Abstract
Mathematical model is the main tool to study the dynamics of infectious diseases, which has played an important role in controlling the spread of infectious diseases. We consider a stochastic SIVS model with saturation incidence in this paper. First of all, we establish the threshold [Formula: see text] for extinction and persistence for the stochastic epidemic model. Additionally, we give the specific expression of the probability density function of the stochastic model near the unique endemic quasi-equilibrium by solving the Fokker–Planck equation. In the end, the supporting theoretical results are verified by numerical simulation.
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