IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i1p52-d304217.html
   My bibliography  Save this article

Nonlinear Spatiotemporal Viral Infection Model with CTL Immunity: Mathematical Analysis

Author

Listed:
  • Jaouad Danane

    (Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O.Box 146, Mohammedia, Morocco)

  • Karam Allali

    (Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O.Box 146, Mohammedia, Morocco)

  • Léon Matar Tine

    (CNRS UMR 5208 Institut Camille Jordan, University Claude Bernard Lyon 1, University de Lyon, 69622 Villeurbanne CEDEX, France
    INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France)

  • Vitaly Volpert

    (CNRS UMR 5208 Institut Camille Jordan, University Claude Bernard Lyon 1, University de Lyon, 69622 Villeurbanne CEDEX, France
    INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
    S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

Abstract

A mathematical model describing viral dynamics in the presence of the latently infected cells and the cytotoxic T-lymphocytes cells (CTL), taking into consideration the spatial mobility of free viruses, is presented and studied. The model includes five nonlinear differential equations describing the interaction among the uninfected cells, the latently infected cells, the actively infected cells, the free viruses, and the cellular immune response. First, we establish the existence, positivity, and boundedness for the suggested diffusion model. Moreover, we prove the global stability of each steady state by constructing some suitable Lyapunov functionals. Finally, we validated our theoretical results by numerical simulations for each case.

Suggested Citation

  • Jaouad Danane & Karam Allali & Léon Matar Tine & Vitaly Volpert, 2020. "Nonlinear Spatiotemporal Viral Infection Model with CTL Immunity: Mathematical Analysis," Mathematics, MDPI, vol. 8(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:52-:d:304217
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/1/52/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/1/52/
    Download Restriction: no
    ---><---

    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:8:y:2020:i:1:p:52-:d:304217. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.