A chemotherapy model for the treatment of cancer with metastasis

Abstract

In this paper, we propose and analyse a mathematical model of cancer treatment by chemotherapy where there is metastasis from a primary to a secondary site by the cancer cells. We view the interactions between normal and cancer cells as being competitive for available resources, and we think of the chemotherapy agent as a predator on both normal and cancer cells. The metastasis may be time delayed. The analysis is carried out both analytically (where possible) and numerically. In particular, we look at the existence and stability of equilibria of our model, which consists of six differential equations. As well, we investigate (numerically) the behavior of solutions for various values of the parameters.