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Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

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  • Adnane Boukhouima
  • Khalid Hattaf
  • Noura Yousfi

Abstract

We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnijde:8372140
    DOI: 10.1155/2017/8372140
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    Cited by:

    1. Daşbaşı, Bahatdin, 2023. "Fractional order bacterial infection model with effects of anti-virulence drug and antibiotic," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. DAŞBAŞI, Bahatdin, 2020. "Stability analysis of the hiv model through incommensurate fractional-order nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Danane, Jaouad & Allali, Karam & Hammouch, Zakia, 2020. "Mathematical analysis of a fractional differential model of HBV infection with antibody immune response," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Naim, Mouhcine & Lahmidi, Fouad & Namir, Abdelwahed & Kouidere, Abdelfatah, 2021. "Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. 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).
    6. Jia, Xinjing & Xu, Rui, 2022. "Global dynamics of a delayed HTLV-I infection model with Beddington-DeAngelis incidence and immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    7. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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