A mathematical model of immune competition related to cancer dynamics

This paper deals with the qualitative analysis of a model describing the competition among cell populations, each of them expressing a peculiar cooperating and organizing behavior. The mathematical framework in which the model has been developed is the kinetic theory for active particles. The main result of this paper is concerned with the analysis of the asymptotic behavior of the solutions. We prove that, if we are in the case when the only equilibrium solution if the trivial one, the system evolves in such a way that the immune system, after being activated, goes back toward a physiological situation while the tumor cells evolve as a sort of progressing travelling waves characterizing a typical equilibrium/latent situation.