A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination
This article is devoted to investigate a mathematical model consisting on susceptible, exposed, infected, quarantined, vaccinated, and recovered compartments of COVID-19. The concerned model describes the transmission mechanism of the disease dynamics with therapeutic measures of vaccination of susc...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi-Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/7236824 |
| _version_ | 1827000641792245760 |
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| author | Kamal Shah Muhammad Sinan Thabet Abdeljawad M.A. El-Shorbagy Bahaaeldin Abdalla Marwan S. Abualrub |
| author_facet | Kamal Shah Muhammad Sinan Thabet Abdeljawad M.A. El-Shorbagy Bahaaeldin Abdalla Marwan S. Abualrub |
| author_sort | Kamal Shah |
| collection | DOAJ |
| description | This article is devoted to investigate a mathematical model consisting on susceptible, exposed, infected, quarantined, vaccinated, and recovered compartments of COVID-19. The concerned model describes the transmission mechanism of the disease dynamics with therapeutic measures of vaccination of susceptible people along with the cure of the infected population. In the said study, we use the fractal-fractional order derivative to understand the dynamics of all compartments of the proposed model in more detail. Therefore, the first model is formulated. Then, two equilibrium points disease-free (DF) and endemic are computed. Furthermore, the basic threshold number is also derived. Some sufficient conditions for global asymptotical stability are also established. By using the next-generation matrix method, local stability analysis is developed. We also attempt the sensitivity analysis of the parameters of the proposed model. Finally, for the numerical simulations, the Adams–Bashforth method is used. Using some available data, the results are displayed graphically using various fractal-fractional orders to understand the mechanism of the dynamics. In addition, we compare our numerical simulation with real data in the case of reported infected cases. |
| first_indexed | 2024-04-11T07:35:52Z |
| format | Article |
| id | doaj.art-ffc83d5138c348c38b48a643c83ef7e8 |
| institution | Directory Open Access Journal |
| issn | 1099-0526 |
| language | English |
| last_indexed | 2025-02-18T10:47:25Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi-Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj.art-ffc83d5138c348c38b48a643c83ef7e82024-11-02T05:27:10ZengHindawi-WileyComplexity1099-05262022-01-01202210.1155/2022/7236824A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with VaccinationKamal Shah0Muhammad Sinan1Thabet Abdeljawad2M.A. El-Shorbagy3Bahaaeldin Abdalla4Marwan S. Abualrub5Department of Mathematics and SciencesSchool of Mathematical SciencesDepartment of Mathematics and SciencesDepartment of MathematicsDepartment of Mathematics and SciencesMathematics Department (Prep.Programm) Faculty of ScienceThis article is devoted to investigate a mathematical model consisting on susceptible, exposed, infected, quarantined, vaccinated, and recovered compartments of COVID-19. The concerned model describes the transmission mechanism of the disease dynamics with therapeutic measures of vaccination of susceptible people along with the cure of the infected population. In the said study, we use the fractal-fractional order derivative to understand the dynamics of all compartments of the proposed model in more detail. Therefore, the first model is formulated. Then, two equilibrium points disease-free (DF) and endemic are computed. Furthermore, the basic threshold number is also derived. Some sufficient conditions for global asymptotical stability are also established. By using the next-generation matrix method, local stability analysis is developed. We also attempt the sensitivity analysis of the parameters of the proposed model. Finally, for the numerical simulations, the Adams–Bashforth method is used. Using some available data, the results are displayed graphically using various fractal-fractional orders to understand the mechanism of the dynamics. In addition, we compare our numerical simulation with real data in the case of reported infected cases.http://dx.doi.org/10.1155/2022/7236824 |
| spellingShingle | Kamal Shah Muhammad Sinan Thabet Abdeljawad M.A. El-Shorbagy Bahaaeldin Abdalla Marwan S. Abualrub A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination Complexity |
| title | A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination |
| title_full | A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination |
| title_fullStr | A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination |
| title_full_unstemmed | A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination |
| title_short | A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination |
| title_sort | detailed study of a fractal fractional transmission dynamical model of viral infectious disease with vaccination |
| url | http://dx.doi.org/10.1155/2022/7236824 |
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