Abstract
The paper considers a stochastic SIQR epidemic model with vaccination and saturated incidence. First, the existence and boundedness of the global positive solution are given. Second, the threshold for disease extinction is established. Then, through building proper Lyapunov function, the existence of an ergodic stationary distribution is obtained. At last, the main results are confirmed by numerical simulations, which manifests that the large white noise gets to repress the occurrence of disease.
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