IJPAM: Volume 54, No. 1 (2009)

Invited Lecture Delivered at
Fifth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2008)


MODEL FOR CANCER THERAPY
WITH PENALTY ON THE COST OF TREATMENT

Urszula Ledzewicz$^1$, Vignon Oussa$^2$, 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: [email protected]
$^3$Department of Electrical and Systems Engineering
Washington University
One Brookings Drive, P.O. Box 1127
St. Louis, Missouri 63130, USA
e-mail: [email protected]


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