A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus
Fractional differential equations are beginning to gain widespread usage in modeling physical and biological processes. It is worth mentioning that the standard mathematical models of integer-order derivatives, including nonlinear models, do not constitute suitable framework in many cases. In this w...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-06-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S221137972200242X |
| _version_ | 1811233827967729664 |
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| author | Andrew Omame Mujahid Abbas Chibueze P. Onyenegecha |
| author_facet | Andrew Omame Mujahid Abbas Chibueze P. Onyenegecha |
| author_sort | Andrew Omame |
| collection | DOAJ |
| description | Fractional differential equations are beginning to gain widespread usage in modeling physical and biological processes. It is worth mentioning that the standard mathematical models of integer-order derivatives, including nonlinear models, do not constitute suitable framework in many cases. In this work, a mathematical model for COVID-19 and Hepatitis B Virus (HBV) co-interaction is developed and studied using the Atangana–Baleanu fractional derivative. The necessary conditions of the existence and uniqueness of the solution of the proposed model are studied. The local stability analysis is carried out when the reproduction number is less than one. Using well constructed Lyapunov functions, the disease free and endemic equilibria are proven to be globally asymptotically stable under certain conditions. Employing fixed point theory, the stability of the iterative scheme to approximate the solution of the model is discussed. The model is fitted to real data from the city of Wuhan, China, and important parameters relating to each disease and their co-infection, are estimated from the fitting. The approximate solutions of the model are compared using the integer and fractional order derivatives. The impact of the fractional derivative on the proposed model is also highlighted. The results proven in this paper illustrate that HBV and COVID-19 transmission rates can greatly impact the dynamics of the co-infection of both diseases. It is concluded that to control the co-circulation of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases. |
| first_indexed | 2024-04-12T11:25:51Z |
| format | Article |
| id | doaj.art-dacaa6d5a4bf4898a27dc7010a4f0f11 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-12T11:25:51Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-dacaa6d5a4bf4898a27dc7010a4f0f112022-12-22T03:35:13ZengElsevierResults in Physics2211-37972022-06-0137105498A fractional order model for the co-interaction of COVID-19 and Hepatitis B virusAndrew Omame0Mujahid Abbas1Chibueze P. Onyenegecha2Department of Mathematics, Federal University of Technology, Owerri, Nigeria; Abdus Salam School of Mathematical Sciences, Government College University Katchery Road, Lahore 54000, Pakistan; Corresponding author at: Department of Mathematics, Federal University of Technology, Owerri, Nigeria.Department of Mathematics, Government College University Katchery Road, Lahore 54000, Pakistan; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, TaiwanDepartment of Physics, Federal University of Technology Owerri, NigeriaFractional differential equations are beginning to gain widespread usage in modeling physical and biological processes. It is worth mentioning that the standard mathematical models of integer-order derivatives, including nonlinear models, do not constitute suitable framework in many cases. In this work, a mathematical model for COVID-19 and Hepatitis B Virus (HBV) co-interaction is developed and studied using the Atangana–Baleanu fractional derivative. The necessary conditions of the existence and uniqueness of the solution of the proposed model are studied. The local stability analysis is carried out when the reproduction number is less than one. Using well constructed Lyapunov functions, the disease free and endemic equilibria are proven to be globally asymptotically stable under certain conditions. Employing fixed point theory, the stability of the iterative scheme to approximate the solution of the model is discussed. The model is fitted to real data from the city of Wuhan, China, and important parameters relating to each disease and their co-infection, are estimated from the fitting. The approximate solutions of the model are compared using the integer and fractional order derivatives. The impact of the fractional derivative on the proposed model is also highlighted. The results proven in this paper illustrate that HBV and COVID-19 transmission rates can greatly impact the dynamics of the co-infection of both diseases. It is concluded that to control the co-circulation of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.http://www.sciencedirect.com/science/article/pii/S221137972200242XCOVID-19HBVCo-infectionFractional derivativeLyapunov functionsStability |
| spellingShingle | Andrew Omame Mujahid Abbas Chibueze P. Onyenegecha A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus Results in Physics COVID-19 HBV Co-infection Fractional derivative Lyapunov functions Stability |
| title | A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus |
| title_full | A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus |
| title_fullStr | A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus |
| title_full_unstemmed | A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus |
| title_short | A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus |
| title_sort | fractional order model for the co interaction of covid 19 and hepatitis b virus |
| topic | COVID-19 HBV Co-infection Fractional derivative Lyapunov functions Stability |
| url | http://www.sciencedirect.com/science/article/pii/S221137972200242X |
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