Bifurcations in a closed-loop model of tumor growth control

Abstract

Model-based therapy generation can open new horizons in medicine. Cancer chemotherapy can be optimized using control theoretic methods based on mathematical models of tumor growth. We carry out the qualitative analysis of such a model using the simplest control scheme, i.e., P type control. We look for bifurcations for realistic values of tumor parameters. We show that it is possible to have bifurcations in the closed-loop system, and the qualitative behaviour depends on the initial conditions, and it is independent of the control gain. The analysis shows that the system has rich dynamics and the model can be used to reproduce complex phenomena occurring during real therapies.