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

Author

Listed:
  • Prachi Garg

    (Department of Mathematics, Chandigarh University, Mohali 140413, India)

  • Surjeet Singh Chauhan Gonder

    (Department of Mathematics, Chandigarh University, Mohali 140413, India)

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.

Suggested Citation

  • Prachi Garg & Surjeet Singh Chauhan Gonder, 2024. "Fractional modeling and analysis of Hepatitis B virus using fixed-point approach," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(07), pages 1-21, July.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:07:n:s0129183124500876
    DOI: 10.1142/S0129183124500876
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