In this paper, first of all, we present a stochastic tumor-immune model with adoptive cell transfer therapy. Then, we derive a threshold parameter \(\lambda \) that classifies the long-term dynamical behavior of tumor cells. When \(\lambda <0\) , the tumor cells are extinct, while \(\lambda >0\) , the tumor cells are persistent and the model has a unique invariant probability measure. Finally, we find that the mathematical expectation of tumor cell population and the stochastic perturbation intensity have a non-monotonic relationship while the threshold \(\lambda \) and the stochastic perturbation intensity have a monotonic relationship. These results further deepen understanding to stochasticity in tumor therapy.
