Kinetic (cellular) models of cell progression and competition with the immune system

This paper deals with the modelling of the immune response to the evolution of progressing (corrupted) endothelial cells, i.e, cancer cells. A mathematical model is proposed, on the basis of mathematical methods of the kinetic theory for a large system of interacting cells. Then a qualitative analysis is carried out to prove the existence of the solutions of the Cauchy problem related to the model and to show some results on the asymptotic behavior. Some computational simulations complete the analysis on the asymptotic behavior of the solutions, which depending on parameters and initial conditions shows either the prevalence of progressing cells or their depletion due to the action of the immune system.