Epidemic Mean-Field Thresholds of SIS Dynamics on Temporal Multiplex Networks with Activity-Driven Layers

Epidemic Mean-Field Thresholds of SIS Dynamics on Temporal Multiplex Networks with Activity-Driven Layers | 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 Epidemic Mean-Field Thresholds of SIS Dynamics on Temporal Multiplex Networks with Activity-Driven Layers Matin Marjani, Shirshendu Chatterjee, Sharmodeep Bhattacharyya, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8899263/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract We investigate the susceptible--infected--susceptible (SIS) process on a temporal multiplex network where a persistent static layer is overlaid with an activity-driven layer of one-step contacts. Simulations on several random network families (Erd\H{o}s--R\'enyi, Watts--Strogatz, Barab\'asi--Albert) show a clear extinction–persistence transition that shifts systematically as the number of contacts per activation is increased. To explain this behavior, we linearize the dynamics near the disease-free state and replace the random temporal contacts by their mean effect, which produces a simple early-time operator: the static adjacency plus a rank-one, all-to-all mixing term. This leads to a compact mean-field onset rule depending only on the spectral radius of the static layer and on the temporal parameters, and it closely tracks the empirical phase boundary obtained from simulations. Overall, the results indicate that a low-dimensional, simulation-guided approximation is sufficient to relate structural metrics and temporal mixing to measurable epidemic outcomes on heterogeneous networks. SIS dynamics temporal networks activity-driven networks multiplex spectral threshold Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 28 Apr, 2026 Reviews received at journal 26 Apr, 2026 Reviewers agreed at journal 18 Mar, 2026 Reviewers agreed at journal 01 Mar, 2026 Reviewers invited by journal 26 Feb, 2026 Editor assigned by journal 18 Feb, 2026 Submission checks completed at journal 18 Feb, 2026 First submitted to journal 17 Feb, 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. 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-8899263","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599405446,"identity":"d7496e19-a182-4f87-8814-02d7628bffdb","order_by":0,"name":"Matin Marjani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYJCCAyCCsQHI+ABmMhgQ0MCM0HJwBrFaEEweYrTotp8/eLgwxy6fuf3swcM2Z+oSG9ibt0ng02J2Jpnh8MxtyZaNPXkJh3NuHE5s4DlWhl/LAaAW3m3MBowNOQaHcz4cSGyQyDHDr+X8Y5CWegPG/jcGhy0+AB0m/4aAlhtgWw4bMM4A2sJwgxloCw8hLY8NgFqOA7W8MTjYc+awcRtPWrEFfoclPv7Mu63awLA/x/jDj2N1sv3shzfewKcFDgwboAw2opSDgDzRKkfBKBgFo2DEAQB+jVHhUTKKOwAAAABJRU5ErkJggg==","orcid":"","institution":"Kansas State University","correspondingAuthor":true,"prefix":"","firstName":"Matin","middleName":"","lastName":"Marjani","suffix":""},{"id":599405448,"identity":"bd58fdd1-5faa-47a4-b957-ad661c6027dd","order_by":1,"name":"Shirshendu Chatterjee","email":"","orcid":"","institution":"City University of New York","correspondingAuthor":false,"prefix":"","firstName":"Shirshendu","middleName":"","lastName":"Chatterjee","suffix":""},{"id":599405449,"identity":"5b72e853-ab37-4803-be04-a318a581955f","order_by":2,"name":"Sharmodeep Bhattacharyya","email":"","orcid":"","institution":"Oregon State University","correspondingAuthor":false,"prefix":"","firstName":"Sharmodeep","middleName":"","lastName":"Bhattacharyya","suffix":""},{"id":599405454,"identity":"b5b6cd4d-c544-4763-93e4-a22f9b7ca2b5","order_by":3,"name":"Caterina Scoglio","email":"","orcid":"","institution":"Kansas State University","correspondingAuthor":false,"prefix":"","firstName":"Caterina","middleName":"","lastName":"Scoglio","suffix":""}],"badges":[],"createdAt":"2026-02-17 08:54:41","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8899263/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8899263/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104779232,"identity":"05589096-8915-4359-b696-a804d6deabc7","added_by":"auto","created_at":"2026-03-17 07:37:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2021591,"visible":true,"origin":"","legend":"","description":"","filename":"LatexManuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8899263/v1_covered_b54f8bff-db46-4f83-8e60-2449d721cd2a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Epidemic Mean-Field Thresholds of SIS Dynamics on Temporal Multiplex Networks with Activity-Driven Layers","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":"applied-network-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apns","sideBox":"Learn more about [Applied Network Science](http://appliednetsci.springeropen.com/)","snPcode":"41109","submissionUrl":"https://submission.nature.com/new-submission/41109/3","title":"Applied Network Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"SIS dynamics, temporal networks, activity-driven networks, multiplex, spectral threshold","lastPublishedDoi":"10.21203/rs.3.rs-8899263/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8899263/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe investigate the susceptible--infected--susceptible (SIS) process on a temporal multiplex network where a persistent static layer is overlaid with an activity-driven layer of one-step contacts. Simulations on several random network families (Erd\\H{o}s--R\\'enyi, Watts--Strogatz, Barab\\'asi--Albert) show a clear extinction\u0026ndash;persistence transition that shifts systematically as the number of contacts per activation is increased. To explain this behavior, we linearize the dynamics near the disease-free state and replace the random temporal contacts by their mean effect, which produces a simple early-time operator: the static adjacency plus a rank-one, all-to-all mixing term. This leads to a compact mean-field onset rule depending only on the spectral radius of the static layer and on the temporal parameters, and it closely tracks the empirical phase boundary obtained from simulations. 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