TITLE:
Optimal Control of Cancer Growth
AUTHORS:
Jens Christian Larsen
KEYWORDS:
Cancer, Models of Cancer Growth, Pontryagin Minimum Principle
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.4,
April
11,
2019
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 depending on the spectral properties of the matrix A, (see below). In section five we determine an optimal strategy for chemo or immune
therapy.