Fractional modeling and analysis of Hepatitis B virus using fixed-point approach

Prachi Garg () and Surjeet Singh Chauhan Gonder
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Prachi Garg: Department of Mathematics, Chandigarh University, Mohali 140413, India
Surjeet Singh Chauhan Gonder: Department of Mathematics, Chandigarh University, Mohali 140413, India

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 07, 1-21

Abstract: In this paper, we delve into the analysis of the Hepatitis B model, specifically the SEIAICR model, within the scope of the Caputo–Fabrizio fractional operator. A new state variable the number of vaccinated individuals is also added to the model. This addition enriches the scope of the hepatitis B model inviting a deeper exploration of the subject matter. Our study proves the existence of a disease-free fixed point within the proposed compartmental model. To ensure the existence and uniqueness of the fixed point, we employ a fixed-point result in the b-complete b-dislocated quasi-metric space, utilizing a Geraghty-type contraction mapping. This approach establishes the fixed point of a disease-free state within the model. Furthermore, we employ a two-step Adams–Bashforth numerical scheme, serving as a validation of both the significance of fractional-order derivatives and the validity of our obtained theoretical results. Together our research presents an innovative perspective on the SEIAICR hepatitis B model pushing the boundaries of understanding and shedding light on the dynamics of disease transmission with the impact of vaccine.

Keywords: Hepatitis B; mathematical modeling; fixed-point approach; two-step Adams–Bashforth method; numerical simulation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500876

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