Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order
In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, w...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/12/844 |
| _version_ | 1797380963217440768 |
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| author | K. A. Aldwoah Mohammed A. Almalahi Kamal Shah |
| author_facet | K. A. Aldwoah Mohammed A. Almalahi Kamal Shah |
| author_sort | K. A. Aldwoah |
| collection | DOAJ |
| description | In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana–Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers–Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana–Baleanu derivatives and an extended Adams–Bashforth–Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor. |
| first_indexed | 2024-03-08T20:45:29Z |
| format | Article |
| id | doaj.art-2bd0cc87f4884117bb2b6d1a3be7f50a |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T20:45:29Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-2bd0cc87f4884117bb2b6d1a3be7f50a2023-12-22T14:09:56ZengMDPI AGFractal and Fractional2504-31102023-11-0171284410.3390/fractalfract7120844Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional OrderK. A. Aldwoah0Mohammed A. Almalahi1Kamal Shah2Department of Mathematics, Faculty of Science, Islamic University of Madinah, Al Madinah 42351, Saudi ArabiaDepartment of Mathematics, Hajjah University, Hajjah 00967, YemenDepartment of Mathematics, University of Malakand, Chakdara Dir(L) 18000, Khyber Pakhtunkhawa, PakistanIn this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana–Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers–Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana–Baleanu derivatives and an extended Adams–Bashforth–Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor.https://www.mdpi.com/2504-3110/7/12/844HBV infectionpiecewise Atangana–Baleanu fractional-order modelstabilitysimulation |
| spellingShingle | K. A. Aldwoah Mohammed A. Almalahi Kamal Shah Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order Fractal and Fractional HBV infection piecewise Atangana–Baleanu fractional-order model stability simulation |
| title | Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order |
| title_full | Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order |
| title_fullStr | Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order |
| title_full_unstemmed | Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order |
| title_short | Theoretical and Numerical Simulations on the Hepatitis B Virus Model through a Piecewise Fractional Order |
| title_sort | theoretical and numerical simulations on the hepatitis b virus model through a piecewise fractional order |
| topic | HBV infection piecewise Atangana–Baleanu fractional-order model stability simulation |
| url | https://www.mdpi.com/2504-3110/7/12/844 |
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