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Global analysis and simulation of a fractional order HBV immune model

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  • Yang, Xue
  • Su, Yongmei
  • Yang, Liangli
  • Zhuo, Xinjian

Abstract

In this paper, a Caputo fractional order HBV humoral and CTL immunity model with more general mass action incidences is established, the existence and uniqueness of positive solutions are proved. We derive five different basic reproductive numbers and their relationship with the corresponding five equilibria, we also derive the general form of Lyapunov functions for fractional order model, the global stability of the five equilibria is analyzed by constructing Lyapunov function. Numerical simulation is also given to test the theory.

Suggested Citation

  • Yang, Xue & Su, Yongmei & Yang, Liangli & Zhuo, Xinjian, 2022. "Global analysis and simulation of a fractional order HBV immune model," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s096007792101002x
    DOI: 10.1016/j.chaos.2021.111648
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    References listed on IDEAS

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    1. Adnane Boukhouima & Khalid Hattaf & Noura Yousfi, 2017. "Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-8, August.
    2. 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).
    3. Ogunmiloro, Oluwatayo Michael, 2021. "Mathematical analysis and approximate solution of a fractional order caputo fascioliasis disease model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.
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    1. Yaagoub, Zakaria & Allali, Karam, 2022. "Fractional HBV infection model with both cell-to-cell and virus-to-cell transmissions and adaptive immunity," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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