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