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Dynamical Analysis of Posttreatment HIV‐1 Infection Model

Author

Listed:
  • M. Pradeesh
  • A. Manivannan
  • S. Lakshmanan
  • F. A. Rihan
  • Prakash Mani

Abstract

This paper aims to explore the dynamic characteristics of the post treatment human immunodeficiency virus (HIV) type‐1 model by proposing the theoretical frameworks. Distinct from the previous works, this study explores the effect of effector cells, loss of functional effector cells, and two types of anti‐retroviral therapies such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs) and also the effect of intracellular time delay. Based on the Routh—Hurwitz criterion and eigenvalue analysis, the stability of the proposed HIV‐1 model is analyzed. To reveal the significance of time delay, the Hopf‐type bifurcation analysis is performed. The optimal control algorithm is designed by choosing the antiviral therapies such as RTI and PI as control parameters. Numerical simulations are performed to validate the effectiveness of the proposed theoretical frameworks.

Suggested Citation

  • M. Pradeesh & A. Manivannan & S. Lakshmanan & F. A. Rihan & Prakash Mani, 2022. "Dynamical Analysis of Posttreatment HIV‐1 Infection Model," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:9752628
    DOI: 10.1155/2022/9752628
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    References listed on IDEAS

    as
    1. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    2. Naveed Iqbal & Yeliz Karaca, 2021. "Complex Fractional-Order Hiv Diffusion Model Based On Amplitude Equations With Turing Patterns And Turing Instability," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-16, August.
    3. Shah Hussain & Elissa Nadia Madi & Naveed Iqbal & Thongchai Botmart & Yeliz Karaca & Wael W. Mohammed, 2021. "Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    4. Nabi, Khondoker Nazmoon & Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Projections and fractional dynamics of COVID-19 with optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Kumar, Pushpendra & Erturk, Vedat Suat & Vellappandi, M. & Trinh, Hieu & Govindaraj, V., 2022. "A study on the maize streak virus epidemic model by using optimized linearization-based predictor-corrector method in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    6. Rihan, F.A. & Lakshmanan, S. & Maurer, H., 2019. "Optimal control of tumour-immune model with time-delay and immuno-chemotherapy," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 147-165.
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    1. Nath, Bhagya Jyoti & Sadri, Khadijeh & Sarmah, Hemanta Kumar & Hosseini, Kamyar, 2024. "An optimal combination of antiretroviral treatment and immunotherapy for controlling HIV infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 226-243.

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