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We study the dynamics of a stochastic SIQR epidemic disease with quarantine-adjusted incidence in this article. In order to find the sufficient conditions for the ergodicity and extermination of the model, we construct suitable stochastic Lyapunov functions and find the results of the stochastic SIQR epidemic model. From the results, we find that when the white noise is relatively large, the infectious diseases will become extinct; this also shows that the intervention of white noise will play an important part in controlling the spread of the disease.

Dynamical Behaviors of a Stochastic SIQR Epidemic Model with Quarantine-Adjusted Incidence