IJPAM: Volume 54, No. 1 (2009)
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Invited Lecture Delivered at
Fifth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2008)
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MODEL FOR CANCER THERAPY
WITH PENALTY ON THE COST OF TREATMENT
Urszula Ledzewicz
, Vignon Oussa
, 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
, Vignon Oussa, 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
Abstract.For a biologically validated mathematical model for tumor
anti-angiogenesis developed by Hahnfeldt et al [#!Hahnfeldt!#]
the scheduling of angiogenic inhibitors is analyzed as an optimal
control problem. In the objective a weighted balance between tumor
reduction and the total amount of angiogenic inhibitors given is
considered. Bifurcations of optimal solutions are illustrated numerically.
Received: August 16, 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: 2009
Volume: 54
Issue: 1