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In this paper, we consider a stochastic epidemic model under regime-switching. We show that our model is well-posed by proving the existence of solution, positivity, and uniqueness. Furthermore, we investigate sufficient conditions for the existence of ergodic stationary distribution to the model, which shows that the hepatitis B epidemic will persist. In addition, we establish sufficient conditions for the extinction of the hepatitis B epidemic. We perform numerical simulations to confirm and illustrate the theoretical results.