IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i9p1366-d797261.html
   My bibliography  Save this article

A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials

Author

Listed:
  • Hashem Najafi

    (Department of Mathematics, College of Sciences, Shiraz University, Shiraz 7187919556, Iran
    These authors contributed equally to this work.)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
    These authors contributed equally to this work.)

  • Nichaphat Patanarapeelert

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Joshua Kiddy K. Asamoah

    (Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
    These authors contributed equally to this work.)

  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    These authors contributed equally to this work.)

  • Thanin Sitthiwirattham

    (Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
    These authors contributed equally to this work.)

Abstract

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD 4 + T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial.

Suggested Citation

  • Hashem Najafi & Sina Etemad & Nichaphat Patanarapeelert & Joshua Kiddy K. Asamoah & Shahram Rezapour & Thanin Sitthiwirattham, 2022. "A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1366-:d:797261
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/9/1366/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/9/1366/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Nazir, Ghazala & Shah, Kamal & Debbouche, Amar & Khan, Rahmat Ali, 2020. "Study of HIV mathematical model under nonsingular kernel type derivative of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    6. Begum, Razia & Tunç, Osman & Khan, Hasib & Gulzar, Haseena & Khan, Aziz, 2021. "A fractional order Zika virus model with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Shabir Ahmad & Aman Ullah & Ali Akgül & Manuel De la Sen & Ning Cai, 2021. "Study of HIV Disease and Its Association with Immune Cells under Nonsingular and Nonlocal Fractal-Fractional Operator," Complexity, Hindawi, vol. 2021, pages 1-12, August.
    8. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    9. Khan, Hasib & Ibrahim, Muhammad & Abdel-Aty, Abdel-Haleem & Khashan, M. Motawi & Khan, Farhat Ali & Khan, Aziz, 2021. "A fractional order Covid-19 epidemic model with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    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. Kanwal, Tanzeela & Hussain, Azhar & Avcı, İbrahim & Etemad, Sina & Rezapour, Shahram & Torres, Delfim F.M., 2024. "Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.

    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. Kanwal, Tanzeela & Hussain, Azhar & Avcı, İbrahim & Etemad, Sina & Rezapour, Shahram & Torres, Delfim F.M., 2024. "Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.
    3. Addai, Emmanuel & Zhang, Lingling & Ackora-Prah, Joseph & Gordon, Joseph Frank & Asamoah, Joshua Kiddy K. & Essel, John Fiifi, 2022. "Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    4. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    6. Avcı, İbrahim & Lort, Hüseyin & Tatlıcıoğlu, Buğce E., 2023. "Numerical investigation and deep learning approach for fractal–fractional order dynamics of Hopfield neural network model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Asamoah, Joshua Kiddy K. & Fatmawati,, 2023. "A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    8. Mohammad Partohaghighi & Ali Akgül & Rubayyi T. Alqahtani, 2022. "New Type Modelling of the Circumscribed Self-Excited Spherical Attractor," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    9. Khan, Hasib & Ahmad, Farooq & Tunç, Osman & Idrees, Muhammad, 2022. "On fractal-fractional Covid-19 mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Tyagi, Swati & Martha, Subash C. & Abbas, Syed & Debbouche, Amar, 2021. "Mathematical modeling and analysis for controlling the spread of infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    11. Shahram Rezapour & Chernet Tuge Deressa & Azhar Hussain & Sina Etemad & Reny George & Bashir Ahmad, 2022. "A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    12. Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    13. Akgül, Ali & Partohaghighi, Mohammad, 2022. "New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    14. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. Mahmood, Tariq & ur Rahman, Mati & Arfan, Muhammad & Kayani, Sadaf-Ilyas & Sun, Mei, 2023. "Mathematical study of Algae as a bio-fertilizer using fractal–fractional dynamic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 207-222.
    16. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    17. Farman, Muhammad & Ahmad, Aqeel & Zehra, Anum & Nisar, Kottakkaran Sooppy & Hincal, Evren & Akgul, Ali, 2024. "Analysis and controllability of diabetes model for experimental data by using fractional operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 133-148.
    18. Hussain, Shah & Tunç, Osman & Rahman, Ghaus ur & Khan, Hasib & Nadia, Elissa, 2023. "Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 130-150.
    19. Jiong Weng & Xiaojing Liu & Youhe Zhou & Jizeng Wang, 2022. "An Explicit Wavelet Method for Solution of Nonlinear Fractional Wave Equations," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    20. Sabermahani, Sedigheh & Ordokhani, Yadollah & Rahimkhani, Parisa, 2023. "Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

    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:gam:jmathe:v:10:y:2022:i:9:p:1366-:d:797261. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.