A note on the modeling of immune-cancer competition in the homogeneous systems

Abstract

This work deals with the model focuses on the study of the early stage of the immune cancer competition. The approach used in this model is based on the kinetic theory of active particles (KTAP), which has been developed to modeling systems constituted by a large number of interacting particles (active particles), whose microscopic state includes not only geometrical and mechanical variables (typically position and velocity) but also biological functions called activities related to the intrinsic biological function of particles. The model consider a scalar activity variable u ∈ (0,∞). The overall system is divided into six (M = 6) different populations (functional subsystems), the first three subsystems contain epithelial (subsystem 1) and cancer cells (subsystems 2,3), the other functional subsystems contain cells of the immune system. After some reasonable assumptions, we obtain for the cancer cells and immune cells of the last hallmark a Lotka-Volterra system that allows us to describe the dynamics of the biological system in a very simple way.