IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4275-d1259165.html
   My bibliography  Save this article

Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions

Author

Listed:
  • Anatolij N. Kanatnikov

    (Department of Mathematical Modeling, Bauman Moscow State Technical University, Moscow 105005, Russia
    These authors contributed equally to this work.)

  • Konstantin E. Starkov

    (Instituto Politecnico Nacional, CITEDI, Av. IPN 1310, Nueva Tijuana 22435, Mexico
    These authors contributed equally to this work.)

Abstract

In this paper we consider the ultimate dynamics of one 4D cancer model which was created for studying the immune response to the two-phenotype tumors. Our approach is based on the localization method of compact invariant sets. The existence of a positively invariant polytope is shown and its size is calculated depending on the parameters of this cancer model. Various convergence conditions to the tumor free equilibrium point were proposed. This property has the biological meaning of global asymptotic tumor eradication (GATE). Further, the case in which local asymptotic tumor eradication (LATE) conditions entail GATE conditions was found. Our theoretical studies of ultimate dynamics are complemented by numerical simulation results.

Suggested Citation

  • Anatolij N. Kanatnikov & Konstantin E. Starkov, 2023. "Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4275-:d:1259165
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4275/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4275/
    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:11:y:2023:i:20:p:4275-:d:1259165. 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.