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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]