Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis
The novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus's expanse have changed individuals' communication processes. Due to physical and financial factors...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Applied Mathematics in Science and Engineering |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2024.2326982 |
| _version_ | 1797249007509045248 |
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| author | Ihtisham Ul Haq Nigar Ali Abdul Bariq Ali Akgül Dumitru Baleanu Mustafa Bayram |
| author_facet | Ihtisham Ul Haq Nigar Ali Abdul Bariq Ali Akgül Dumitru Baleanu Mustafa Bayram |
| author_sort | Ihtisham Ul Haq |
| collection | DOAJ |
| description | The novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus's expanse have changed individuals' communication processes. Due to physical and financial factors, the population's density is more likely to interact and spread the virus. We establish a mathematical model to present the spread of the COVID-19 in worldwide. In this article, we propose a novel mathematical model (‘[Formula: see text]’) to assess the impact of using hospitalization, quarantine measures, and pathogen quantity in controlling the COVID-19 pandemic. We analyse the boundedness of the model's solution by employing the Laplace transform approach to solve the fractional Gronwall's inequality. To ensure the uniqueness and existence of the solution, we rely on the Picard-Lindelof theorem. The model's basic reproduction number, a crucial indicator of epidemic potential, is determined based on the greatest eigenvalue of the next-generation matrix. We then employ stability theory of fractional differential equations to qualitatively examine the model. Our findings reveal that both locally and globally, the endemic equilibrium and disease-free solutions demonstrate symptomatic stability. These results shed light on the effectiveness of the proposed interventions in managing and containing the COVID-19 outbreak. |
| first_indexed | 2024-04-24T20:23:38Z |
| format | Article |
| id | doaj.art-4a9fcc63b4bf45c7b8cf992ca9f9f816 |
| institution | Directory Open Access Journal |
| issn | 2769-0911 |
| language | English |
| last_indexed | 2024-04-24T20:23:38Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj.art-4a9fcc63b4bf45c7b8cf992ca9f9f8162024-03-22T07:01:27ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112024-12-0132110.1080/27690911.2024.2326982Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysisIhtisham Ul Haq0Nigar Ali1Abdul Bariq2Ali Akgül3Dumitru Baleanu4Mustafa Bayram5Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Laghman University, Mehtarlam City, Laghman, AfghanistanDepartment of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonDepartment of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonDepartment of Computer Engineering, Biruni University, Istanbul, TurkeyThe novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus's expanse have changed individuals' communication processes. Due to physical and financial factors, the population's density is more likely to interact and spread the virus. We establish a mathematical model to present the spread of the COVID-19 in worldwide. In this article, we propose a novel mathematical model (‘[Formula: see text]’) to assess the impact of using hospitalization, quarantine measures, and pathogen quantity in controlling the COVID-19 pandemic. We analyse the boundedness of the model's solution by employing the Laplace transform approach to solve the fractional Gronwall's inequality. To ensure the uniqueness and existence of the solution, we rely on the Picard-Lindelof theorem. The model's basic reproduction number, a crucial indicator of epidemic potential, is determined based on the greatest eigenvalue of the next-generation matrix. We then employ stability theory of fractional differential equations to qualitatively examine the model. Our findings reveal that both locally and globally, the endemic equilibrium and disease-free solutions demonstrate symptomatic stability. These results shed light on the effectiveness of the proposed interventions in managing and containing the COVID-19 outbreak.https://www.tandfonline.com/doi/10.1080/27690911.2024.2326982Caputo fractional derivativesKarsnosels'kil's fixed point theoremArzela Ascoli theoremLyapunov function techniquetrace-determinant approach26A33 |
| spellingShingle | Ihtisham Ul Haq Nigar Ali Abdul Bariq Ali Akgül Dumitru Baleanu Mustafa Bayram Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis Applied Mathematics in Science and Engineering Caputo fractional derivatives Karsnosels'kil's fixed point theorem Arzela Ascoli theorem Lyapunov function technique trace-determinant approach 26A33 |
| title | Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis |
| title_full | Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis |
| title_fullStr | Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis |
| title_full_unstemmed | Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis |
| title_short | Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis |
| title_sort | mathematical modelling of covid 19 outbreak using caputo fractional derivative stability analysis |
| topic | Caputo fractional derivatives Karsnosels'kil's fixed point theorem Arzela Ascoli theorem Lyapunov function technique trace-determinant approach 26A33 |
| url | https://www.tandfonline.com/doi/10.1080/27690911.2024.2326982 |
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