Dynamic Properties Of Stochastic Tumor-Immune Model With Regime Switching

Stochastic differential equations of state switching driven by Markov chains are widely used,and it describes the stochastic dynamic behavior including both continuous states and discrete events.In this paper,we study the dynamical properties of a stochastic tumor-immune model with regime switching,including the extinction and persistence of tumor cells.The main techniques used in this paper include stochastic Lyapunov analysis,stochastic differential equation comparison theorem and strong ergodicity theorem.Firstly,the existence and uniqueness and positive properties of the solutions of the switched random tumor-immune model are given,and then we get the moment boundedness of the solution.When the threshold (?) is less than 0,the extinction of tumor cells is obtained,and the ergodicity of effector cells is studied.We also obtain the asymptotic properties of effector cells.In addition,it is proved that the solution of the stochastic tumor-immune model has a unique invariant measure when the threshold (?) is greater than 0,and the asymptotic estimation of effector cells and tumor cells under time mean is investigated.Finally,two examples and numerical experiments are given to verify our theoretical results.