IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2016y2016i1n2979414.html

State‐Dependent Impulsive Control Strategies for a Tumor‐Immune Model

Author

Listed:
  • Kwang Su Kim
  • Giphil Cho
  • Lin-Fei Nie
  • Il Hyo Jung

Abstract

Controlling the number of tumor cells leads us to expect more efficient strategies for treatment of tumor. Towards this goal, a tumor‐immune model with state‐dependent impulsive treatments is established. This model may give an efficient treatment schedule to control tumor’s abnormal growth. By using the Poincaré map and analogue of Poincaré criterion, some conditions for the existence and stability of a positive order‐1 periodic solution of this model are obtained. Moreover, we carry out numerical simulations to illustrate the feasibility of our main results and compare fixed‐time impulsive treatment effects with state‐dependent impulsive treatment effects. The results of our simulations say that, in determining optimal treatment timing, the model with state‐dependent impulsive control is more efficient than that with fixed‐time impulsive control.

Suggested Citation

  • Kwang Su Kim & Giphil Cho & Lin-Fei Nie & Il Hyo Jung, 2016. "State‐Dependent Impulsive Control Strategies for a Tumor‐Immune Model," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:2979414
    DOI: 10.1155/2016/2979414
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2016/2979414
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/2979414?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
    ---><---

    References listed on IDEAS

    as
    1. Gao, Ting & Wang, Wendi & Liu, Xianning, 2011. "Mathematical analysis of an HIV model with impulsive antiretroviral drug doses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 653-665.
    Full references (including those not matched with items on IDEAS)

    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. Dubey, Preeti & Dubey, Uma S. & Dubey, Balram, 2018. "Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 120-137.
    2. Xiying Wang & Wei Xu & Yujun Cui & Xiaomei Wang, 2014. "Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Wang, Xiying & Liu, Xinzhi & Xie, Wei-chau & Xu, Wei & Xu, Yong, 2016. "Global stability and persistence of HIV models with switching parameters and pulse control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 123(C), pages 53-67.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnddns:v:2016:y:2016:i:1:n:2979414. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3059 .

    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.