IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921007839.html
   My bibliography  Save this article

Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method

Author

Listed:
  • Attaullah,
  • Jan, Rashid
  • Yüzbaşı, Şuayip

Abstract

In this paper, we formulate the intricate process of Human Immunodeficiency Virus (HIV) infection in a mathematical model. In the formulation of the model, the density of CD4+ T-cells is categorized into healthy and infected classes while the density of free HIV viruses in the human host’s blood is considered a separate class. It is reported that when HIV enters a human’s body, it infects a large amount of CD4+ T-cells and unbalance the supply of new cells from the thymus. Therefore, we incorporate variable source term relying on the viral load for the supply of new cells instead of using a fixed value for the supply of these cells. We implement a continuous Galerkin Petrov time discretization scheme, particularly cGP(2)-scheme to visualize the dynamical behavior of the mentioned model and a detailed description of the effects of different physical parameters of interest are depicts graphically and discuss that how the level of healthy, infected CD4+ T-cells and free HIV particles varies concerning the emerging parameters in the model. In the proposed cGP(2)-method, two unknowns terms can be found by solving a 2×2 block system. This method is accurate of order 3 in the whole time interval and shows even superconvergence of order 4 in the discrete-time points. Furthermore, determine the solution of the model utilizing the fourth-order Runge-Kutta (RK4)-method and find out the absolute errors between the solutions obtained from both approaches. Finally, the validity and reliability of the proposed scheme are verified by comparing the numerical and graphical results with the RK-4 method. We examine the accuracy of the cGP(2)-sheme and observe that it produces more accurate results at relatively larger step sizes as in comparison to RK-4 scheme. Correspondence between the findings of cGP(2)-method and RK4-method reveal that the new technique is a promising tool for obtaining approximate solutions to the nonlinear systems of real-world problems.

Suggested Citation

  • Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007839
    DOI: 10.1016/j.chaos.2021.111429
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921007839
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111429?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. 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).
    3. Mojaver, Aida & Kheiri, Hossein, 2015. "Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 258-270.
    4. Alan S. Perelson & Paulina Essunger & Yunzhen Cao & Mika Vesanen & Arlene Hurley & Kalle Saksela & Martin Markowitz & David D. Ho, 1997. "Decay characteristics of HIV-1-infected compartments during combination therapy," Nature, Nature, vol. 387(6629), pages 188-191, May.
    5. Cheng, Yan & Li, Mingtao & Zhang, Fumin, 2019. "A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 62-70.
    6. Liu, Qun & Jiang, Daqing, 2020. "Dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Jan, Rashid & Khan, Muhammad Altaf & Kumam, Poom & Thounthong, Phatiphat, 2019. "Modeling the transmission of dengue infection through fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 189-216.
    8. Mann Manyombe, M.L. & Mbang, J. & Chendjou, G., 2021. "Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    9. Abdel-Aty, Abdel-Haleem & Khater, Mostafa M.A. & Dutta, Hemen & Bouslimi, Jamel & Omri, M., 2020. "Computational solutions of the HIV-1 infection of CD4+T-cells fractional mathematical model that causes acquired immunodeficiency syndrome (AIDS) with the effect of antiviral drug therapy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Alex Sigal & Jocelyn T. Kim & Alejandro B. Balazs & Erez Dekel & Avi Mayo & Ron Milo & David Baltimore, 2011. "Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy," Nature, Nature, vol. 477(7362), pages 95-98, September.
    11. 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.
    12. Carla M. A. Pinto & Ana R. M. Carvalho & Dumitru Baleanu & Hari M. Srivastava, 2019. "Efficacy of the Post-Exposure Prophylaxis and of the HIV Latent Reservoir in HIV Infection," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    13. Gilad Doitsh & Nicole L. K. Galloway & Xin Geng & Zhiyuan Yang & Kathryn M. Monroe & Orlando Zepeda & Peter W. Hunt & Hiroyu Hatano & Stefanie Sowinski & Isa Muñoz-Arias & Warner C. Greene, 2014. "Cell death by pyroptosis drives CD4 T-cell depletion in HIV-1 infection," Nature, Nature, vol. 505(7484), pages 509-514, January.
    14. Wang, Ying & Liu, Lishan & Zhang, Xinguang & Wu, Yonghong, 2015. "Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 312-324.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Şuayip Yüzbaşı & Gamze Yıldırım, 2023. "A Pell–Lucas Collocation Approach for an SIR Model on the Spread of the Novel Coronavirus (SARS CoV-2) Pandemic: The Case of Turkey," Mathematics, MDPI, vol. 11(3), pages 1-22, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christian L Althaus & Beda Joos & Alan S Perelson & Huldrych F Günthard, 2014. "Quantifying the Turnover of Transcriptional Subclasses of HIV-1-Infected Cells," PLOS Computational Biology, Public Library of Science, vol. 10(10), pages 1-11, October.
    2. Noura H. AlShamrani & Ahmed Elaiw & Aeshah A. Raezah & Khalid Hattaf, 2023. "Global Dynamics of a Diffusive Within-Host HTLV/HIV Co-Infection Model with Latency," Mathematics, MDPI, vol. 11(6), pages 1-47, March.
    3. A. M. Elaiw & N. H. AlShamrani & E. Dahy & A. A. Abdellatif & Aeshah A. Raezah, 2023. "Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection," Mathematics, MDPI, vol. 11(3), pages 1-26, January.
    4. Mojaver, Aida & Kheiri, Hossein, 2015. "Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 258-270.
    5. Wang, Jinliang & Guo, Min & Liu, Xianning & Zhao, Zhitao, 2016. "Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 149-161.
    6. Zhang, Tongqian & Xu, Xinna & Wang, Xinzeng, 2023. "Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Günerhan, Hatıra & Dutta, Hemen & Dokuyucu, Mustafa Ali & Adel, Waleed, 2020. "Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Tao Lu & Yangxin Huang & Min Wang & Feng Qian, 2014. "A refined parameter estimating approach for HIV dynamic model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1645-1657, August.
    9. Mangal, Shiv & Misra, O.P. & Dhar, Joydip, 2023. "Fractional-order deterministic epidemic model for the spread and control of HIV/AIDS with special reference to Mexico and India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 82-102.
    10. González, Ramón E.R. & Coutinho, Sérgio & Zorzenon dos Santos, Rita Maria & de Figueirêdo, Pedro Hugo, 2013. "Dynamics of the HIV infection under antiretroviral therapy: A cellular automata approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4701-4716.
    11. Martinez, V.M. & Barbosa, A.N. & Mancera, P.F.A. & Rodrigues, D.S. & Camargo, R.F., 2021. "A fractional calculus model for HIV dynamics: real data, parameter estimation and computational strategies," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. 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).
    13. Arshad, Sadia & Defterli, Ozlem & Baleanu, Dumitru, 2020. "A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    14. Sutimin, & Wijaya, Karunia Putra & Páez Chávez, Joseph & Tian, Tianhai, 2021. "An in-host HIV-1 infection model incorporating quiescent and activated CD4+ T cells as well as CTL response," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    15. Renée R. C. E. Schreurs & Athanasios Koulis & Thijs Booiman & Brigitte Boeser-Nunnink & Alexandra P. M. Cloherty & Anusca G. Rader & Kharishma S. Patel & Neeltje A. Kootstra & Carla M. S. Ribeiro, 2024. "Autophagy-enhancing ATG16L1 polymorphism is associated with improved clinical outcome and T-cell immunity in chronic HIV-1 infection," Nature Communications, Nature, vol. 15(1), pages 1-19, December.
    16. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    17. Yongyi Gu & Fanning Meng, 2019. "Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods," Complexity, Hindawi, vol. 2019, pages 1-11, August.
    18. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    19. Iraj Hosseini & Feilim Mac Gabhann, 2012. "Multi-Scale Modeling of HIV Infection in vitro and APOBEC3G-Based Anti-Retroviral Therapy," PLOS Computational Biology, Public Library of Science, vol. 8(2), pages 1-17, February.
    20. E Fabian Cardozo & Adriana Andrade & John W Mellors & Daniel R Kuritzkes & Alan S Perelson & Ruy M Ribeiro, 2017. "Treatment with integrase inhibitor suggests a new interpretation of HIV RNA decay curves that reveals a subset of cells with slow integration," PLOS Pathogens, Public Library of Science, vol. 13(7), pages 1-18, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007839. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.