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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 151 - 165, Volume 10, Issue 1, February 2013      doi:10.3934/mbe.2013.10.151

 
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Elena Fimmel - Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 Mannheim, Germany (email)
Yury S. Semenov - Moscow State University of Railway Engineering, Obraztsova 15, Moscow, 127994, Russian Federation (email)
Alexander S. Bratus - Moscow State University of Railway Engineering, Obraztsova 15, Moscow, 127994, Russian Federation (email)

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.

Keywords:  Optimal therapy control, chemotherapy, cancer model.
Mathematics Subject Classification:  49J15.

Received: March 2012;      Accepted: August 2012;      Available Online: December 2012.

 References