On optimal and suboptimal treatment strategies for a mathematical model of  leukemia

Elena Fimmel; Yury S. Semenov; Alexander S. Bratus

doi:10.3934/mbe.2013.10.151

Article Contents

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: February 29, 2012

Revised: July 31, 2012

Published: November 2012

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Abstract

In this work an optimization problem for a leukemia treatment model based on the Gompertzian law of cell growth is considered. The quantities of the leukemic and of the healthy cells at the end of the therapy are chosen as the criterion of the treatment quality. In the case where the number of healthy 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 therapy processes is given. If this is not the case, a control strategy called alternative is suggested.

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Mathematics Subject Classification: 49J15.

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