Abstract: We considered a stochastic SEIQR monkeypox epidemic model with  Gaussian white noise. Firstly, the existence and uniqueness of the global positive solution for the stochastic model were proved by using stopping time theory. By constructing a Lyapunov function and combining it with  Ito formula, the asymptotic behavior of the solutions of stochastic model near the disease-free equilibrium point and endemic equilibrium point of the corresponding deterministic model was given. Secondly, we gave conditions for the average persistence of the solutions and disease extinction of the stochastic model. Finally, numerical simulations were conducted to examine the impact of noise on the model. The results show  that the stochastic model perturbs near the equilibrium point of the deterministic model, and  the degree of perturbation is  positively correlated with  the noise intensity. When the noise is sufficiently large, the disease will become extinct.

Key words:  , monkeypox epidemic model, Ito formula, random effect, persistence,  , extinction