The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission
This study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the Θ-Hilfer operator, we analyze the...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Results in Control and Optimization |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720724001267 |
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| author | K. Ramalakshmi B. Sundara Vadivoo Kottakkaran Sooppy Nisar Suliman Alsaeed |
| author_facet | K. Ramalakshmi B. Sundara Vadivoo Kottakkaran Sooppy Nisar Suliman Alsaeed |
| author_sort | K. Ramalakshmi |
| collection | DOAJ |
| description | This study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the Θ-Hilfer operator, we analyze the epidemic’s behavior. The research proposes control strategies, such as treatment and vaccination, aimed at reducing both acute and chronic infections. To achieve optimal control, we employ Pontryagin’s Maximum Principle. Through simulations, we demonstrate the effectiveness of our approach using the Non-Standard Two-Step Lagrange Interpolation Method (NS2LIM), supported by numerical findings and graphical representations. Additionally, we identify two control variables to minimize the populations of acute and chronic infections while enhancing recovery rates. |
| format | Article |
| id | doaj-art-ec5b69dbdc494828b8cdb71a6fb21fe1 |
| institution | OA Journals |
| issn | 2666-7207 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj-art-ec5b69dbdc494828b8cdb71a6fb21fe12025-08-20T01:57:52ZengElsevierResults in Control and Optimization2666-72072024-12-011710049610.1016/j.rico.2024.100496The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmissionK. Ramalakshmi0B. Sundara Vadivoo1Kottakkaran Sooppy Nisar2Suliman Alsaeed3Department of Mathematics, Alagappa University, Karaikudi 630 004, IndiaDepartment of Mathematics, Central University of Tamil Nadu, Thiruvarur 610 005, IndiaDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia; Saveetha School of Engineering, SIMATS, Chennai, India; Corresponding author at: Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia.Mathematics Department, College of Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaThis study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the Θ-Hilfer operator, we analyze the epidemic’s behavior. The research proposes control strategies, such as treatment and vaccination, aimed at reducing both acute and chronic infections. To achieve optimal control, we employ Pontryagin’s Maximum Principle. Through simulations, we demonstrate the effectiveness of our approach using the Non-Standard Two-Step Lagrange Interpolation Method (NS2LIM), supported by numerical findings and graphical representations. Additionally, we identify two control variables to minimize the populations of acute and chronic infections while enhancing recovery rates.http://www.sciencedirect.com/science/article/pii/S2666720724001267Hepatitis B virusFractional optimal control problemsΘ-Hilfer derivativeNS2LIM |
| spellingShingle | K. Ramalakshmi B. Sundara Vadivoo Kottakkaran Sooppy Nisar Suliman Alsaeed The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission Results in Control and Optimization Hepatitis B virus Fractional optimal control problems Θ-Hilfer derivative NS2LIM |
| title | The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission |
| title_full | The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission |
| title_fullStr | The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission |
| title_full_unstemmed | The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission |
| title_short | The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission |
| title_sort | θ hilfer fractional order model for the optimal control of the dynamics of hepatitis b virus transmission |
| topic | Hepatitis B virus Fractional optimal control problems Θ-Hilfer derivative NS2LIM |
| url | http://www.sciencedirect.com/science/article/pii/S2666720724001267 |
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