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Global stability analysis of a fractional differential system in hepatitis B

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  • Cardoso, Lislaine Cristina
  • Camargo, Rubens Figueiredo
  • dos Santos, Fernando Luiz Pio
  • Dos Santos, José Paulo Carvalho

Abstract

This paper describes the dynamics of hepatitis B by a fractional-order model in the Caputo sense. The basic results of the fractional hepatitis B model are presented. Two equilibrium point for the model exists, the disease-free point and the infected point. The local and global stability analysis of the system is given in terms of the basic reproductive number. We execute the global stability analysis using the extended Barbalat’s lemma to the fractional-order system. The results show that the extension of Barbalat’s Lemma is a robust tool for the asymptotic analysis of the fractional dynamic systems. Moreover, numerical simulations by Nonstandard Finite Difference Schemes show that the solutions converge to an equilibrium point as predicted in the stability analysis.

Suggested Citation

  • Cardoso, Lislaine Cristina & Camargo, Rubens Figueiredo & dos Santos, Fernando Luiz Pio & Dos Santos, José Paulo Carvalho, 2021. "Global stability analysis of a fractional differential system in hepatitis B," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920310109
    DOI: 10.1016/j.chaos.2020.110619
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    References listed on IDEAS

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    1. José Paulo Carvalho dos Santos & Lislaine Cristina Cardoso & Evandro Monteiro & Nelson H. T. Lemes, 2015. "A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-10, July.
    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. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    4. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
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    Cited by:

    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).
    2. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    3. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.

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