Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis
-
1.
Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899
-
2.
Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653
-
3.
Dept. of Mathematics and Statistic, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653
-
Received:
01 February 2010
Accepted:
29 June 2018
Published:
01 April 2011
-
-
MSC :
Primary: 49N35; Secondary: 49K15, 92C50.
-
-
We describe optimal protocols for a class of mathematical models for
tumor anti-angiogenesis for the problem of minimizing the tumor
volume with an a priori given amount of vessel disruptive agents.
The family of models is based on a biologically validated model by
Hahnfeldt et al. [9] and includes a modification by
Ergun et al. [6], but also provides two new variations that
interpolate the dynamics for the vascular support between these
existing models. The biological reasoning for the modifications of
the models will be presented and we will show that despite quite
different modeling assumptions, the qualitative structure of optimal
controls is robust. For all the systems in the class of models
considered here, an optimal singular arc is the defining element and
all the syntheses of optimal controlled trajectories are
qualitatively equivalent with quantitative differences easily
computed.
Citation: Heinz Schättler, Urszula Ledzewicz, Benjamin Cardwell. Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 355-369. doi: 10.3934/mbe.2011.8.355
-
Abstract
We describe optimal protocols for a class of mathematical models for
tumor anti-angiogenesis for the problem of minimizing the tumor
volume with an a priori given amount of vessel disruptive agents.
The family of models is based on a biologically validated model by
Hahnfeldt et al. [9] and includes a modification by
Ergun et al. [6], but also provides two new variations that
interpolate the dynamics for the vascular support between these
existing models. The biological reasoning for the modifications of
the models will be presented and we will show that despite quite
different modeling assumptions, the qualitative structure of optimal
controls is robust. For all the systems in the class of models
considered here, an optimal singular arc is the defining element and
all the syntheses of optimal controlled trajectories are
qualitatively equivalent with quantitative differences easily
computed.
-
-
-
-