Analysis of a kinetic cellular model for tumor-immune system interaction

Starting at a kinetic level from the equations for the evolution of dominance in populations of interacting organisms, and taking proliferative and destructive encounters into account, a simple model describing the competition between tumor cells and immune system is studied in some detail. Under reasonable assumptions, a closed set of macroscopic balance equations for macroscopic observables is derived by a moment procedure, and analyzed in the frame of the theory of dynamical systems. It is shown that a transcritical bifurcation of equilibria generates a region in the phase space in which, according to the model, the immune system defeats the tumor and leads to its depletion. Numerical results are presented and briefly commented on.