Analytical study of a Hepatitis B epidemic model using a discrete generalized nonsingular kernel

Muhammad Farman; Ali Akgül; J. Alberto Conejero; Aamir Shehzad; Kottakkaran Sooppy Nisar; Dumitru Baleanu; Muhammad Farman; Ali Akgül; J. Alberto Conejero; Aamir Shehzad; Kottakkaran Sooppy Nisar; Dumitru Baleanu

doi:10.3934/math.2024824

AIMS Mathematics

2024, Volume 9, Issue 7: 16966-16997. doi: 10.3934/math.2024824

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Analytical study of a Hepatitis B epidemic model using a discrete generalized nonsingular kernel

1.
Faculty of Arts and Sciences, Department of Mathematics, University of Kyrenia, Kyrenia, TRNC, Mersin 10, Turkey
2.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
4.
Instituto de Matemática Pura y Aplicada. Universitat Politè cnica de València, València, Spain
5.
Mathematical Research Center, Department of Mathematics, Near East University, Nicosia, North Cyprus, 99138, Turkey
6.
Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

Received: 26 December 2023 Revised: 05 May 2024 Accepted: 06 May 2024 Published: 15 May 2024
MSC : 34A08, 92B05

Hepatitis B is a worldwide viral infection that causes cirrhosis, hepatocellular cancer, the need for liver transplantation, and death. This work proposed a mathematical representation of Hepatitis B Virus (HBV) transmission traits emphasizing the significance of applied mathematics in comprehending how the disease spreads. The work used an updated Atangana-Baleanu fractional difference operator to create a fractional-order model of HBV. The qualitative assessment and well-posedness of the mathematical framework were looked at, and the global stability of equilibrium states as measured by the Volterra-type Lyapunov function was summarized. The exact answer was guaranteed to be unique using the Lipschitz condition. Additionally, there were various analyses of this new type of operator to support the operator's efficacy. We observe that the explored discrete fractional operators will be $ \chi^2 $-increasing or decreasing in certain domains of the time scale $ \mathbb{N}_j: = {j, j + 1, ... } $ by looking at the fundamental characteristics of the proposed discrete fractional operators along with $ \chi $-monotonicity descriptions. For numerical simulations, solutions were constructed in the discrete generalized form of the Mittag-Leffler kernel, highlighting the impacts of the illness caused by numerous causes. The order of the fractional derivative had a significant influence on the dynamical process utilized to construct the HBV model. Researchers and policymakers can benefit from the suggested model's ability to forecast infectious diseases such as HBV and take preventive action.
- Hepatitis B model,
- discrete Mittag-Leffler kernel,
- $ \chi $-monotonicity investigations,
- Volterra-type Lyapunov function
Citation: Muhammad Farman, Ali Akgül, J. Alberto Conejero, Aamir Shehzad, Kottakkaran Sooppy Nisar, Dumitru Baleanu. Analytical study of a Hepatitis B epidemic model using a discrete generalized nonsingular kernel[J]. AIMS Mathematics, 2024, 9(7): 16966-16997. doi: 10.3934/math.2024824

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Abstract

Hepatitis B is a worldwide viral infection that causes cirrhosis, hepatocellular cancer, the need for liver transplantation, and death. This work proposed a mathematical representation of Hepatitis B Virus (HBV) transmission traits emphasizing the significance of applied mathematics in comprehending how the disease spreads. The work used an updated Atangana-Baleanu fractional difference operator to create a fractional-order model of HBV. The qualitative assessment and well-posedness of the mathematical framework were looked at, and the global stability of equilibrium states as measured by the Volterra-type Lyapunov function was summarized. The exact answer was guaranteed to be unique using the Lipschitz condition. Additionally, there were various analyses of this new type of operator to support the operator's efficacy. We observe that the explored discrete fractional operators will be $ \chi^2 $-increasing or decreasing in certain domains of the time scale $ \mathbb{N}_j: = {j, j + 1, ... } $ by looking at the fundamental characteristics of the proposed discrete fractional operators along with $ \chi $-monotonicity descriptions. For numerical simulations, solutions were constructed in the discrete generalized form of the Mittag-Leffler kernel, highlighting the impacts of the illness caused by numerous causes. The order of the fractional derivative had a significant influence on the dynamical process utilized to construct the HBV model. Researchers and policymakers can benefit from the suggested model's ability to forecast infectious diseases such as HBV and take preventive action.

References

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