Analysis of a Fractional SIRS Epidemic Model with Diffusion Using the Homotopy Perturbation Sumudu Transform Method

Analysis of a Fractional SIRS Epidemic Model with Diffusion Using the Homotopy Perturbation Sumudu Transform Method | 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 Analysis of a Fractional SIRS Epidemic Model with Diffusion Using the Homotopy Perturbation Sumudu Transform Method Aafrin Gouri, Shivani Sharma, RAVI SHANKER DUBEY, G. L. SAINI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7287004/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Nov, 2025 Read the published version in Fixed Point Theory and Algorithms for Sciences and Engineering → Version 1 posted 17 You are reading this latest preprint version Abstract This research presents a new approach to tackle the fractional SIRS epidemic model, incorporating spatial diffusion and non-linear incidence rates. The SIRS model represents three compartments: susceptible (S), infected (I), and recovered (R), where susceptible individuals can contract the disease from infected ones and later recover. We utilize the Homotopy Perturbation Transform Method (HPTM) combined with the Sumudu transform to propose a solution. The model is analyzed using both Caputo and Caputo-Fabrizio fractional operators to observe solution behavior. Additionally, the existence, uniqueness, and boundedness of the solution are established. Graphical results are provided to demonstrate the behavior of the solutions. The findings highlight the simplicity, accuracy, robustness, and effectiveness of the proposed method, confirming its validity. SIRS epidemic model Sumudu transform method Homo- topy perturbation method Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Nov, 2025 Read the published version in Fixed Point Theory and Algorithms for Sciences and Engineering → Version 1 posted Editorial decision: Revision requested 16 Aug, 2025 Reviews received at journal 16 Aug, 2025 Reviews received at journal 14 Aug, 2025 Reviewers agreed 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 agreed 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 agreed at journal 13 Aug, 2025 Reviewers agreed at journal 13 Aug, 2025 Reviewers invited by journal 13 Aug, 2025 Editor assigned by journal 12 Aug, 2025 Submission checks completed at journal 11 Aug, 2025 First submitted to journal 04 Aug, 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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