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A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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).
    2. 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).

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