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Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method

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  • Naik, Parvaiz Ahmad
  • Zu, Jian
  • Ghoreishi, Mohammad

Abstract

Viruses have different mechanisms in causing a disease in an organism, which largely depend on the viral species. The recent advancement, through coupling data analysis and mathematical modeling, has allowed the identification and characterization of the nature of the virus. In the present paper, the homotopy analysis method is applied to provide an approximate solution of the basic HIV viral dynamic model describing the viral dynamics in a susceptible population. The proposed method allows for the solution of the governing system of differential equations to be calculated in the form of an infinite series with components which can be easily calculated. The homotopy analysis method utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. By using the homotopy series solutions, firstly, several β−curves using an appropriate ratio are plotted to demonstrate the regions of convergence and the optimum value of ℏ, then the residual and absolute errors are obtained for different values of these regions. Secondly, the residual error functions are applied to show the accuracy of the applied homotopy analysis method. Also, the convergence theorem of homotopy analysis method for the HIV viral dynamic model is proved. Mathematica software is used for the calculations and numerical results. The results obtained show the effectiveness and strength of the homotopy analysis method.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304527
    DOI: 10.1016/j.chaos.2019.109500
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Essam R. El-Zahar & Ghaliah F. Al-Boqami & Haifa S. Al-Juaydi, 2024. "Approximate Analytical Solutions for Strongly Coupled Systems of Singularly Perturbed Convection–Diffusion Problems," Mathematics, MDPI, vol. 12(2), pages 1-24, January.
    2. Samad Noeiaghdam & Sanda Micula, 2021. "Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection," Mathematics, MDPI, vol. 9(9), pages 1-24, May.
    3. 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).
    4. Liu, Tao, 2022. "Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. Naik, Parvaiz Ahmad & Owolabi, Kolade M. & Yavuz, Mehmet & Zu, Jian, 2020. "Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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