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This paper investigates dynamic behaviors of the tumor-immune systemperturbed by environmental noise. The model describes the response of thecytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The mainmethods are stochastic Lyapunov analysis, comparison theorem for stochasticdifferential equations (SDEs) and strong ergodicity theorem. Firstly, we provethe existence and uniqueness of the global positive solution for thetumor-immune system. Then we go a further step to study the boundaries ofmoments for tumor cells and effector cells and the asymptotic behavior in theboundary equilibrium points. Furthermore, we discuss the existence anduniqueness of stationary distribution and stochastic permanence of thetumor-immune system. Finally, we give several examples and numericalsimulations to verify our results.

Dynamical Behaviors of the Tumor-immune System in a Stochastic Environment