DYNAMICS OF GLIOMA-IMMUNE SYSTEM WITH STOCHASTIC NOISE

In this paper, a glioma-immune stochastic model with logistic growth is studied to explore the growth of glioma cells in a microenvironment. We can understand the dynamics of glioma-immune interactions by deterministic differential equations. However, stochastic interference plays a pivotal role in glioma-immune interactions. Using the law of large numbers, the comparison theorem, and the Itô’s formula, we prove that a stochastic system has a unique global solution with arbitrary initial values and study the stationary ergodic distribution of the positive solution of the system, where the equilibrium of the solution fluctuates up and down in the deterministic case, resulting in stochastic glioma cells persistence, provide threshold conditions to ensure tumor elimination and persistence. The above results are verified by the numerical simulation. The results show that white noise affects the dynamics of gliomas, white noise intensity is a key factor in the treatment of gliomas, and the addition of stochastic conditions has theoretical guiding significance for clinical medicine to control tumor growth.