DYNAMICAL BEHAVIORS OF A TUMOR-IMMUNE-VITAMIN MODEL WITH RANDOM PERTURBATION

Abstract

This paper mainly explores the stochastic behaviors of the interaction between tumor cells and immune cells when vitamins are added. First, it is shown that the stochastic tumor-immune-vitamin model has a unique global positive solution. Second, we obtain that the solution of our model is stochastically ultimately bounded, stochastically permanent, extinct and persistent in mean under some threshold conditions. Moreover, when the perturbation is weak, the stochastic model has a unique stationary distribution. Finally, numerical simulations are performed to verify the theoretical results.