Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernels
A fractional model for the transmission dynamics of Hepatitis B was designed. Hepatitis B disease has a great impact on global human health conditions and economical systems. The spreading of HBV disease has several phases, i.e., acute and chronicle carriers phases have a key role. The chronicle car...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-08-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722004296 |
| _version_ | 1818196842240802816 |
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| author | Peijiang Liu Anwarud Din Rahat Zarin |
| author_facet | Peijiang Liu Anwarud Din Rahat Zarin |
| author_sort | Peijiang Liu |
| collection | DOAJ |
| description | A fractional model for the transmission dynamics of Hepatitis B was designed. Hepatitis B disease has a great impact on global human health conditions and economical systems. The spreading of HBV disease has several phases, i.e., acute and chronicle carriers phases have a key role. The chronicle carrier’s cases do not have any signs and are capable of transmitting the Hepatitis B infection. In this article, we investigated the transmission due to different infection phases of the Hepatitis B virus and constructed a nonlinear epidemic. Next, a fractional hepatitis B virus model with Atangana–Baleanu derivative (AB derivative) is formulated with vaccine effects. Firstly, we calculated the basic reproductive value and equilibria of the proposed model. Qualitative analysis of the approximate root of the said problem has been derived with the help of Fixed Point Theory. The Iterative approximate technique with the help of the Adams–Bashforth predictor–corrector scheme for evaluating the considered fractional system having the ABC derivative is expressed. In the last, a graphical representation is established to show the obtained scheme findings and compare different non-integer orders of Ψ. |
| first_indexed | 2024-12-12T01:40:30Z |
| format | Article |
| id | doaj.art-f42af01d0abe4ec1bf9c0ba7c794e772 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-12T01:40:30Z |
| publishDate | 2022-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-f42af01d0abe4ec1bf9c0ba7c794e7722022-12-22T00:42:44ZengElsevierResults in Physics2211-37972022-08-0139105757Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernelsPeijiang Liu0Anwarud Din1Rahat Zarin2School of Statistics and Mathematics, Guangdong University of Finance and Economics, Big data and Educational Statistics Application Laboratory, Guangzhou 510320, PR China; School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, PR ChinaDepartment of Mathematics Sun Yat-sen University Guangzhou, 510275, PR China; Corresponding authors.Department of Basic Sciences, University of Engineering and Technology Peshawar, Khyber Pakhtunkhwa, PakistanA fractional model for the transmission dynamics of Hepatitis B was designed. Hepatitis B disease has a great impact on global human health conditions and economical systems. The spreading of HBV disease has several phases, i.e., acute and chronicle carriers phases have a key role. The chronicle carrier’s cases do not have any signs and are capable of transmitting the Hepatitis B infection. In this article, we investigated the transmission due to different infection phases of the Hepatitis B virus and constructed a nonlinear epidemic. Next, a fractional hepatitis B virus model with Atangana–Baleanu derivative (AB derivative) is formulated with vaccine effects. Firstly, we calculated the basic reproductive value and equilibria of the proposed model. Qualitative analysis of the approximate root of the said problem has been derived with the help of Fixed Point Theory. The Iterative approximate technique with the help of the Adams–Bashforth predictor–corrector scheme for evaluating the considered fractional system having the ABC derivative is expressed. In the last, a graphical representation is established to show the obtained scheme findings and compare different non-integer orders of Ψ.http://www.sciencedirect.com/science/article/pii/S2211379722004296Mittag-LefflerFractional derivativeVaccinationAdams–BashforthNumerical simulations |
| spellingShingle | Peijiang Liu Anwarud Din Rahat Zarin Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernels Results in Physics Mittag-Leffler Fractional derivative Vaccination Adams–Bashforth Numerical simulations |
| title | Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernels |
| title_full | Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernels |
| title_fullStr | Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernels |
| title_full_unstemmed | Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernels |
| title_short | Numerical dynamics and fractional modeling of hepatitis B virus model with non-singular and non-local kernels |
| title_sort | numerical dynamics and fractional modeling of hepatitis b virus model with non singular and non local kernels |
| topic | Mittag-Leffler Fractional derivative Vaccination Adams–Bashforth Numerical simulations |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722004296 |
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