Mathematical Modelling of Dengue Transmission with Adaptive Fuzzy Backstepping Control and RK-5 Numerical Method

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dc.contributor.authorG. M. Vijayalakshmi
dc.contributor.authorM. Ariyanatchi
dc.contributor.authorAli Akgül
dc.date.accessioned2025-05-13T06:19:38Z
dc.date.available2025-05-13T06:19:38Z
dc.date.issued2025-04-25
dc.departmentFakülteler, Fen-Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractThe aim of this research is to create an adaptive nonlinear fuzzy backstepping robust controller for a dengue disease outbreak model. We use an SIR-SI compartmental mathematical model to analyse the diffusion mechanism of dengue disease. A nonlinear adaptive controller regulates prevention strategies for susceptible human beings and enhances hospitalization-based treatment for the infected people. Besides, the spraying of chemical insecticides will reduce the infected mosquito population. Adaptation laws are used to derive fuzzy system parameters, enhancing the system's adaptability. Then we construct a suitable Lyapunov function, which guarantees convergence, robustness, and stability for a closed-loop system. Finally, we plot all the system's control variables graphically and calculate their numerical approximations using the Runge–Kutta technique of fifth order. These simulations demonstrate that the proposed adaptive controllers can effectively control the dengue disease and ensure the stability of the system. Hence, we conclude that adaptive backstepping control measures can protect more people from dengue infection.
dc.identifier.citationVijayalakshmi, G. M., Ariyanatchi, M., & Akgül, A. (2025). Mathematical Modelling of Dengue Transmission with Adaptive Fuzzy Backstepping Control and RK-5 Numerical Method. International Journal of Applied and Computational Mathematics, 11(3), 1-29.
dc.identifier.doi10.1007/s40819-025-01889-8
dc.identifier.issn2349-5103
dc.identifier.issn2199-5796
dc.identifier.issue3
dc.identifier.scopus2-s2.0-105003823775
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1007/s40819-025-01889-8
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8657
dc.identifier.volume11
dc.indekslendigikaynakScopus
dc.institutionauthorAkgül, Ali
dc.institutionauthorid0000-0001-9832-1424
dc.publisherSpringer Science and Business Media LLC
dc.relation.ispartofInternational Journal of Applied and Computational Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectAdaptive back stepping
dc.subjectDengue model
dc.subjectFuzzy system
dc.subjectLyapunov function
dc.subjectRunge–Kutta method
dc.titleMathematical Modelling of Dengue Transmission with Adaptive Fuzzy Backstepping Control and RK-5 Numerical Method
dc.typejournal-article
oaire.citation.issue3
oaire.citation.volume11

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