Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative
The monkeypox virus causes a respiratory illness called monkeypox, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Using the Antangana–Baleanu fractional order approach, this...
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MDPI AG
2023-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/8/1605 |
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| author | Tharmalingam Gunasekar Shanmugam Manikandan Vediyappan Govindan Piriadarshani D Junaid Ahmad Walid Emam Isra Al-Shbeil |
| author_facet | Tharmalingam Gunasekar Shanmugam Manikandan Vediyappan Govindan Piriadarshani D Junaid Ahmad Walid Emam Isra Al-Shbeil |
| author_sort | Tharmalingam Gunasekar |
| collection | DOAJ |
| description | The monkeypox virus causes a respiratory illness called monkeypox, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Using the Antangana–Baleanu fractional order approach, this study aims to propose a new monkeypox transmission model that represents the interaction between the infected human and rodent populations. An iterative method and the fixed-point theorem are used to prove the existence and uniqueness of the symmetry model’s system of solutions. It shows that the symmetry model has equilibrium points when there are epidemics and no diseases. As well as the local asymptotic stability of the disease-free equilibrium point, conditions for the endemic equilibrium point’s existence have also been demonstrated. For this purpose, the existence of optimal control is first ensured. The aim of the proposed optimal control problem is to minimize both the treatment and prevention costs, and the number of infected individuals. Optimal conditions are acquired Pontryagin’s maximum principle is used. Then, the stability of the symmetry model is discussed at monkeypox-free and endemic equilibrium points with treatment strategies to control the spread of the disease. Numerical simulations clearly show how necessary and successful the proposed combined control strategy is in preventing the disease from becoming epidemic. |
| first_indexed | 2024-03-10T23:32:45Z |
| format | Article |
| id | doaj.art-850f4aece7d14ab680e1145bf038a52e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T23:32:45Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-850f4aece7d14ab680e1145bf038a52e2023-11-19T03:12:09ZengMDPI AGSymmetry2073-89942023-08-01158160510.3390/sym15081605Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional DerivativeTharmalingam Gunasekar0Shanmugam Manikandan1Vediyappan Govindan2Piriadarshani D3Junaid Ahmad4Walid Emam5Isra Al-Shbeil6Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai 600062, IndiaDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai 600062, IndiaDepartment of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam 603103, IndiaDepartment of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam 603103, IndiaDepartment of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanThe monkeypox virus causes a respiratory illness called monkeypox, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Using the Antangana–Baleanu fractional order approach, this study aims to propose a new monkeypox transmission model that represents the interaction between the infected human and rodent populations. An iterative method and the fixed-point theorem are used to prove the existence and uniqueness of the symmetry model’s system of solutions. It shows that the symmetry model has equilibrium points when there are epidemics and no diseases. As well as the local asymptotic stability of the disease-free equilibrium point, conditions for the endemic equilibrium point’s existence have also been demonstrated. For this purpose, the existence of optimal control is first ensured. The aim of the proposed optimal control problem is to minimize both the treatment and prevention costs, and the number of infected individuals. Optimal conditions are acquired Pontryagin’s maximum principle is used. Then, the stability of the symmetry model is discussed at monkeypox-free and endemic equilibrium points with treatment strategies to control the spread of the disease. Numerical simulations clearly show how necessary and successful the proposed combined control strategy is in preventing the disease from becoming epidemic.https://www.mdpi.com/2073-8994/15/8/1605monkeypoxAB-fractional derivativefixed pointexistence of solutionoptimal control |
| spellingShingle | Tharmalingam Gunasekar Shanmugam Manikandan Vediyappan Govindan Piriadarshani D Junaid Ahmad Walid Emam Isra Al-Shbeil Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative Symmetry monkeypox AB-fractional derivative fixed point existence of solution optimal control |
| title | Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative |
| title_full | Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative |
| title_fullStr | Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative |
| title_full_unstemmed | Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative |
| title_short | Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative |
| title_sort | symmetry analyses of epidemiological model for monkeypox virus with atangana baleanu fractional derivative |
| topic | monkeypox AB-fractional derivative fixed point existence of solution optimal control |
| url | https://www.mdpi.com/2073-8994/15/8/1605 |
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