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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 1: 163-183. doi: 10.3934/mbe.2015.12.163
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On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells

  • 1.
    Moscow State University, GSP-1, Leninskie Gory, Moscow
  • 2.
    Federal Science and Clinical Center of the Federal Medical and Biological Agency, 28 Orehovuy boulevard, Moscow, 115682
  • 3.
    Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 Mannheim
  • Received: 01 November 2013 Accepted: 29 June 2018 Published: 01 December 2014

  • MSC : 49J20.

  • A mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. Additionally, we assume some phase constraints for the number of the malignant and the healthy cells and for the total dose of the drug during the whole treatment process.
       We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy.

    Citation: Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel. On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells[J]. Mathematical Biosciences and Engineering, 2015, 12(1): 163-183. doi: 10.3934/mbe.2015.12.163

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  • A mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. Additionally, we assume some phase constraints for the number of the malignant and the healthy cells and for the total dose of the drug during the whole treatment process.
       We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy.


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  • This article has been cited by:

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    2. Alexander Bratus, Igor Samokhin, Ivan Yegorov, Daniil Yurchenko, Maximization of viability time in a mathematical model of cancer therapy, 2017, 294, 00255564, 110, 10.1016/j.mbs.2017.10.011
    3. Mohsen Yousefnezhad, Chiu-Yen Kao, Seyyed Abbas Mohammadi, Optimal Chemotherapy for Brain Tumor Growth in a Reaction-Diffusion Model, 2021, 81, 0036-1399, 1077, 10.1137/20M135995X
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