Cancer development: a population theoretical perspective

In the history of life, immune system and cancer have been engaged in an evolutionary arms race driven by the twin forces of mutation and selection. Ideally therapies should be a resolutive weapon, but, despite great progresses during the last 50 years or so, the race still goes on. The aim of this paper is to present a mathematical model, which can be used as in silico laboratory, to provide some indication on the effectiveness of therapies. Here we focus on two cancer populations competing for resources and subjected to the action of two types of immune system cells: thus the model results in a system of 4 differential equation that is analytically and computationally studied to elucidate its properties and emerging behaviors. At the beginning, some speci.c subsystems are analyzed and the effects of different therapies simulated; in particular .rst the system comprising a single cancer and immune cells type is considered and next the case of two cancer clones in absence of the immune cells. The complete model is then presented, which yields a rich variety of behaviors; in particular it is shown that for strong intertumoral competition, and high recognition levels by the immune system, stable stationary states are replaced by sustained oscillations. Finally some conclusion about therapy effectiveness are drawn, based on the results of simulations