Mathematical modeling and control strategies for tumor-induced angiogenesis

A numerical analysis for a mathematical model of the tumor angiogenesis and tumor immune system interaction was performed in this paper. The optimal control was characterized related to chemotherapy treatment administration. The model is expressed in terms of ordinary differential equations and describes the dependency of the tumor size, protein production and vessel density on the effective vessel density and effector-immune cells. The goal was to numerically simulate the model and determine the optimal drug dose that must be administrated in order to destroy the tumor cells and correlate it with the real biological systems. The results of the numerical simulation showed that the tumor will stop growing, and decrease in size, after applying the control. The results show a good correspondence with the real cases, thus proving the validity of the model.