We propose a mathematical model to describe the interaction of cancer stem cells, tumor cells, and the immune system in order to better understand tumor growth in the presence of cancer stem cells. We consider the system in two scenarios: with no-treatment and with a chemotherapy treatment regimen. We develop a system of differential equations, fit the parameters to experimental data, and perform sensitivity and stability analysis. The model simulations show that the tumor cells grow as predicted with no-treatment and that with chemotherapy, which targets only the tumor cells, the cancer will eventually relapse. As chemotherapy does not target the cancer stem cells, we conclude that the tumor cells recover due to the presence of cancer stem cells.
Keywords: cancer stem cell; chemotherapy; mathematical model; mathematical oncology; transforming growth factor.