Optimal Control of Cancer Growth - Applied Mathematics

AM > Vol.10 No.4, April 2019

Optimal Control of Cancer Growth ()

HTML XML

Download as PDF (Size: 576KB) PP. 173-195

DOI: 10.4236/am.2019.104014 660 Downloads 1,313 Views

Author(s)

Jens Christian Larsen

Affiliation(s)

Vanlose Alle 50 2. mf. tv, 2720 Vanlose, Copenhagen, Denmark.

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.

KEYWORDS

Cancer, Models of Cancer Growth, Pontryagin Minimum Principle

Share and Cite:

Larsen, J. (2019) Optimal Control of Cancer Growth. Applied Mathematics, 10, 173-195. doi: 10.4236/am.2019.104014.

Journals Menu