The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model
We investigate and analyze the dynamics of hepatitis B with various infection phases and multiple routes of transmission. We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo–Fabrizio operator. Once we develo...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/8752161 |
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| _version_ | 1832552550379814912 |
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| author | Tahir Khan Zi-Shan Qian Roman Ullah Basem Al Alwan Gul Zaman Qasem M. Al-Mdallal Youssef El Khatib Khaled Kheder |
| author_facet | Tahir Khan Zi-Shan Qian Roman Ullah Basem Al Alwan Gul Zaman Qasem M. Al-Mdallal Youssef El Khatib Khaled Kheder |
| author_sort | Tahir Khan |
| collection | DOAJ |
| description | We investigate and analyze the dynamics of hepatitis B with various infection phases and multiple routes of transmission. We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo–Fabrizio operator. Once we develop the model under consideration, existence and uniqueness analysis will be discussed. We use fixed point theory for the existence and uniqueness analysis. We also prove that the model under consideration possesses a bounded and positive solution. We then find the basic reproductive number to perform the steady-state analysis and to show that the fractional-order epidemiological model is locally and globally asymptotically stable under certain conditions. For the local and global analysis, we use linearization, mean value theorem, and fractional Barbalat’s lemma, respectively. Finally, we perform some numerical findings to support the analytical work with the help of graphical representations. |
| format | Article |
| id | doaj-art-1eb4fbd3ff764ec18956a84086eab8cf |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-1eb4fbd3ff764ec18956a84086eab8cf2025-02-03T05:58:23ZengWileyComplexity1099-05262021-01-01202110.1155/2021/8752161The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological ModelTahir Khan0Zi-Shan Qian1Roman Ullah2Basem Al Alwan3Gul Zaman4Qasem M. Al-Mdallal5Youssef El Khatib6Khaled Kheder7Department of ComputingSchool of Physical SciencesGeneral Requirements DepartmentChemical Engineering DepartmentDepartment of MathematicsDepartment of Mathematical SciencesDepartment of Mathematical SciencesCivil Engineering DepartmentWe investigate and analyze the dynamics of hepatitis B with various infection phases and multiple routes of transmission. We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo–Fabrizio operator. Once we develop the model under consideration, existence and uniqueness analysis will be discussed. We use fixed point theory for the existence and uniqueness analysis. We also prove that the model under consideration possesses a bounded and positive solution. We then find the basic reproductive number to perform the steady-state analysis and to show that the fractional-order epidemiological model is locally and globally asymptotically stable under certain conditions. For the local and global analysis, we use linearization, mean value theorem, and fractional Barbalat’s lemma, respectively. Finally, we perform some numerical findings to support the analytical work with the help of graphical representations.http://dx.doi.org/10.1155/2021/8752161 |
| spellingShingle | Tahir Khan Zi-Shan Qian Roman Ullah Basem Al Alwan Gul Zaman Qasem M. Al-Mdallal Youssef El Khatib Khaled Kheder The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model Complexity |
| title | The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model |
| title_full | The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model |
| title_fullStr | The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model |
| title_full_unstemmed | The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model |
| title_short | The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model |
| title_sort | transmission dynamics of hepatitis b virus via the fractional order epidemiological model |
| url | http://dx.doi.org/10.1155/2021/8752161 |
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