Cancer growth dynamics: stochastic models and noise induced effects

Abstract

In the framework of the Michaelis-Menten (MM) reaction kinetics, we analyze the cancer growth dynamics in the presence of the immune response. We found the coexistence of noise enhanced stability (NES) and resonant activation (RA) phenomena which act in an opposite way with respect to the extinction of the tumor The role of the stochastic resonance (SR) in the case of weak cancer therapy has been analyzed. The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a Monte Carlo approach. We analyzed the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. We show how the patient response to the therapy changes when an high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations.