu, Long Zhang, Zhidong Teng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9241770/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 14 You are reading this latest preprint version Abstract In this paper, a virus suppressed and delayed immune impairment model is proposed to characterize the immunity mediated HIV infection dynamics, with virus-to-cell and cell-to-cell transmission routes. First, criteria on the existence and globally asymptotical stability of infection-free, immune-free and immune-activated infection equilibria are established. Saddle-node bifurcation on the immune-activated infection equilibrium is further detailedly discussed. Furthermore, criteria on the Hopf bifurcation with both inhibition and delay as bifurcation parameters are obtained either separately or simultaneously by crossing curves. Finally, the theoretical results are demonstrated by numerical simulations. We find that if immune suppression or delay is considered respectively, there would undergo Hopf bifurcation, while the simultaneous effect of both factors may lead to chaos. Meanwhile, the human immune system would become chaotic if the threshold value of virus suppression is always within a certain range, otherwise, the HIV infection would become controllable. Virus suppression Backward bifurcation Saddle-node bifurcation Crossing curves Two-parameter Hopf bifurcation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 12 May, 2026 Reviews received at journal 11 May, 2026 Reviews received at journal 05 May, 2026 Reviews received at journal 05 May, 2026 Reviews received at journal 25 Apr, 2026 Reviewers agreed at journal 15 Apr, 2026 Reviewers agreed at journal 10 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers invited by journal 09 Apr, 2026 Editor assigned by journal 28 Mar, 2026 Submission checks completed at journal 28 Mar, 2026 First submitted to journal 27 Mar, 2026 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. 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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-9241770","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624382364,"identity":"594af193-e26a-4663-8b70-0edde45c1624","order_by":0,"name":"Bing Song","email":"","orcid":"","institution":"Xinjiang University","correspondingAuthor":false,"prefix":"","firstName":"Bing","middleName":"","lastName":"Song","suffix":""},{"id":624382366,"identity":"35ce1a27-3ac4-47d8-8a77-0544109b2a22","order_by":1,"name":"Hao Wu","email":"","orcid":"","institution":"Xinjiang University","correspondingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Wu","suffix":""},{"id":624382367,"identity":"cb5b8652-958c-4086-ac37-d264a626e97f","order_by":2,"name":"Long Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYBACPhDB2ADhGHxgYEggqIUNWYvhDJK1MPMQpYW99/DLnzvs8uQdeAyKbf7Y5BkcYH746AY+LTzn0iwkzyQXGx5gSzDObUsrNjjAZmycg0+LRI6ZgWEbc+LGBuYDxrkNhxM3HOBhkyaoJbGtHqiFscHY4g9xWowfHGw7nDifAWgLAxsxWnjOmDE2th1P3MDAlmDY25aWOPMwAb/ws/cYf/zZVp04v4HHzODHH5vEvuPNDx/j0wJ2G4g0uP+AzQDMZ8avHKzkA4iUb2BgfkBY8SgYBaNgFIxEAAB480vmiFxeUwAAAABJRU5ErkJggg==","orcid":"","institution":"Xinjiang University","correspondingAuthor":true,"prefix":"","firstName":"Long","middleName":"","lastName":"Zhang","suffix":""},{"id":624382368,"identity":"ca07ba0c-85ac-4531-9efe-8de0bc076d43","order_by":3,"name":"Zhidong Teng","email":"","orcid":"","institution":"Xinjiang Medical University","correspondingAuthor":false,"prefix":"","firstName":"Zhidong","middleName":"","lastName":"Teng","suffix":""}],"badges":[],"createdAt":"2026-03-27 07:53:58","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9241770/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9241770/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107481925,"identity":"baa87eda-db3f-4b18-96c3-03d8be446a6b","added_by":"auto","created_at":"2026-04-22 02:20:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1634885,"visible":true,"origin":"","legend":"","description":"","filename":"ND.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9241770/v1_covered_ec675ffd-bab4-4d4e-8857-8d1a6566a728.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The influence of virus suppression and delayed immunity mediation on an HIV model with virus-to-cell and cell-to-cell infections","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":"Virus suppression, Backward bifurcation, Saddle-node bifurcation, Crossing curves, Two-parameter Hopf bifurcation","lastPublishedDoi":"10.21203/rs.3.rs-9241770/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9241770/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, a virus suppressed and delayed immune impairment model is proposed to characterize the immunity mediated HIV infection dynamics, with virus-to-cell and cell-to-cell transmission routes. 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