IJPAM: Volume 49, No. 4 (2008)

BANG-BANG CONTROLS FOR ANTI-ANGIOGENESIS
UNDER LOGISTIC GROWTH OF THE TUMOR

Urszula Ledzewicz$^1$, James Munden$^2$, Heinz Schättler$^3$
$^{1,2}$Department of Mathematics and Statistics
Southern Illinois University at Edwardsville
P.O. Box 1653, Edwardsville, Illinois, 62026-1653, USA
$^1$e-mail: uledzew@siue.edu
$^3$Department of Electrical and Systems Engineering
Washington University
One Brookings Drive, P.O. Box 1127
St. Louis, Missouri, 63130, USA
e-mail: hms@wustl.edu


Abstract.The scheduling of angiogenic inhibitors is analyzed as an optimal control problem for a mathematical model for tumor anti-angiogenesis proposed by Ergun et al [#!ECW!#] with a logistic growth function modeling tumor growth. It is shown that optimal controls are bang-bang with at most two switchings.

Received: August 14, 2008

AMS Subject Classification: 49J15, 93C50

Key Words and Phrases: optimal control, cancer treatments, maximum principle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4