Analysis of a stochastic tumor-immune model with regime switching and impulsive perturbations

In this article, an impulsive stochastic tumor-immune model with regime switching is formulated and explored. Firstly, it is proven that the model has a unique global positive solution. Then sufficient criteria for extinction, non-persistence in the mean, weak persistence and stochastic permanence are provided. The threshold value between extinction and weak persistence is gained. In addition, the lower- and the upper-growth rates of tumor cells are estimated. The results demonstrate that the dynamics of the model are intimately associated with the random perturbations and impulsive perturbations. Finally, biological implications of the results are addressed with the help of real data and numerical simulations.