Fractional-Order Analysis of HIV–TB Co-Infection Model Using Caputo, Atangana–Baleanu–Caputo, and Caputo–Fabrizio Operators with TB Treatment

Fractional-Order Analysis of HIV–TB Co-Infection Model Using Caputo, Atangana–Baleanu–Caputo, and Caputo–Fabrizio Operators with TB Treatment | 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 Fractional-Order Analysis of HIV–TB Co-Infection Model Using Caputo, Atangana–Baleanu–Caputo, and Caputo–Fabrizio Operators with TB Treatment Agbata Benedict Celestine, Mehmet Gümüş, A.K. Awasthi, Homan Emadifar, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7834907/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Feb, 2026 Read the published version in BMC Infectious Diseases → Version 1 posted 16 You are reading this latest preprint version Abstract The global burden of HIV/AIDS-tuberculosis co-infection presents significant public health challenges, particularly in regions with varying levels of treatment accessibility. This study develops and analyzes a novel mathematical model examining the dynamics of HIV/AIDS-tuberculosis co-infection transmission across treated and untreated human populations, while incorporating disease progression through multiple compartments. We investigate the system through three distinct arbitrary-order derivative operators: the Caputo derivative with power law, the Caputo-Fabrizio derivative with non-singular kernel, and the Atangana-Baleanu derivative incorporating the Mittag-Leffler function. The model explicitly considered the impact of treatment accessibility on disease transmission rates, recovery patterns, and intervention effectiveness. Through numerical simulations, we demonstrate that dually infected populations experience significantly higher infection peaks (approximately 8.2 million cases) compared to singly infected populations (approximately 5.8 million cases). Our analysis reveals how varying fractional orders ( Ф = 0.95, 0.85, and 0.75) influence the temporal memory effects and overall disease dynamics. The model parameters, estimated from current epidemiological data and literature, provide insights into the critical role of treatment accessibility in disease mitigation. Surface plots analyzing the basic reproduction number R₀ against various parameters demonstrate the sensitivity of disease spread to contact rates, treatment rates, and accessibility status. These findings emphasize the importance of integrating treatment accessibility measures into public health interventions for effective HIV/AIDS-tuberculosis co-infection control, particularly in vulnerable populations. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 14 Feb, 2026 Read the published version in BMC Infectious Diseases → Version 1 posted Editorial decision: Revision requested 29 Oct, 2025 Reviews received at journal 28 Oct, 2025 Reviews received at journal 25 Oct, 2025 Reviews received at journal 19 Oct, 2025 Reviewers agreed at journal 19 Oct, 2025 Reviewers agreed at journal 16 Oct, 2025 Reviews received at journal 15 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers invited by journal 14 Oct, 2025 Editor invited by journal 14 Oct, 2025 Editor assigned by journal 13 Oct, 2025 Submission checks completed at journal 13 Oct, 2025 First submitted to journal 11 Oct, 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-7834907","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":534566372,"identity":"a652008e-efa0-42aa-bde6-37457123f9ea","order_by":0,"name":"Agbata Benedict Celestine","email":"data:image/png;base64,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","orcid":"","institution":"Confluence University of Science and Technology, Osara, Nigeria.","correspondingAuthor":true,"prefix":"","firstName":"Agbata","middleName":"Benedict","lastName":"Celestine","suffix":""},{"id":534566373,"identity":"d75cc904-fc62-4803-8a20-756388e35254","order_by":1,"name":"Mehmet Gümüş","email":"","orcid":"","institution":"Zonguldak Bülent Ecevit University","correspondingAuthor":false,"prefix":"","firstName":"Mehmet","middleName":"","lastName":"Gümüş","suffix":""},{"id":534566374,"identity":"2a3ac910-b63c-4a55-994f-7dcdb2ed2490","order_by":2,"name":"A.K. 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