{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:56:02Z","timestamp":1787327762915,"version":"build-2736575974"},"reference-count":61,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T00:00:00Z","timestamp":1743379200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>Due to its various uses, the dynamical system is a significant research area in the field of mathematical biology. The model is first developed by applying the usual derivative with combined recovery measures of humans as well as animals for leptospirosis transmission and then converted into a generalized form of the fractal fractional sense with power law kernel, exponential law kernel, and Mittag-Leffler kernel. We verify all the fundamental characteristics of the newly developed model for the validation analysis of the system such as equilibrium points, local stability, positivity of solutions, reproductive number, and existence of a unique solution. Also, bifurcation analysis has been used for newly developed systems to observe the impact of each sub-compartment with the effect of different parameters. The results on Hyers Ulam stability are established by utilizing different kernels to observe its stable state. We used a numerical scheme based on the Lagrange polynomials for all three cases of fractal fractional derivatives having different kernels. The efficiency of the fractional operators with comparative analysis of different kernels is shown in simulation form to verify the validity and real behavior of leptospirosis transmission for humans as well as animals. he graphical explanation of our model\u2019s solution depicts the effectiveness of our techniques applied and this study helps for future predictions and developing better control strategies.<\/jats:p>","DOI":"10.1371\/journal.pone.0314095","type":"journal-article","created":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T20:16:26Z","timestamp":1743452186000},"page":"e0314095","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hyers Ulam stability and bifurcation control of leptospirosis disease dynamics and preventations: Modeling with singular and non-singular kernels"],"prefix":"10.1371","volume":"20","author":[{"given":"Muhammad","family":"Farman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7754-9355","authenticated-orcid":true,"given":"Aqeel","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Usama","family":"Atta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdul","family":"Ghaffar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2025,3,31]]},"reference":[{"key":"pone.0314095.ref001","doi-asserted-by":"crossref","first-page":"102173","DOI":"10.1016\/j.inffus.2023.102173","article-title":"Analysis of the influence of trust in opposing opinions: an inclusiveness-degree based Signed Deffuant\u2013Weisbush model","volume":"104","author":"B Jiang","year":"2024","journal-title":"Inf Fusion"},{"key":"pone.0314095.ref002","article-title":"The mathematics of diseases","volume":"14","author":"M Keeling","year":"2001","journal-title":"Plus Magaz."},{"key":"pone.0314095.ref003","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvcm4gk0","article-title":"Modeling infectious diseases in humans and animals","author":"MJ Keeling","year":"2011"},{"issue":"2","key":"pone.0314095.ref004","first-page":"123","article-title":"Leptospirosis, an emerging zoonotic disease in Malaysia","volume":"35","author":"S Thayaparan","year":"2013","journal-title":"Malays J Pathol."},{"issue":"7","key":"pone.0314095.ref005","doi-asserted-by":"crossref","first-page":"2300266","DOI":"10.2807\/1560-7917.ES.2024.29.7.2300266","article-title":"Epidemiology of reported cases of leptospirosis in the EU\/EEA, 2010 to 2021","volume":"29","author":"J Beaut\u00e9","year":"2024","journal-title":"Euro Surveill"},{"key":"pone.0314095.ref006","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/j.ins.2022.11.101","article-title":"On the role of community structure in evolution of opinion formation: a new bounded confidence opinion dynamics","volume":"621","author":"Y Peng","year":"2023","journal-title":"Inf Sci"},{"key":"pone.0314095.ref007","doi-asserted-by":"crossref","first-page":"121292","DOI":"10.1016\/j.eswa.2023.121292","article-title":"Opinion formation analysis for Expressed and Private Opinions (EPOs) models: reasoning private opinions from behaviors in group decision-making systems","volume":"236","author":"J Dong","year":"2024","journal-title":"Exp Syst Appl"},{"issue":"4","key":"pone.0314095.ref008","doi-asserted-by":"crossref","first-page":"61","DOI":"10.5495\/wjcid.v6.i4.61","article-title":"Leptospirosis: a clinical review of evidence based diagnosis, treatment and prevention","volume":"6","author":"AB Lane","year":"2016","journal-title":"WJCID"},{"issue":"3","key":"pone.0314095.ref009","first-page":"457","article-title":"Leptospirosis: transmission, diagnosis and prevention","volume":"15","author":"W Al-orry","year":"2016","journal-title":"Int J Innov Appl Stud."},{"key":"pone.0314095.ref010","first-page":"3","article-title":"Introduction to fractional calculus with brief historical background. 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