  This paper investigates dynamic behaviors of the tumor-immune system
perturbed by environmental noise. The model describes the response of the
cytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The main
methods are stochastic Lyapunov analysis, comparison theorem for stochastic
differential equations (SDEs) and strong ergodicity theorem. Firstly, we prove
the existence and uniqueness of the global positive solution for the
tumor-immune system. Then we go a further step to study the boundaries of
moments for tumor cells and effector cells and the asymptotic behavior in the
boundary equilibrium points. Furthermore, we discuss the existence and
uniqueness of stationary distribution and stochastic permanence of the
tumor-immune system. Finally, we give several examples and numerical
simulations to verify our results.
