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Optimal control analysis of a leukemia model under imatinib treatment

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  • Rădulescu, I.R.
  • Cândea, D.
  • Halanay, A.

Abstract

The paper is devoted to the study of a mathematical model of drug therapy for Chronic Myelogenous Leukemia (CML). The disease dynamics are given by a couple of delay differential equations that describe the interaction between a stem-like population of CML cells and a more mature, differentiated one, without self-renewal properties. A molecular targeted therapy, such as Imatinib, is considered. The objective is to minimize the size of the tumoral cells’ mass while minimizing the amount of drug (thus, minimizing both the adverse effects and the costs). The optimal control is calculated using a discretization scheme. The results are supported by numerical simulations.

Suggested Citation

  • Rădulescu, I.R. & Cândea, D. & Halanay, A., 2016. "Optimal control analysis of a leukemia model under imatinib treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 1-11.
    • Handle: RePEc:eee:matcom:v:121:y:2016:i:c:p:1-11
    DOI: 10.1016/j.matcom.2015.03.002
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    References listed on IDEAS

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    1. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    2. Franziska Michor & Timothy P. Hughes & Yoh Iwasa & Susan Branford & Neil P. Shah & Charles L. Sawyers & Martin A. Nowak, 2005. "Dynamics of chronic myeloid leukaemia," Nature, Nature, vol. 435(7046), pages 1267-1270, June.
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    Cited by:

    1. Svetlana Bunimovich-Mendrazitsky & Benzion Shklyar, 2017. "Optimization of Combined Leukemia Therapy by Finite-Dimensional Optimal Control Modeling," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 218-235, October.
    2. Pan, Sonjoy & Raha, Soumyendu & Chakrabarty, Siddhartha P., 2020. "A quantitative study on the role of TKI combined with Wnt/β-catenin signaling and IFN-α in the treatment of CML through deterministic and stochastic approaches," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).

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