一类具有饱和发生率的随机SIRS模型全局正解的渐近行为

研究了一类具有饱和发生率并且移出率受到白噪声影响的随机SIRS模型.讨论了系统全局正解的存在唯一性与有界性，并通过构造Lyapunov函数，证明了当基本再生数不大于1时，无病平衡点的随机渐近稳定性，给出基本再生数大于1时，随机模型的解围绕确定性模型地方病平衡点震荡的充分条件，最后通过数值仿真验证结论.

Asymptotic Behavior of Global Positive Solution of a Stochastic SIRS Model with Saturation Incidence

A stochastic SIRS model with saturation incidence was explored,in which the recovery rate is influenced by white noise.The global existence,uniqueness and boundness of the positive solution of the system were discussed and the stochastical asymptotical stability of disease-free equilibrium was proved when the basic reproduction number is not more than 1 by constructing Lyapunov function.A sufficient criteria for the solution of the stochastic model oscillating around the endemic equilibrium of the deterministic model was also given out while the basic reproduction number is more than 1.Finally,numerical simulations were presented to illustrate the mathematical findings.