Global stability to a chemotaxis-May-Nowak model with exposed state

Global stability to a chemotaxis-May-Nowak model with exposed state | 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Global stability to a chemotaxis-May-Nowak model with exposed state Qingshan Zhang, Erhui Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2573514/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Jul, 2023 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted 7 You are reading this latest preprint version Abstract Note: Please see pdf for full abstract with equations. This paper deals with the Neumann initial-boundary value problem for the chemotaxis-May-Nowak model with exposed state for virus dynamics u t = Δu − χ∇ · (u∇v) + κ − d 1 u − βuw, z t = Δz + βuw − (d2 + c)z, v t = Δv + cz − d 3 v, w t = Δw + kv − d 4 w in a smooth bounded domain Ω ⊂ R n (n ≥ 1) . Here χ ∈ R and κ, β, c, k, di (i = 1, 2, 3, 4) are positive constants. We prove that for sufficiently smooth initial data the problem possesses a unique global classical solution which is uniformly bounded with small size of | χ |. Moreover, the large time behavior of the obtained solution is investigated with respect to the basic reproduction number as a threshold. Mathematics Subject Classification (2010). 35A09, 35B40, 35K51, 92C17. chemotaxis-May-Nowak model exposed state global existence virus dynamics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Jul, 2023 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted Editorial decision: Major revision 26 May, 2023 Reviews received at journal 26 May, 2023 Reviewers agreed at journal 14 Feb, 2023 Reviewers invited by journal 13 Feb, 2023 Editor assigned by journal 13 Feb, 2023 Submission checks completed at journal 11 Feb, 2023 First submitted to journal 10 Feb, 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. 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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-2573514","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":175242370,"identity":"6f4c44f6-03ce-4c87-b660-8a5653519493","order_by":0,"name":"Qingshan 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und Physik","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"chemotaxis-May-Nowak model, exposed state, global existence, virus dynamics","lastPublishedDoi":"10.21203/rs.3.rs-2573514/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2573514/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNote: Please see pdf for full abstract with equations.\u003c/p\u003e\n\u003cp\u003eThis paper deals with the Neumann initial-boundary value problem for the chemotaxis-May-Nowak model with exposed state for virus dynamics\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eu\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e = Δu − χ∇ · (u∇v) + κ − d\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eu − βuw,\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e = Δz + βuw − (d2 + c)z,\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e = Δv + cz − d\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003ev,\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e = Δw + kv − d\u003c/em\u003e\u003csub\u003e\u003cem\u003e4\u003c/em\u003e\u003c/sub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003ein a smooth bounded domain \u003cem\u003eΩ ⊂ R\u003c/em\u003e\u003csup\u003e\u003cem\u003en\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e (n ≥ 1)\u003c/em\u003e. Here\u003cem\u003e χ ∈ R\u003c/em\u003e and \u003cem\u003eκ, β, c, k, di (i = 1, 2, 3, 4)\u003c/em\u003e are positive constants. We prove that for sufficiently smooth initial data the problem possesses a unique global classical solution which is uniformly bounded with small size of |\u003cem\u003eχ\u003c/em\u003e|. Moreover, the large time behavior of the obtained solution is investigated with respect to the basic reproduction number as a threshold.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMathematics Subject Classification (2010).\u003c/strong\u003e 35A09, 35B40, 35K51, 92C17.\u003c/p\u003e","manuscriptTitle":"Global stability to a chemotaxis-May-Nowak model with exposed state","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-02-14 23:15:25","doi":"10.21203/rs.3.rs-2573514/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-05-26T12:55:16+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-05-26T12:32:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"eea110ef-6483-467d-ae96-508a14f3e60e","date":"2023-02-14T13:43:38+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-02-14T02:00:15+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-02-13T13:10:21+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-02-11T07:47:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"Zeitschrift für angewandte Mathematik und Physik","date":"2023-02-10T15:00:40+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"zeitschrift-fur-angewandte-mathematik-und-physik","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"zamp","sideBox":"Learn more about [Zeitschrift für angewandte Mathematik und Physik](http://link.springer.com/journal/33)","snPcode":"33","submissionUrl":"https://submission.nature.com/new-submission/33/3","title":"Zeitschrift für angewandte Mathematik und Physik","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"e815faee-17ff-449c-8bbb-53c2eba8e9a4","owner":[],"postedDate":"February 14th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T21:49:41+00:00","versionOfRecord":{"articleIdentity":"rs-2573514","link":"https://doi.org/10.1007/s00033-023-02050-5","journal":{"identity":"zeitschrift-fur-angewandte-mathematik-und-physik","isVorOnly":false,"title":"Zeitschrift für angewandte Mathematik und Physik"},"publishedOn":"2023-07-05 21:32:12","publishedOnDateReadable":"July 5th, 2023"},"versionCreatedAt":"2023-02-14 23:15:25","video":"","vorDoi":"10.1007/s00033-023-02050-5","vorDoiUrl":"https://doi.org/10.1007/s00033-023-02050-5","workflowStages":[]},"version":"v1","identity":"rs-2573514","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2573514","identity":"rs-2573514","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}