Mathematical Biosciences and Engineering, 2011, 8(2): 355-369. doi: 10.3934/mbe.2011.8.355.

Primary: 49N35; Secondary: 49K15, 92C50.

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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

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.
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Keywords singular arcs; optimal control; Tumor anti-angiogenesis; synthesis.

Citation: Heinz Schättler, Urszula Ledzewicz, Benjamin Cardwell. Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Mathematical Biosciences and Engineering, 2011, 8(2): 355-369. doi: 10.3934/mbe.2011.8.355

 

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