Analysis of optimal controls for a mathematical model of tumour anti-angiogenesis

Anti-angiogenic therapy is a novel treatment approach for cancer that aims at preventing a tumour from developing its own blood supply system that it needs for growth. In this paper we consider a mathematical model where the endogenous stimulation term in the dynamics is taken proportional to the number of endothelial cells. This system is an example from a class of mathematical models for anti-angiogenic treatment that were derived from a biologically validated model by Hahnfeldt, Panigrahy, Folkman and Hlatky. 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.