The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination

A model of delayed stochastic SIRS type with temporary immunity and vaccination is investigated. The existence and uniqueness of the global positive solution of the model is proved. The threshold of the stochastic SIRS epidemic model is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system. The vaccination immunity period can also affect the threshold of stochastic and deterministic model. Numerical simulations are carried out to support our theoretical results.