Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission
The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The infection is very destructive to human lives and caused millions of deaths. Various approaches have been made recently to understand the complex dynamics of COVID-19. The mathematical modeling...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-07-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016821006773 |
| _version_ | 1811334133338603520 |
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| author | Arshad Alam Khan Rohul Amin Saif Ullah Wojciech Sumelka Mohamed Altanji |
| author_facet | Arshad Alam Khan Rohul Amin Saif Ullah Wojciech Sumelka Mohamed Altanji |
| author_sort | Arshad Alam Khan |
| collection | DOAJ |
| description | The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The infection is very destructive to human lives and caused millions of deaths. Various approaches have been made recently to understand the complex dynamics of COVID-19. The mathematical modeling approach is one of the considerable tools to study the disease spreading pattern. In this article, we develop a fractional order epidemic model for COVID-19 in the sense of Caputo operator. The model is based on the effective contacts among the population and environmental impact to analyze the disease dynamics. The fractional models are comparatively better in understanding the disease outbreak and providing deeper insights into the infectious disease dynamics. We first consider the classical integer model studied in recent literature and then we generalize it by introducing the Caputo fractional derivative. Furthermore, we explore some fundamental mathematical analysis of the fractional model, including the basic reproductive number R0 and equilibria stability utilizing the Routh-Hurwitz and the Lyapunov function approaches. Besides theoretical analysis, we also focused on the numerical solution. To simulate the model, we use the well-known generalized Adams–Bashforth Moulton Scheme. Finally, the influence of some of the model essential parameters on the dynamics of the disease is demonstrated graphically. |
| first_indexed | 2024-04-13T17:04:15Z |
| format | Article |
| id | doaj.art-6ce1cb0f32c14ec7b529861c74a82508 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-13T17:04:15Z |
| publishDate | 2022-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-6ce1cb0f32c14ec7b529861c74a825082022-12-22T02:38:33ZengElsevierAlexandria Engineering Journal1110-01682022-07-0161750835095Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmissionArshad Alam Khan0Rohul Amin1Saif Ullah2Wojciech Sumelka3Mohamed Altanji4Department of Mathematics, University of Peshawar, 25120 Khyber, Pukhtunkhwa, PakistanDepartment of Mathematics, University of Peshawar, 25120 Khyber, Pukhtunkhwa, PakistanDepartment of Mathematics, University of Peshawar, 25120 Khyber, Pukhtunkhwa, PakistanInstitute of Structural Analysis, Poznan University of Technology, Piotrowo 5 Street, 60-965 Poznan, Poland; Corresponding author.Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia; Corresponding author.The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The infection is very destructive to human lives and caused millions of deaths. Various approaches have been made recently to understand the complex dynamics of COVID-19. The mathematical modeling approach is one of the considerable tools to study the disease spreading pattern. In this article, we develop a fractional order epidemic model for COVID-19 in the sense of Caputo operator. The model is based on the effective contacts among the population and environmental impact to analyze the disease dynamics. The fractional models are comparatively better in understanding the disease outbreak and providing deeper insights into the infectious disease dynamics. We first consider the classical integer model studied in recent literature and then we generalize it by introducing the Caputo fractional derivative. Furthermore, we explore some fundamental mathematical analysis of the fractional model, including the basic reproductive number R0 and equilibria stability utilizing the Routh-Hurwitz and the Lyapunov function approaches. Besides theoretical analysis, we also focused on the numerical solution. To simulate the model, we use the well-known generalized Adams–Bashforth Moulton Scheme. Finally, the influence of some of the model essential parameters on the dynamics of the disease is demonstrated graphically.http://www.sciencedirect.com/science/article/pii/S1110016821006773Caputo fractional derivativeAdams–Bashforth methodCOVID-19Stability |
| spellingShingle | Arshad Alam Khan Rohul Amin Saif Ullah Wojciech Sumelka Mohamed Altanji Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission Alexandria Engineering Journal Caputo fractional derivative Adams–Bashforth method COVID-19 Stability |
| title | Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission |
| title_full | Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission |
| title_fullStr | Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission |
| title_full_unstemmed | Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission |
| title_short | Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission |
| title_sort | numerical simulation of a caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission |
| topic | Caputo fractional derivative Adams–Bashforth method COVID-19 Stability |
| url | http://www.sciencedirect.com/science/article/pii/S1110016821006773 |
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