Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis - Heinz Schättler; Urszula Ledzewicz; Benjamin Cardwell (Mathematical Biosciences and Engineering)
We describe optimal protocols for a class of mathematical models fortumor anti-angiogenesis for the problem of minimizing the tumorvolume with an a priori given amount of vessel disruptive agents.The family of models is based on a biologically validated model byHahnfeldt et al. [9] and includes a modification byErgun et al. [6], but also provides two new variations thatinterpolate the dynamics for the vascular support between theseexisting models. The biological reasoning for the modifications ofthe models will be presented and we will show that despite quitedifferent modeling assumptions, the qualitative structure of optimalcontrols is robust. For all the systems in the class of modelsconsidered here, an optimal singular arc is the defining element andall the syntheses of optimal controlled trajectories arequalitatively equivalent with quantitative differences easilycomputed.