Dynamics Behavior Of A Stochastic Delayed SIRS Model With Saturation Incidence

In this paper ,we consider a stochastic SIRS epdemic model with delay as follows:whereB_i(t)(i=1,2)are independent standard Brownian motions.The uniqueness andexistence of the global positive solution to the above system are analyzed and provedthrough variable transformation and theorem of uniqueness and existence of solutions.Wealso discuss the solution's asymptotic behavior around the disease-free equilibrium andendemic equilibrium.It is proved that the solution vibrate stochasticly around the disease-free equilibrium and a determinate point,the intensity is related with the strength of whitenoiseσ_i~2 (i = 1, 2). The weaker the strength of white noise is,the shorter the distance be-tween disease-free equilibrium and the determinate point becomes.