Dynamics of a stochastic tumor–immune interaction system

Abstract

To investigate the effects of environmental factors on tumor growth and the immune response, we have developed a stochastic model of the tumor–immune system, which encompasses tumor cells, NK cells, CD\(8^+\) T cells, and dendritic cells. Initially, we analyzed the deterministic version of the system, deriving the threshold conditions for the local asymptotic stability of the equilibrium point in accordance with the stability theory of differential equations. For the stochastic version, we utilized Itô’s formula and Lyapunov analysis techniques to confirm the existence of a unique global positive solution and to identify sufficient conditions for the mean persistence of the system. Furthermore, we applied the stochastic maximum principle to devise optimal control strategies for the prevention and control of tumor cell proliferation. Our numerical simulations reveal that varying levels of noise intensity result in different outcomes for tumor cells, NK cells, CD\(8^+\) T cells, and dendritic cells, including persistence and extinction. These findings offer critical insights that can guide the development of strategies for preventing and managing tumor progression.