Analysis of a nonlinear perturbed HLIV model with viral production and multiple latent stages

Analysis of a nonlinear perturbed HLIV model with viral production and multiple latent stages | 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 Analysis of a nonlinear perturbed HLIV model with viral production and multiple latent stages Qun Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1939620/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 In this paper, we establish and analyze a nonlinear stochastically perturbed HLIV model with viral production and multiple latent stages, which is described by a series of stochastic differential equations with nonlinear perturbations. Firstly, we prove that there exists a unique global positive solution to the proposed model for any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system. Especially, under some mild conditions which are used to ensure the existence and local asymptotic stability of the endemic equilibrium of the deterministic system, we obtain the exact expression of the probability density around the endemic equilibrium of the deterministic system. In addition, we build up sufficient criteria for wiping out of the infected cells and free viruses. Finally, numerical simulations are performed to illustrate our theoretical findings. HLIV model Multiple latent stages Nonlinear perturbations Stationary distribution Ergodicity Probability density Extinction. 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. 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-1939620","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":127526542,"identity":"be30af41-8202-40dc-8e40-440c3d5c48a7","order_by":0,"name":"Qun Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYBACPmYwJVHPxt7Y+OCDgY0dQS1sEC0WCXw8hw8bzihISyasBUJVJMhJuKVJ83w4xNhAUAs7j+Ft3h0SeWwSPMbGNgYHmBnYDx/dgN9hPMbWvGckitmkewwf5xjc4WPgSUu7QUCLmTRvmwRjm8wZY+Mcg2fMDBI8ZkRqkcgxk7YwOMzYQKyWxDaJtDRpBuK0sBVbzm2TMGYDBXKPQVoyGyG/8PMf3njjbVudnHw7MCp//LGx42c/fAyvFhCQQLWXkHJMLaNgFIyCUTAK0AEATnQ9qdaLqVQAAAAASUVORK5CYII=","orcid":"","institution":"Northeast Normal University","correspondingAuthor":true,"prefix":"","firstName":"Qun","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2022-08-08 05:14:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1939620/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1939620/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":26839990,"identity":"82920c26-3f71-4be1-b3da-5c6712c2ffd0","added_by":"auto","created_at":"2022-09-22 18:29:25","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":661407,"visible":true,"origin":"","legend":"","description":"","filename":"HLIVmodel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1939620/v1_covered.pdf"},{"id":25096783,"identity":"8b72c3e2-d0f5-40c5-b4fb-f67ccfbd0cee","added_by":"auto","created_at":"2022-08-11 16:36:08","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":661515,"visible":true,"origin":"","legend":"","description":"","filename":"HLIVmodel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1939620/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analysis of a nonlinear perturbed HLIV model with viral production and multiple latent stages","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1939620/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":"HLIV model, Multiple latent stages, Nonlinear perturbations, Stationary distribution, Ergodicity, Probability density, Extinction.","lastPublishedDoi":"10.21203/rs.3.rs-1939620/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1939620/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, we establish and analyze a nonlinear stochastically perturbed HLIV model with viral production and multiple latent stages, which is described by a series of stochastic differential equations with nonlinear perturbations. 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