Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability
Abstract This paper utilizes a mathematical model based on the Atangana–Baleanu fractal-fractional derivative to investigate different epidemiological aspects of monkeypox virus infection. The goal is to evaluate the effects of treatment and vaccination on the transmission dynamics of the virus. Ini...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02013-x |
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| author | Tharmalingam Gunasekar Shanmugam Manikandan Salma Haque Murgan Suba Nabil Mlaiki |
| author_facet | Tharmalingam Gunasekar Shanmugam Manikandan Salma Haque Murgan Suba Nabil Mlaiki |
| author_sort | Tharmalingam Gunasekar |
| collection | DOAJ |
| description | Abstract This paper utilizes a mathematical model based on the Atangana–Baleanu fractal-fractional derivative to investigate different epidemiological aspects of monkeypox virus infection. The goal is to evaluate the effects of treatment and vaccination on the transmission dynamics of the virus. Initially, the model utilizes integer-order nonlinear differential equations, integrating imperfect vaccination and treatment as control strategies within the human population. Subsequently, the model is reformulated using a fractal fractional-order derivative based on a power law to offer a more comprehensive insight into disease dynamics. Conditions are established for the basic reproduction number and equilibrium points, and the feasible region of the model is identified. Stability analysis of the endemic equilibrium is conducted using the Lyapunov function approach. The fixed-point method is used to explore the existence and uniqueness of solutions in the Atangana–Baleanu model with fractal-fractional derivative order. Additionally, the study examines Ulam–Hyer’s stability. The numerical scheme applies Lagrange’s interpolation polynomial, enabling precise model interpolation. We present numerical comparisons for various fractional and fractal orders to showcase the accuracy of our approach. |
| format | Article |
| id | doaj-art-d41ca1341d934ad0855551d2cc22bc55 |
| institution | DOAJ |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-d41ca1341d934ad0855551d2cc22bc552025-08-20T02:48:30ZengSpringerOpenBoundary Value Problems1687-27702025-02-012025113410.1186/s13661-025-02013-xFractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stabilityTharmalingam Gunasekar0Shanmugam Manikandan1Salma Haque2Murgan Suba3Nabil Mlaiki4Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and TechnologyDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and TechnologyDepartment of Mathematics and Sciences, Prince Sultan UniversityDepartment of Mathematics, S.A. Engineering College (Autonomous)Department of Mathematics and Sciences, Prince Sultan UniversityAbstract This paper utilizes a mathematical model based on the Atangana–Baleanu fractal-fractional derivative to investigate different epidemiological aspects of monkeypox virus infection. The goal is to evaluate the effects of treatment and vaccination on the transmission dynamics of the virus. Initially, the model utilizes integer-order nonlinear differential equations, integrating imperfect vaccination and treatment as control strategies within the human population. Subsequently, the model is reformulated using a fractal fractional-order derivative based on a power law to offer a more comprehensive insight into disease dynamics. Conditions are established for the basic reproduction number and equilibrium points, and the feasible region of the model is identified. Stability analysis of the endemic equilibrium is conducted using the Lyapunov function approach. The fixed-point method is used to explore the existence and uniqueness of solutions in the Atangana–Baleanu model with fractal-fractional derivative order. Additionally, the study examines Ulam–Hyer’s stability. The numerical scheme applies Lagrange’s interpolation polynomial, enabling precise model interpolation. We present numerical comparisons for various fractional and fractal orders to showcase the accuracy of our approach.https://doi.org/10.1186/s13661-025-02013-xFractal-fractionalFixed pointExistence and uniquenessUlam–Hyer’s stability |
| spellingShingle | Tharmalingam Gunasekar Shanmugam Manikandan Salma Haque Murgan Suba Nabil Mlaiki Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability Boundary Value Problems Fractal-fractional Fixed point Existence and uniqueness Ulam–Hyer’s stability |
| title | Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability |
| title_full | Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability |
| title_fullStr | Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability |
| title_full_unstemmed | Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability |
| title_short | Fractal-fractional mathematical modeling of monkeypox disease and analysis of its Ulam–Hyers stability |
| title_sort | fractal fractional mathematical modeling of monkeypox disease and analysis of its ulam hyers stability |
| topic | Fractal-fractional Fixed point Existence and uniqueness Ulam–Hyer’s stability |
| url | https://doi.org/10.1186/s13661-025-02013-x |
| work_keys_str_mv | AT tharmalingamgunasekar fractalfractionalmathematicalmodelingofmonkeypoxdiseaseandanalysisofitsulamhyersstability AT shanmugammanikandan fractalfractionalmathematicalmodelingofmonkeypoxdiseaseandanalysisofitsulamhyersstability AT salmahaque fractalfractionalmathematicalmodelingofmonkeypoxdiseaseandanalysisofitsulamhyersstability AT murgansuba fractalfractionalmathematicalmodelingofmonkeypoxdiseaseandanalysisofitsulamhyersstability AT nabilmlaiki fractalfractionalmathematicalmodelingofmonkeypoxdiseaseandanalysisofitsulamhyersstability |