IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v190y2021icp1-14.html
   My bibliography  Save this article

Analysis of tumor cells in the absence and presence of chemotherapeutic treatment: The case of Caputo-Fabrizio time fractional derivative

Author

Listed:
  • Kumar, S.
  • Das, Subir
  • Ong, S.H.

Abstract

In this work, a study of the mathematical model of uncontrolled growth of tumor cells in the presence of chemotherapy is proposed. The fractional form of the model with the non-singular exponential kernel is considered. This model consists of four coupled partial differential equations (PDEs) which depict the relationship among the normal, tumor, immune cells, and the chemotherapy parameter. The purpose is to investigate the behavior of all types of cells with a change in the fractional order parameter and to show the effect of chemotherapeutic treatment on tumor cells with different levels of immune system. Before applying the proposed numerical method, an approximate expression for the fractional-order Caputo-Fabrizio (C-F) derivative of polynomial function xk is derived. A shifted Chebyshev operational matrix of fractional order derivative is deduced by using an approximation of the C-F fractional derivative of the function and some properties of the orthogonal polynomials. The system of four coupled fractional order PDEs is studied by using the operational matrix method. The dynamics of all the aforementioned cells with respect to different fractional order derivatives are derived and computed numerically for the prescribed values of parameters. These are depicted through graphs to study the diffusive nature of cells and the effect of chemotherapy on all types of cells, before and after applying the therapy. This study shows that tumor cell growth decreases with time when chemotherapy treatment is started. The concentration of tumor cells is more in the invasive fronts of the tumor site as compared to the center of the tumor. It is concluded that the growth of tumor cells is less due to chemotherapy treatment for a person with a strong immune system.

Suggested Citation

  • Kumar, S. & Das, Subir & Ong, S.H., 2021. "Analysis of tumor cells in the absence and presence of chemotherapeutic treatment: The case of Caputo-Fabrizio time fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1-14.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:1-14
    DOI: 10.1016/j.matcom.2021.05.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421001786
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.05.007?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Abernethy, Sam & Gooding, Robert J., 2018. "The importance of chaotic attractors in modelling tumour growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 268-277.
    2. A. H. Bhrawy & D. Baleanu & L. M. Assas & J. A. Tenreiro Machado, 2013. "On a Generalized Laguerre Operational Matrix of Fractional Integration," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, March.
    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. Bambe Moutsinga, Claude Rodrigue & Pindza, Edson & Maré, Eben, 2021. "Comparative performance of time spectral methods for solving hyperchaotic finance and cryptocurrency systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Kumar, Sachin & Nieto, Juan J. & Ahmad, Bashir, 2022. "Chebyshev spectral method for solving fuzzy fractional Fredholm–Volterra integro-differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 501-513.
    3. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. Yan, Shaohui & Wang, Ertong & Gu, Binxian & Wang, Qiyu & Ren, Yu & Wang, Jianjian, 2022. "Analysis and finite-time synchronization of a novel double-wing chaotic system with transient chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    5. Das, Parthasakha & Mukherjee, Sayan & Das, Pritha, 2019. "An investigation on Michaelis - Menten kinetics based complex dynamics of tumor - immune interaction," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 297-305.
    6. Konstantin E. Starkov & Alexander P. Krishchenko, 2024. "On the Dynamics of Immune-Tumor Conjugates in a Four-Dimensional Tumor Model," Mathematics, MDPI, vol. 12(6), pages 1-16, March.
    7. Guimarães, O. & Labecca, W. & Piqueira, José R.C., 2022. "Solving 2nd order BVPs in planar irregular domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 1-22.

    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:eee:matcom:v:190:y:2021:i:c:p:1-14. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.