IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v349y2019icp118-133.html
   My bibliography  Save this article

A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia

Author

Listed:
  • Rodrigues, D.S.
  • Mancera, P.F.A.
  • Carvalho, T.
  • Gonçalves, L.F.

Abstract

Immunotherapy is currently regarded as the most promising treatment to fight against cancer. This is particularly true in the treatment of chronic lymphocytic leukemia, an indolent neoplastic disease of B-lymphocytes which eventually causes the immune system’s failure. In this and other areas of cancer research, mathematical modeling is pointed out as a prominent tool to analyze theoretical and practical issues. Its lack in studies of chemoimmunotherapy of chronic lymphocytic leukemia is what motivated us to come up with a simple ordinary differential equation model. It is based on ideas of de Pillis and Radunskaya and on standard pharmacokinetics-pharmacodynamics assumptions. In order to check the positivity of the state variables, we first establish an invariant region where these time-dependent variables remain positive. Afterwards, the action of the immune system, as well as the chemoimmunotherapeutic role in promoting cancer cure are investigated by means of numerical simulations and the classical linear stability analysis. The role of adoptive cellular immunotherapy is also addressed. Our overall conclusion is that chemoimmunotherapeutic protocols can be effective in treating chronic lymphocytic leukemia provided that chemotherapy is not a limiting factor to the immunotherapy efficacy.

Suggested Citation

  • Rodrigues, D.S. & Mancera, P.F.A. & Carvalho, T. & Gonçalves, L.F., 2019. "A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 118-133.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:118-133
    DOI: 10.1016/j.amc.2018.12.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031831049X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.12.008?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. Sébastien Benzekry & Clare Lamont & Afshin Beheshti & Amanda Tracz & John M L Ebos & Lynn Hlatky & Philip Hahnfeldt, 2014. "Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth," PLOS Computational Biology, Public Library of Science, vol. 10(8), pages 1-19, August.
    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. Rodrigues, Diego S. & Mancera, Paulo F.A. & Carvalho, Tiago & Gonçalves, Luiz Fernando, 2020. "Sliding mode control in a mathematical model to chemoimmunotherapy: The occurrence of typical singularities," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    2. Chieregato Vicentin, Daniel & Mancera, Paulo F. A. & Carvalho, Tiago & Fernando Gonçalves, Luiz, 2020. "Mathematical model of an antiretroviral therapy to HIV via Filippov theory," Applied Mathematics and Computation, Elsevier, vol. 387(C).

    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. Ahmed, Najma & Shah, Nehad Ali & Taherifar, Somaye & Zaman, F.D., 2021. "Memory effects and of the killing rate on the tumor cells concentration for a one-dimensional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Cabrales, Luis Enrique Bergues & Montijano, Juan I. & Schonbek, Maria & Castañeda, Antonio Rafael Selva, 2018. "A viscous modified Gompertz model for the analysis of the kinetics of tumors under electrochemical therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 96-110.
    3. Bulai, I.M. & De Bonis, M.C. & Laurita, C. & Sagaria, V., 2023. "Modeling metastatic tumor evolution, numerical resolution and growth prediction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 721-740.
    4. Alex Root, 2019. "Mathematical Modeling of The Challenge to Detect Pancreatic Adenocarcinoma Early with Biomarkers," Challenges, MDPI, vol. 10(1), pages 1-15, April.
    5. Charalambos Loizides & Demetris Iacovides & Marios M Hadjiandreou & Gizem Rizki & Achilleas Achilleos & Katerina Strati & Georgios D Mitsis, 2015. "Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-18, December.
    6. Hamzeh Zureigat & Mohammed Al-Smadi & Areen Al-Khateeb & Shrideh Al-Omari & Sharifah Alhazmi, 2023. "Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells," IJERPH, MDPI, vol. 20(4), pages 1-13, February.
    7. Gregory Baramidze & Victoria Baramidze & Ying Xu, 2021. "Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-31, November.
    8. Ella Ya Tyuryumina & Alexey A Neznanov, 2018. "Consolidated mathematical growth model of the primary tumor and secondary distant metastases of breast cancer (CoMPaS)," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-16, July.
    9. Pelayo Martínez-Fernández & Zulima Fernández-Muñiz & Ana Cernea & Juan Luis Fernández-Martínez & Andrzej Kloczkowski, 2023. "Three Mathematical Models for COVID-19 Prediction," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    10. Marcia Cruz-Correa & Elba C. Díaz-Toro & Jorge L. Falcón & Enid J. García-Rivera & Humberto M. Guiot & Wanda T. Maldonado-Dávila & Karen G. Martínez & William Méndez-Latalladi & Cynthia M. Pérez & Myr, 2020. "Public Health Academic Alliance for COVID-19 Response: The Role of a National Medical Task Force in Puerto Rico," IJERPH, MDPI, vol. 17(13), pages 1-14, July.

    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:apmaco:v:349:y:2019:i:c:p:118-133. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.