Mathematical modelling of tumor-immune system by considering the regulatory T cells role

Abstract

The immune system has an important role in protecting the body from tumors. However, several clinical studies have shown that not all immune cells in the body work positively against tumors, such as regulatory T cells which are known to modulate the function of effector cells and inhibit their cytotoxic activity. The purpose of this paper is to analyze the mathematical model of tumor-immune system dynamics by considering the regulatory T cells role. Based on the model analysis results obtained eight equilibrium points, where two equilibrium points are unstable, namely the equilibrium point of normal, tumor, effector cells extinction and the equilibrium point of normal, tumor cells extinction, then four equilibrium points are conditionally asymptotically stable, namely the equilibrium point of normal and effector cells extinction, tumor and effector cells extinction, tumor cells extinction, and effector cells extinction, and two equilibrium points are thought to tend to be asymptotically stable when the existence conditions are satisfied, namely the equilibrium point of normal cells extinction and coexistence. The numerical simulation results show that regulatory T cells play an important role in inhibiting effector cells and promoting tumor cell growth. Furthermore, a numerical bifurcation analysis is performed which shows the presence of saddle-node bifurcation and bistable behavior in the system.