Analysis of a Mathematical Model for Tumor Anti-Angiogenesis

Anti-angiogenic therapy is a novel treatment approach for cancer that aims at preventing a tumor from developing its own blood supply system that it needs for growth. In this paper we consider a mathematical model where the stimulation term in the dynamics is proportional to the number of endothelial cells. This model is an example from a class of mathematical models for anti-angiogenic treatment that were developed and medically validated by Hahnfeldt, Panigrahy, Folkman and Hlatky [8]. The problem how to schedule a given amount of angiogenic inhibitors to achieve a maximum reduction in the primary cancer volume is considered as an optimal control problem and it is shown that optimal controls are bang-bang of the type 0a0 with 0 denoting a trajectory corresponding to no treatment and a a trajectory with treatment at maximum dose along which all inhibitors are being exhausted.

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