Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate
The current study analyzes a fractional compartmental epidemic model for the transmission of infectious disease in a community. This study uses the Caputo derivative as well as Atangana–Baleanu derivative to consider a SIR fractional epidemic model with a convex incidence rate. We demonstrate the ex...
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| Format: | Article |
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Elsevier
2023-11-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723008823 |
| _version_ | 1797615938865987584 |
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| author | Asma Rashid Butt Aitzaz Ahmad Saqib Abu Bakar Dilber Uzun Ozsahin Hijaz Ahmad Bandar Almohsen |
| author_facet | Asma Rashid Butt Aitzaz Ahmad Saqib Abu Bakar Dilber Uzun Ozsahin Hijaz Ahmad Bandar Almohsen |
| author_sort | Asma Rashid Butt |
| collection | DOAJ |
| description | The current study analyzes a fractional compartmental epidemic model for the transmission of infectious disease in a community. This study uses the Caputo derivative as well as Atangana–Baleanu derivative to consider a SIR fractional epidemic model with a convex incidence rate. We demonstrate the existence and uniqueness of solutions by using the idea of fixed-point theory. Comprehensive mathematical approaches show the physical properties of solutions, such as non-negativity and boundedness. The basic reproduction number is evaluated using the next-generation matrix method, determining whether the infection will spread in society. The stability analysis is performed with phase portraits, which show that the infection-free and infection-present steady states of the considered model are locally and globally asymptotically stable. The sensitivity of the basic reproduction number is carried out through 3D graphs, which indicate the most sensitive and impactful parameters. Finally, for the numerical solution of the underlying model, a numerical technique is applied and these solutions evaluate the theoretical results through numerical simulations. Numerical simulations that aim to decrease the fractional parameter and convex incidence rate can bring about a significant change in infected individuals. |
| first_indexed | 2024-03-11T07:34:06Z |
| format | Article |
| id | doaj.art-994b1f489e92495e9c8fe1f55ed55689 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-11T07:34:06Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-994b1f489e92495e9c8fe1f55ed556892023-11-17T05:26:29ZengElsevierResults in Physics2211-37972023-11-0154107089Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rateAsma Rashid Butt0Aitzaz Ahmad Saqib1Abu Bakar2Dilber Uzun Ozsahin3Hijaz Ahmad4Bandar Almohsen5Department of Mathematics, University of Engineering and Technology, Lahore, PakistanDepartment of Mathematics, University of Engineering and Technology, Lahore, PakistanDepartment of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, PakistanDepartment of Medical Diagnostic Imaging, College of Health Science, University of Sharjah, Sharjah, United Arab Emirates; Research Institute for Medical and Health Sciences, University of Sharjah, Sharjah, United Arab Emirates; Corresponding author at: Department of Medical Diagnostic Imaging, College of Health Science, University of Sharjah, Sharjah, United Arab Emirates.Section of Mathematics, International Telematic University, Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy; Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey; Department of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonDepartment of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaThe current study analyzes a fractional compartmental epidemic model for the transmission of infectious disease in a community. This study uses the Caputo derivative as well as Atangana–Baleanu derivative to consider a SIR fractional epidemic model with a convex incidence rate. We demonstrate the existence and uniqueness of solutions by using the idea of fixed-point theory. Comprehensive mathematical approaches show the physical properties of solutions, such as non-negativity and boundedness. The basic reproduction number is evaluated using the next-generation matrix method, determining whether the infection will spread in society. The stability analysis is performed with phase portraits, which show that the infection-free and infection-present steady states of the considered model are locally and globally asymptotically stable. The sensitivity of the basic reproduction number is carried out through 3D graphs, which indicate the most sensitive and impactful parameters. Finally, for the numerical solution of the underlying model, a numerical technique is applied and these solutions evaluate the theoretical results through numerical simulations. Numerical simulations that aim to decrease the fractional parameter and convex incidence rate can bring about a significant change in infected individuals.http://www.sciencedirect.com/science/article/pii/S2211379723008823Atangana–Baleanu derivativeConvex incidence rateStability analysisNumerical solutionSensitivity analysis |
| spellingShingle | Asma Rashid Butt Aitzaz Ahmad Saqib Abu Bakar Dilber Uzun Ozsahin Hijaz Ahmad Bandar Almohsen Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate Results in Physics Atangana–Baleanu derivative Convex incidence rate Stability analysis Numerical solution Sensitivity analysis |
| title | Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate |
| title_full | Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate |
| title_fullStr | Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate |
| title_full_unstemmed | Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate |
| title_short | Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate |
| title_sort | investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate |
| topic | Atangana–Baleanu derivative Convex incidence rate Stability analysis Numerical solution Sensitivity analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723008823 |
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