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Given the susceptibility of epidemic spread to environmental noise and its intricate dynamics, an adaptive sliding mode controller based on an integral sliding surface and an adaptive control law is proposed. This controller is capable of stabilizing the constructed model and effectively suppressing the spread of the disease. The main contributions of this paper include the following: establishing a comprehensive and realistic stochastic SIR model that accounts for the complex impacts of telegraph noise (symbolizing periodic environmental changes) and L\u00e9vy noise (representing sudden environmental shocks) on the dynamics of disease transmission; employing T-S fuzzy modeling, which considers the design of fuzzy rules and the symmetry of membership functions, to ensure linearization of the model; constructing an integral sliding surface and designing an adaptive sliding mode controller for the fuzzy-processed model. Finally, the effectiveness of the proposed control method is validated through numerical simulations.<\/jats:p>","DOI":"10.3390\/sym17060963","type":"journal-article","created":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T11:53:14Z","timestamp":1750161194000},"page":"963","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sliding Mode Control for Stochastic SIR Models with Telegraph and L\u00e9vy Noise: Theory and Applications"],"prefix":"10.3390","volume":"17","author":[{"given":"Lu","family":"Liu","sequence":"first","affiliation":[{"name":"Faculty of Science, Shenyang University of Technology, Shenyang 110142, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4211-1601","authenticated-orcid":false,"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Faculty of Science, Shenyang University of Technology, Shenyang 110142, China"}]},{"given":"Yufeng","family":"Tian","sequence":"additional","affiliation":[{"name":"College of Automation, Chongqing University, Chongqing 400044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3575-617X","authenticated-orcid":false,"given":"Dapeng","family":"Wei","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Generic Technology and System of Service Robots, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China"}]},{"given":"Zhanjun","family":"Huang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Aircraft Configuration Design, School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1007\/s11019-020-09971-2","article-title":"COVID-19 and the ethics of quarantine: A lesson from the Eyam plague","volume":"23","author":"Spitale","year":"2020","journal-title":"Med. 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B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s11071-020-05929-4","article-title":"Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: Application to COVID-19 pandemic","volume":"102","author":"Khyar","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.aej.2020.08.040","article-title":"On global dynamics of COVID-19 by using SQIR type model under non-linear saturated incidence rate","volume":"60","author":"Algehyne","year":"2021","journal-title":"Alex. Eng. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1638571","DOI":"10.1155\/2022\/1638571","article-title":"A Numerical and Analytical Study of a Stochastic Epidemic SIR Model in the Light of White Noise","volume":"2022","author":"Hussain","year":"2022","journal-title":"Adv. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Geng, J., Wang, Y., Liu, Y., and Yan, J. (2023). Analysis of an avian influenza model with Allee effect and stochasticity. Int. J. Biomath., 16.","DOI":"10.1142\/S179352452250111X"},{"key":"ref_12","first-page":"127329","article-title":"A stochastic SIQR epidemic model with Levy jumps and three-time delays","volume":"431","author":"Zhang","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1186\/s13662-021-03396-8","article-title":"Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion","volume":"2021","author":"Tesfay","year":"2021","journal-title":"Adv. Differ. Equ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"109881","DOI":"10.1016\/j.automatica.2021.109881","article-title":"A Markovian regime-switching stochastic hybrid time-delayed epidemic model with vaccination","volume":"133","author":"Boukanjime","year":"2021","journal-title":"Automatica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"113017","DOI":"10.1016\/j.chaos.2022.113017","article-title":"Epidemic threshold and ergodicity of an SEIR model with vertical transmission under the telegraph noise","volume":"167","author":"Lan","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3209","DOI":"10.1007\/s11071-020-05742-z","article-title":"Sliding mode control for uncertain active vehicle suspension systems: An event-triggered H?T control scheme","volume":"103","author":"Yang","year":"2021","journal-title":"Nonlinear Dyn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"104763","DOI":"10.1016\/j.conengprac.2021.104763","article-title":"Robust path tracking of a quadrotor using adaptive fuzzy terminal sliding mode control","volume":"110","author":"Nekoukar","year":"2021","journal-title":"Control Eng. Pract."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"104764","DOI":"10.1155\/2014\/104764","article-title":"Robust sliding control of SEIR epidemic models","volume":"103","author":"Ibeas","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Teklu, S.W. (2024). Impacts of optimal control strategies on the HBV and COVID-19 co-epidemic spreading dynamics. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-55111-8"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"9709","DOI":"10.3934\/mbe.2022451","article-title":"T-S fuzzy observer-based adaptive tracking control for biological system with stage structure","volume":"19","author":"Zhang","year":"2022","journal-title":"Math. Biosci. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.automatica.2015.11.007","article-title":"Observer-based adaptive sliding mode control for nonlinear Markovian jump systems","volume":"64","author":"Li","year":"2016","journal-title":"Automatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/41.184818","article-title":"Sliding mode control design principles and applications to electric drives","volume":"40","author":"Utkin","year":"2002","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1007\/s11071-015-2059-4","article-title":"Synchronization of delayed neural networks with Levy noise and Markovian switching via sampled data","volume":"81","author":"Yang","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1007\/s00034-023-02520-1","article-title":"Dissipative filtering of markovian jumping systems via adaptive sliding mode control","volume":"43","author":"Zhai","year":"2023","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3594","DOI":"10.1109\/TFUZZ.2018.2838552","article-title":"A novel robust fuzzy integral sliding mode control for nonlinear semi-Markovian jump T-S fuzzy systems","volume":"26","author":"Jiang","year":"2018","journal-title":"IEEE Trans. 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