Dynamics and Analysis of Dengue Epidemics: A Fractional Order SIR Model with Next-Generation Matrix Methodology

Dynamics and Analysis of Dengue Epidemics: A Fractional Order SIR Model with Next-Generation Matrix Methodology | 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 and Analysis of Dengue Epidemics: A Fractional Order SIR Model with Next-Generation Matrix Methodology Ammar Alsinai, Azmat Ullah Khan Niazi, Easha Ramay, Bilal Ahmed This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3744826/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract One of the major infectious diseases in the world is dengue. Dengue fever, a mosquito-borne viral infection, continues to pose a significant public health threat in tropical and subtropical countries. In this article, we analyze the susceptible-infected-recuperated (SIR) model-based fractional order differential equation of the dengue epidemic system and we analyze of fractional model for the dengue transmission utilizing the new term Human hospitalized. The next-generation matrix methodology is used to obtain the threshold quantity value $R_{0}$, which is comparable to the essential reproduction value. In the case of constant controls, we evaluate the presence and consistency of the disease-free and infectious equilibrium simulation alternatives. The disease-free equilibrium (DFE) point and the endemic equilibrium point's local stability are discussed. We were able to determine that DFE is locally asymptotically stable when $R_{0}1$ by applying the linearization theorem. Numerical simulations are conducted to validate the proposed model against real-world dengue data. For various parameter values of the derivative $\alpha$ order, numerical simulations are provided. The proposed model is validated using published every year (390 millions) dengue cases are reported in world wide. The presented model, it is noted, offers a more accurate means of analyzing the dynamics of the disease dengue. 2010 MSC: 26A33, 34K37. Dengue fever Basic reproduction number Fractional-order SIR model Stability Epidemiology Mathematical modeling Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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-3744826","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":259812848,"identity":"f6ac664a-3206-4c27-9273-33caea25cee7","order_by":0,"name":"Ammar Alsinai","email":"","orcid":"","institution":"Department of Mathematics, Ibb university, Ibb, Yemen","correspondingAuthor":false,"prefix":"","firstName":"Ammar","middleName":"","lastName":"Alsinai","suffix":""},{"id":259812849,"identity":"8b219b11-03ed-46af-a1b2-a7a8fc68d4b8","order_by":1,"name":"Azmat Ullah Khan Niazi","email":"data:image/png;base64,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","orcid":"","institution":"The University of Lahore","correspondingAuthor":true,"prefix":"","firstName":"Azmat","middleName":"Ullah Khan","lastName":"Niazi","suffix":""},{"id":259812850,"identity":"bfc4b5f1-3bff-46e3-9b12-cc28b6461e88","order_by":2,"name":"Easha Ramay","email":"","orcid":"","institution":"The University of Lahore","correspondingAuthor":false,"prefix":"","firstName":"Easha","middleName":"","lastName":"Ramay","suffix":""},{"id":259812851,"identity":"2aba765d-c6f3-4f1e-af2a-4cb3fa250b0b","order_by":3,"name":"Bilal Ahmed","email":"","orcid":"","institution":"University of Science and technology of Fujairah UAE","correspondingAuthor":false,"prefix":"","firstName":"Bilal","middleName":"","lastName":"Ahmed","suffix":""}],"badges":[],"createdAt":"2023-12-12 16:14:20","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-3744826/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-3744826/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51567744,"identity":"2207b5d3-48fb-4b0f-b6b1-467c36fb8bb4","added_by":"auto","created_at":"2024-02-23 20:02:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":620802,"visible":true,"origin":"","legend":"","description":"","filename":"PONEDclean.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3744826/v2_covered_f87e43b9-130e-4d6f-b4a1-40ab76af1d5d.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Dynamics and Analysis of Dengue Epidemics: A Fractional Order SIR Model with Next-Generation Matrix Methodology","fulltext":[],"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":true,"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":"Dengue fever, Basic reproduction number, Fractional-order SIR model, Stability, Epidemiology, Mathematical modeling","lastPublishedDoi":"10.21203/rs.3.rs-3744826/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3744826/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOne of the major infectious diseases in the world is dengue. Dengue fever, a mosquito-borne viral infection, continues to pose a significant public health threat in tropical and subtropical countries. In this article, we analyze the susceptible-infected-recuperated (SIR) model-based fractional order differential equation of the dengue epidemic system and we analyze of fractional model for the dengue transmission utilizing the new term Human hospitalized. The next-generation matrix methodology is used to obtain the threshold quantity value $R_{0}$, which is comparable to the essential reproduction value. In the case of constant controls, we evaluate the presence and consistency of the disease-free and infectious equilibrium simulation alternatives. The disease-free equilibrium (DFE) point and the endemic equilibrium point's local stability are discussed. We were able to determine that DFE is locally asymptotically stable when $R_{0}\u0026lt;1$ and unstable when $R_{0}\u0026gt;1$ by applying the linearization theorem. Numerical simulations are conducted to validate the proposed model against real-world dengue data. For various parameter values of the derivative $\\alpha$ order, numerical simulations are provided. The proposed model is validated using published every year (390 millions) dengue cases are reported in world wide. 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