IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2344-d855695.html
   My bibliography  Save this article

Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2

Author

Listed:
  • Kaushik Dehingia

    (Department of Mathematics, Sonari College, Sonari 785690, Assam, India
    These authors contributed equally to this work.)

  • Ahmed A. Mohsen

    (Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad 10071, Iraq
    Ministry of Education, Rusafa 1, Baghdad 10071, Iraq
    These authors contributed equally to this work.)

  • Sana Abdulkream Alharbi

    (Department of Mathematics & Statistics, College of Science, Taibah University, Yanbu 41911, Almadinah Almunawarah, Saudi Arabia)

  • Reima Daher Alsemiry

    (Department of Mathematics & Statistics, College of Science, Taibah University, Yanbu 41911, Almadinah Almunawarah, Saudi Arabia)

  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan)

Abstract

The prime objective of the current study is to propose a novel mathematical framework under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for the existence of equilibria of the model and computed the basic reproduction number R 0 . We used mathematical analysis to establish the proposed model’s local and global stability results. Some numerical resolutions of our theoretical results are presented. The main result of this study is that as the fractional derivative order increases, the approach of the solution to the equilibrium points becomes faster. It is also observed that the value of R 0 increases as the value of β and π v increases.

Suggested Citation

  • Kaushik Dehingia & Ahmed A. Mohsen & Sana Abdulkream Alharbi & Reima Daher Alsemiry & Shahram Rezapour, 2022. "Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2344-:d:855695
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2344/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2344/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vasiliy N. Afonyushkin & Ilya R. Akberdin & Yulia N. Kozlova & Ivan A. Schukin & Tatyana E. Mironova & Anna S. Bobikova & Viktoriya S. Cherepushkina & Nikolaj A. Donchenko & Yulia E. Poletaeva & Fedor, 2022. "Multicompartmental Mathematical Model of SARS-CoV-2 Distribution in Human Organs and Their Treatment," Mathematics, MDPI, vol. 10(11), pages 1-21, June.
    2. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Yingdong Yin & Yupeng Xi & Cheng Xu & Qiwen Sun, 2022. "The Basic Reproduction Number and Delayed Action of T Cells for Patients Infected with SARS-CoV-2," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    4. Sana Abdulkream Alharbi & Azmin Sham Rambely, 2020. "A New ODE-Based Model for Tumor Cells and Immune System Competition," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    5. Khalid Hattaf & Noura Yousfi, 2020. "Global Stability for Fractional Diffusion Equations in Biological Systems," Complexity, Hindawi, vol. 2020, pages 1-6, August.
    6. Abdulkafi M. Saeed & Mohammed S. Abdo & Mdi Begum Jeelani, 2021. "Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives," Mathematics, MDPI, vol. 9(20), pages 1-17, October.
    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. Huda Abdul Satar & Raid Kamel Naji, 2023. "A Mathematical Study for the Transmission of Coronavirus Disease," Mathematics, MDPI, vol. 11(10), pages 1-20, May.

    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. Kouidere, Abdelfatah & Balatif, Omar & Rachik, Mostafa, 2021. "Analysis and optimal control of a mathematical modeling of the spread of African swine fever virus with a case study of South Korea and cost-effectiveness," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. 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).
    4. 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.
    5. Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Alotaibi, Naif D., 2021. "A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Batabyal, Saikat, 2021. "COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Chen, Jinbao & Zheng, Yang & Liu, Dong & Du, Yang & Xiao, Zhihuai, 2023. "Quantitative stability analysis of complex nonlinear hydraulic turbine regulation system based on accurate calculation," Applied Energy, Elsevier, vol. 351(C).
    8. Trikha, Pushali & Mahmoud, Emad E. & Jahanzaib, Lone Seth & Matoog, R.T. & Abdel-Aty, Mahmoud, 2021. "Fractional order biological snap oscillator: Analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    9. Yin, Xuecheng & Büyüktahtakın, İ. Esra & Patel, Bhumi P., 2023. "COVID-19: Data-Driven optimal allocation of ventilator supply under uncertainty and risk," European Journal of Operational Research, Elsevier, vol. 304(1), pages 255-275.
    10. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.
    11. Babaei, A. & Jafari, H. & Banihashemi, S. & Ahmadi, M., 2021. "Mathematical analysis of a stochastic model for spread of Coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    12. 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).
    13. Christopher Nicholas Angstmann & Byron Alexander Jacobs & Bruce Ian Henry & Zhuang Xu, 2020. "Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    14. Sajjad, Assad & Farman, Muhammad & Hasan, Ali & Nisar, Kottakkaran Sooppy, 2023. "Transmission dynamics of fractional order yellow virus in red chili plants with the Caputo–Fabrizio operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 347-368.
    15. Jianyu Wang & Chunhua Fang & Guifeng Zhang, 2023. "Multi-Effective Collocation Methods for Solving the Volterra Integral Equation with Highly Oscillatory Fourier Kernels," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    16. Abdel-Rehim, E.A. & Hassan, R.M. & El-Sayed, A.M.A., 2021. "On simulating the short and long memory of ergodic Markov and Non-Markov genetic diffusion processes on the long run," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    17. Dmitry Grebennikov & Antonina Karsonova & Marina Loguinova & Valentina Casella & Andreas Meyerhans & Gennady Bocharov, 2022. "Predicting the Kinetic Coordination of Immune Response Dynamics in SARS-CoV-2 Infection: Implications for Disease Pathogenesis," Mathematics, MDPI, vol. 10(17), pages 1-27, September.
    18. Fernando Alcántara-López & Carlos Fuentes & Carlos Chávez & Jesús López-Estrada & Fernando Brambila-Paz, 2022. "Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data," Mathematics, MDPI, vol. 10(5), pages 1-18, March.
    19. Baba, Isa Abdullahi & Nasidi, Bashir Ahmad, 2021. "Fractional Order Model for the Role of Mild Cases in the Transmission of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    20. Alexander Domoshnitsky & Alexander Sitkin & Lea Zuckerman, 2022. "Mathematical Modeling of COVID-19 Transmission in the Form of System of Integro-Differential Equations," Mathematics, MDPI, vol. 10(23), pages 1-17, November.

    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:13:p:2344-:d:855695. 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.