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Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection

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  • Dubey, Preeti
  • Dubey, Uma S.
  • Dubey, Balram

Abstract

This paper deals with the study of a virus dynamics model in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). RTIs prevent viral replication/entry within the infected CD4+ T cells while PIs block the virus assembly and thus further propagation and production of new virions. The proliferation of uninfected CD4+ T cells has been assumed to be as full logistic growth term to capture the dynamics of HIV virus. The model also considers two important components of the acquired immune response, namely the cytotoxic T lymphocyte (CTL) immune response (self stimulation due to infection and stimulation due to infected cells have been considered) and antibody immune response. Critical threshold conditions for the existence of equilibrium points have been determined. We studied the analytical behavior of these equilibrium points locally as well as globally using Lasalle’s invariance principle and Lyapunov’s direct method. We explored the sensitivity of the therapeutic drugs on the model system. Further, the behavior of the proposed model system has been studied numerically through simulation tools.

Suggested Citation

  • Dubey, Preeti & Dubey, Uma S. & Dubey, Balram, 2018. "Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 120-137.
    • Handle: RePEc:eee:matcom:v:144:y:2018:i:c:p:120-137
    DOI: 10.1016/j.matcom.2017.07.006
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    References listed on IDEAS

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    1. Gao, Ting & Wang, Wendi & Liu, Xianning, 2011. "Mathematical analysis of an HIV model with impulsive antiretroviral drug doses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 653-665.
    2. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
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    2. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Noura H. AlShamrani & Reham H. Halawani & Ahmed M. Elaiw, 2023. "Effect of Impaired B-Cell and CTL Functions on HIV-1 Dynamics," Mathematics, MDPI, vol. 11(20), pages 1-39, October.
    4. AlShamrani, N.H., 2021. "Stability of a general adaptive immunity HIV infection model with silent infected cell-to-cell spread," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Naik, Parvaiz Ahmad & Zu, Jian & Ghoreishi, Mohammad, 2020. "Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. Kumar Das, Dhiraj & Khatua, Anupam & Kar, T.K. & Jana, Soovoojeet, 2021. "The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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