A Hybrid Daubechies Wavelet Collocation Approach for a Fractional-Order SIR Epidemic Model with Delay Effects

A Hybrid Daubechies Wavelet Collocation Approach for a Fractional-Order SIR Epidemic Model with Delay Effects | 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 Article A Hybrid Daubechies Wavelet Collocation Approach for a Fractional-Order SIR Epidemic Model with Delay Effects Nimai Sarkar, Mausumi Sen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7112523/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted 14 You are reading this latest preprint version Abstract This work investigates a fractional-order SIR epidemic model with a discrete delay to describe the short-term transmission dynamics of influenza. The model incorporates memory effects via the Caputo fractional derivative and accounts for biologically motivated delays, such as incubation periods or delayed immune responses. To solve this model, we propose a hybridized collocation method based on the Dubecshi wavelet basis, which effectively handles both the fractional-order nature and the delay structure of the system. The accuracy and robustness of the proposed scheme are assessed through comparison with established numerical methods, including the classical Runge-Kutta method (RK4), the Rational Polynomial Spectral Method of order 7 (RPSM7), the Generalized Wavelet Collocation Method (GWCM), and the Genocchi wavelet method. Numerical simulations clearly demonstrate that our Dubecshi wavelet-based approach yields superior performance in terms of convergence, stability, and the ability to capture both memory and delay effects. Furthermore, it outperforms previously employed techniques by achieving better approximation accuracy with lower computational complexity. Mathematics Subject Classification. 34K37, 65M70, 92D30 Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Fractional-order SIR model Time delay Daubechies wavelets Hybrid collocation method Caputo derivative Epidemic modeling Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 25 Aug, 2025 Reviews received at journal 23 Aug, 2025 Reviews received at journal 23 Aug, 2025 Reviewers agreed at journal 15 Aug, 2025 Reviewers agreed at journal 14 Aug, 2025 Reviews received at journal 13 Aug, 2025 Reviewers agreed at journal 13 Aug, 2025 Reviewers agreed at journal 13 Aug, 2025 Reviewers agreed at journal 13 Aug, 2025 Reviewers invited by journal 13 Aug, 2025 Editor assigned by journal 13 Aug, 2025 Editor invited by journal 07 Aug, 2025 Submission checks completed at journal 16 Jul, 2025 First submitted to journal 16 Jul, 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. 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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-7112523","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":501082801,"identity":"b820d2e4-1251-4b91-b63f-7ec8c3ceaf6b","order_by":0,"name":"Nimai Sarkar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIiWNgGAWjYDACZiBOAGIJBgbGBx8qbIBMxsYDxGphNpxxJg2kpQG/FhgAamGT5m07DObg1WLOzp344cEfu3zJ9rMPpHnOnLdb234YaEuNTTQuLZbNvJslEtuSLWfzpBsYzqm4nbztTCJQy7G03AYcWgwO826QSGxgNpBjSGNIeHPmdrLZAaAWxobD+LRs/pHwp95Ajv8ZwwHetnPJZucfEtSyTSKB7bCBtEQaYyNv2wE7sxuEbdlmkdh23EByxjNmxhlnkhPMbgBtScDnl/NnN9/88afaQOJ8GvuPDxV29mbn0x8++FBjg1MLBkgEq0wgVjkI2JOieBSMglEwCkYGAAAQ92WP0n/N+gAAAABJRU5ErkJggg==","orcid":"","institution":"VIT-AP University","correspondingAuthor":true,"prefix":"","firstName":"Nimai","middleName":"","lastName":"Sarkar","suffix":""},{"id":501082802,"identity":"b71b60a9-eb2b-4c28-b537-f434adbe2bdc","order_by":1,"name":"Mausumi Sen","email":"","orcid":"","institution":"National Institute of Technology Silchar","correspondingAuthor":false,"prefix":"","firstName":"Mausumi","middleName":"","lastName":"Sen","suffix":""}],"badges":[],"createdAt":"2025-07-13 09:53:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7112523/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7112523/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-32483-z","type":"published","date":"2025-12-20T15:57:15+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98814595,"identity":"5b7feedc-68eb-46d6-bc0e-4254c6667926","added_by":"auto","created_at":"2025-12-22 16:12:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1368568,"visible":true,"origin":"","legend":"","description":"","filename":"SPRINGER4SIRMODELDW.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7112523/v1_covered_40de8226-b4ad-4b73-a07b-fc23bbf90707.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Hybrid Daubechies Wavelet Collocation Approach for a Fractional-Order SIR Epidemic Model with Delay Effects","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Fractional-order SIR model, Time delay , Daubechies wavelets, Hybrid collocation method , Caputo derivative, Epidemic modeling","lastPublishedDoi":"10.21203/rs.3.rs-7112523/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7112523/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work investigates a fractional-order SIR epidemic model with a discrete delay to describe the short-term transmission dynamics of influenza. 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