具有随机扰动的SIQS传染病系统的渐近行为

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 R0 ＞ 1,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.%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.