Dynamics analysis of a spatially extended SIS epidemic model with nonlocal disease transmission

Dynamics analysis of a spatially extended SIS epidemic model with nonlocal disease transmission | 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 Dynamics analysis of a spatially extended SIS epidemic model with nonlocal disease transmission Guoxin Zhong, Ruizhi Yang, Yong An This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8453332/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Infectious diseases that permit reinfection, such as various bacterial and viral pathogens, present enduring public health challenges characterized by recurrent outbreaks and complex spatial heterogeneity. To elucidate the mechanisms underlying these dynamics, we develop and analyze a Susceptible-Infectious-Susceptible (SIS) epidemic model with saturating incidence rate and nonlocal disease transmission.We analyze the system across three frameworks: a non-spatial ordinary differential equation (ODE) model, a spatially explicit system with local disease transmission, and a system incorporating nonlocal disease transmission. For the ODE model, bifurcation analysis identifies a Hopf bifurcation, which implies that disease control requires reducing transmission significantly below the outbreak threshold. In the spatially extended model, diffusion-driven Turing instability gives rise to stationary infection patterns, representing the spontaneous emergence of localized endemic hotspots. Furthermore, the inclusion of nonlocal transmission reveals a complex dual role, while the integral averaging effect tends to suppress pattern amplitude, the nonlocal interaction range serves as a critical parameter that can drive the system into spatiotemporal chaos. Overall, the results demonstrate how synergistic infection, behavioral feedback, and heterogeneous transmission pathways interact to produce rich epidemic dynamics, providing a theoretical foundation for understanding reinfection-driven diseases and mechanistic insights for their control. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 20 Apr, 2026 Reviews received at journal 15 Mar, 2026 Reviews received at journal 16 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers invited by journal 07 Jan, 2026 Editor assigned by journal 30 Dec, 2025 Submission checks completed at journal 30 Dec, 2025 First submitted to journal 26 Dec, 2025 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-8453332","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":571261553,"identity":"5b4d2864-3e7e-460b-9881-9f6dcf498ae7","order_by":0,"name":"Guoxin Zhong","email":"","orcid":"","institution":"Northeast Forestry University","correspondingAuthor":false,"prefix":"","firstName":"Guoxin","middleName":"","lastName":"Zhong","suffix":""},{"id":571261554,"identity":"e8957ba8-af64-45af-a399-562aff018f6a","order_by":1,"name":"Ruizhi Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYPACGwYG5gNAmo14LWlA1QmkaTlMghaD42cPv674cz6Pn43HgOFD2WEG/tkNBLScyUuzPMNzu1iyjceAcca5wwwSdw4Q0HIgx8ywQeJ24ob7PQbMvG2HGQwkEghoOf8GqMXgXOL+YzwGzH+J0nIjx/hhQ8KBxA1AvzAzEqNF8sYbM8aGA8mJM46xFRzsOZfOI3GDgBa+8znGHxv+2CX2tzFvfPCjzFqOfwYBLQoHGNgkYJwDQMyDXz0QyDcwMH8gqGoUjIJRMApGNgAARDVFEa+UGPoAAAAASUVORK5CYII=","orcid":"","institution":"Northeast Forestry University","correspondingAuthor":true,"prefix":"","firstName":"Ruizhi","middleName":"","lastName":"Yang","suffix":""},{"id":571261555,"identity":"a1b4a413-f1de-43e7-9751-8fdd4875145c","order_by":2,"name":"Yong An","email":"","orcid":"","institution":"Northeast Forestry University","correspondingAuthor":false,"prefix":"","firstName":"Yong","middleName":"","lastName":"An","suffix":""}],"badges":[],"createdAt":"2025-12-26 08:08:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8453332/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8453332/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99817417,"identity":"a9746c0b-c96b-473a-a16d-8a03c05587bc","added_by":"auto","created_at":"2026-01-08 14:49:20","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4900,"visible":true,"origin":"","legend":"","description":"","filename":"8ab6c39aef2049eea583d644105fb030.json","url":"https://assets-eu.researchsquare.com/files/rs-8453332/v1/a616b5d22aee7cdf53e906c7.json"},{"id":99817474,"identity":"847272bf-10a9-4b53-8046-bae62f36eadf","added_by":"auto","created_at":"2026-01-08 14:49:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10276500,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8453332/v1_covered_4b5fa870-f74a-43d4-bb99-1e9c714cfa8b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamics analysis of a spatially extended SIS epidemic model with nonlocal disease transmission","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":"","lastPublishedDoi":"10.21203/rs.3.rs-8453332/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8453332/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Infectious diseases that permit reinfection, such as various bacterial and viral pathogens, present enduring public health challenges characterized by recurrent outbreaks and complex spatial heterogeneity. 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