A Kinetic Model of Tumor/Immune System Cellular Interactions

Abstract

In this paper, a model of cellular tumor dynamics in competition with the immune system is proposed. The characteristic scale of the phenomenon is the cellular one and the model is developed with probabilistic methods analogous to those of the kinetic theory. The interacting individuals are the cells of the populations involved in the competition between the tumor and the immune system. Interactions can change the activation state of the tumor and cause tumor proliferation or destruction. The model is expressed in terms of a bi-linear system of integro-differential equations. Some preliminary mathematical analysis of the model as well as computational simulations are presented.