IJPAM: Volume 49, No. 4 (2008)
BANG-BANG CONTROLS FOR ANTI-ANGIOGENESIS
UNDER LOGISTIC GROWTH OF THE TUMOR
UNDER LOGISTIC GROWTH OF THE TUMOR
Urszula Ledzewicz, James Munden, Heinz Schättler
Department of Mathematics and Statistics
Southern Illinois University at Edwardsville
P.O. Box 1653, Edwardsville, Illinois, 62026-1653, USA
e-mail: uledzew@siue.edu
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
Department of Mathematics and Statistics
Southern Illinois University at Edwardsville
P.O. Box 1653, Edwardsville, Illinois, 62026-1653, USA
e-mail: uledzew@siue.edu
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