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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 1: 151-165. doi: 10.3934/mbe.2013.10.151
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On optimal and suboptimal treatment strategies for a mathematical model of leukemia

  • 1.
    Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 Mannheim
  • 2.
    Moscow State University of Railway Engineering, Obraztsova 15, Moscow, 127994
  • Received: 01 March 2012 Accepted: 29 June 2018 Published: 01 December 2012

  • MSC : 49J15.

  • In this work an optimization problem for a leukemia treatment modelbased on the Gompertzian law of cell growth is considered. The quantitiesof the leukemic and of the healthy cells at the end of the therapy are chosenas the criterion of the treatment quality. In the case where the number ofhealthy cells at the end of the therapy is higher than a chosen desired number,an analytical solution of the optimization problem for a wide class of therapyprocesses is given. If this is not the case, a control strategy called alternative issuggested.

    Citation: Elena Fimmel, Yury S. Semenov, Alexander S. Bratus. On optimal and suboptimal treatment strategies for a mathematical model of leukemia[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 151-165. doi: 10.3934/mbe.2013.10.151

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  • In this work an optimization problem for a leukemia treatment modelbased on the Gompertzian law of cell growth is considered. The quantitiesof the leukemic and of the healthy cells at the end of the therapy are chosenas the criterion of the treatment quality. In the case where the number ofhealthy cells at the end of the therapy is higher than a chosen desired number,an analytical solution of the optimization problem for a wide class of therapyprocesses is given. If this is not the case, a control strategy called alternative issuggested.


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