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Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system

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  • Boukhobza, Meriem
  • Debbouche, Amar
  • Shangerganesh, Lingeshwaran
  • Torres, Delfim F.M.

Abstract

We investigate the dynamics of the hepatitis B virus by integrating variable-order calculus and discrete analysis. Specifically, we utilize the Caputo variable-order difference operator in this study. To establish the existence and uniqueness results of the model, we employ a fixed-point technique. Furthermore, we prove that the model exhibits bounded and positive solutions. Additionally, we explore the local stability of the proposed model by determining the basic reproduction number. Finally, we present several numerical simulations to illustrate the richness of our results.

Suggested Citation

  • Boukhobza, Meriem & Debbouche, Amar & Shangerganesh, Lingeshwaran & Torres, Delfim F.M., 2024. "Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005393
    DOI: 10.1016/j.chaos.2024.114987
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    References listed on IDEAS

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    1. Amira Rachah & Delfim F. M. Torres, 2015. "Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-9, May.
    2. Tyagi, Swati & Martha, Subash C. & Abbas, Syed & Debbouche, Amar, 2021. "Mathematical modeling and analysis for controlling the spread of infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Tailei Zhang & Kai Wang & Xueliang Zhang, 2015. "Modeling and Analyzing the Transmission Dynamics of HBV Epidemic in Xinjiang, China," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-14, September.
    4. Gao, Fei & Li, Xiling & Li, Wenqin & Zhou, Xianjin, 2021. "Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Tahir Khan & Zi-Shan Qian & Roman Ullah & Basem Al Alwan & Gul Zaman & Qasem M. Al-Mdallal & Youssef El Khatib & Khaled Kheder & Mustafa Cagri Kutlu, 2021. "The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model," Complexity, Hindawi, vol. 2021, pages 1-18, December.
    6. Meriem Boukhobza & Amar Debbouche & Lingeshwaran Shangerganesh & Juan J. Nieto, 2024. "The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time," Mathematics, MDPI, vol. 12(8), pages 1-24, April.
    7. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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