中文摘要：

讨论接触率在环境白噪声干扰下建立的随机SIQS传染病系统,通过选择恰当的Lyapunov函数,证明了：当R0≤1时,随机系统的无病平衡点是随机大范围渐近稳定的,即疾病将灭绝;当R0〉1时,给出了随机系统在地方病平衡点P＊附近的渐近行为.结果表明,当白噪声较小时,疾病将流行.

英文摘要：

Authors discussed the stochastic SIQS epidemic model with environment white noise.Choosing the appropriate Lyapunov function,we proved that when R0≤1,the disease-free equilibrium point of the stochastic system is stochastically asymptotically stable in the large scale,which means the disease dies out.For R01,we gave the asymptotic behavior of the stochastic system around the endemic equilibrium P＊.The result shows that the disease will prevail when the white noise is small.