Combination of antiangiogenic treatment with chemotherapy as a multi‐input optimal control problem

摘要

We analyze a mathematical model for the combination of chemotherapy with antiangiogenic treatment as a multi‐input optimal control problem. Assuming that the total amounts of both agents to be given have been determined a priori based on a medical assessment of side effects, we consider the problem to minimize a weighted average of tumor volume and the carrying capacity of the tumor vasculature. For medically realistic initial conditions and data, based on a thorough theoretical analysis of the necessary conditions for optimality given by the Pontryagin maximum principle, in this paper, the optimal administration regimen for the antiangiogenic agent is determined.