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On the threshold dynamics of the stochastic SIRS epidemic model using adequate stopping times

On the threshold dynamics of the stochastic SIRS epidemic model using adequate stopping times

As it is well known, the dynamics of the stochastic SIRS epidemic model with mass action is governed by a threshold $ \mathcal{R_S} $. If $ \mathcal{R_S}<1 $ the disease dies out from the population, while if $ \mathcal{R_S}> 1 $ the disease persists. However, when $ \mathcal{R_S} = 1 …