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Optimization of Cytostatic Leukemia Therapy in an Advection–Reaction–Diffusion Model

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  • Chahrazed Benosman

    (Université de Tlemcen)

  • Bedr’Eddine Aïnseba

    (Université de Bordeaux)

  • Arnaud Ducrot

    (Université de Bordeaux)

Abstract

In this work, we study an advection–reaction–diffusion system involving normal and cancer hematopoietic cells (HC) and modeling the development of leukemia in the bone marrow. The effects of a targeted cytostatic therapy, which inhibits the regeneration of cancer HC, are studied through an optimal control system. We prove the existence of a positive bounded solution and the existence of an optimal controls by semigroup techniques. Conditions of optimality are in terms of the dual system. The effects of targeted cytostatic therapy, upon the dynamics of normal and cancer HC, are discussed through numerical simulations.

Suggested Citation

  • Chahrazed Benosman & Bedr’Eddine Aïnseba & Arnaud Ducrot, 2015. "Optimization of Cytostatic Leukemia Therapy in an Advection–Reaction–Diffusion Model," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 296-325, October.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-014-0667-7
    DOI: 10.1007/s10957-014-0667-7
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    References listed on IDEAS

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    1. V. Barbu & M. Iannelli, 1999. "Optimal Control of Population Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 1-14, July.
    2. Wenxue Ma & Alejandro Gutierrez & Daniel J Goff & Ifat Geron & Anil Sadarangani & Christina A M Jamieson & Angela C Court & Alice Y Shih & Qingfei Jiang & Christina C Wu & Kang Li & Kristen M Smith & , 2012. "NOTCH1 Signaling Promotes Human T-Cell Acute Lymphoblastic Leukemia Initiating Cell Regeneration in Supportive Niches," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-14, June.
    3. Tannishtha Reya & Sean J. Morrison & Michael F. Clarke & Irving L. Weissman, 2001. "Stem cells, cancer, and cancer stem cells," Nature, Nature, vol. 414(6859), pages 105-111, November.
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    Cited by:

    1. Emmanuelle Augeraud-Véron & Catherine Choquet & Éloïse Comte, 2017. "Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 941-966, June.

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