关键词: 随机微分方程, 存在唯一性, 大范围渐近稳定, Lyapunov函数, 渐近行为

Abstract:

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.

Key words: stochastic differential equation, existence and uniqueness, asymptotically stable in the large scale, Lyapunov function, asymptotic behavior