In this paper, we consider a stochastic delayed SIRS epidemic model with seasonal variation. Firstly, we prove that the system is mathematically and biologically well-posed by showing the global existence, positivity and stochastically ultimate boundneness of the solution. Secondly, some sufficient conditions on the permanence and extinction of the positive solutions with probability one are presented. Thirdly, we show that the solution of the system is asymptotical around of the disease-free periodic solution and the intensity of the oscillation depends of the intensity of the noise. Lastly, the existence of stochastic nontrivial periodic solution for the system is obtained.

在本文中，我们考虑了具有季节性变化的随机时滞SIRS流行病模型。首先，我们通过显示该解的整体存在性，正性和随机极限极限来证明该系统在数学和生物学上都是正确的。其次，给出了概率为1的正解的持久性和灭绝的充分条件。第三，我们证明了系统的解在无病周期解附近是渐近的，并且振荡的强度取决于噪声的强度。最后，获得了系统随机非平凡周期解的存在性。