Optimal Control of Cancer Growth

Abstract

The purpose of the present paper is to apply the Pontryagin Minimum Principle to mathematical models of cancer growth. In [1], I presented a discrete affine model T of cancer growth in the variables C for cancer, GF for growth factors and GI for growth inhibitors. One can sometimes find an affine vector field X on whose time one map is T . It is to this vector field we apply the Pontryagin Minimum Principle. We also apply the Discrete Pontryagin Minimum Principle to the model T . So we prove that maximal chemo therapy can be optimal and also that it might not depend ing on the spectral properties of the matrix A , ( see below ) . In section five we determine an optimal strategy for chemo or immune therapy.