Activation of the Immune Response by Cytokines and its Effect on Tumour Cells: A Mathematical Model

Abstract

In this paper, we present a mathematical model at the cellular level of the tumour-immune competition mediated by the cytokines. The model consists of a system of nonlinear differential equations describing the intracellular interactions between the tumour and the immune cells in the presence of the cytokines. A detailed phenomenological description of the model based on the kinetic theory for active particle approach is carried out to formulate the model. Well-posedness is presented to establish local and global existence. Numerical simulations are addressed to show how initial conditions and model parameters influence the output of the model. Under a suitable choice of the model's key parameters and the cytokines' initial activation levels, the simulation results show that the activated immune system is able to achieve a total elimination of the cancer cells.