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Curz Vargas et al. studied the dynamics of a deterministic SIRI epidemic model, but it did not take into account the influence of environmental noise on system parameters, in the paper, we consider that the important parameters are disturbed by Ornstein-Uhlenbeck process and we can get a stochastic SIRI epidemic model. First of all, we study the existence and uniqueness of positive solution of system. The second, we also get the stationary distribution of the model. In the end, we get expression of the density function of the stochastic model. Compared with this deterministic model, the dynamical analysis of the system is more reasonable.
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