Modelling the complex immune system response to cancer cells

Abstract

This paper deals with the modeling of the immune system response to cancer cells. A mathematical model is proposed for a large system of interacting cells, by means of the mathematical methods of the kinetic theory for active particles. The first part of the paper deals with the assessment of the mathematical framework suitable for the derivation of specific models. Then a qualitative analysis is carried out to prove the existence of the solutions of the Cauchy problem related to the model. Some simulations visualize the applicability of the model to the description of biological events characterizing the immune competition.