Abstract: We considered the influence of discontinuous noise on the disease transmission process with an incubation period, and established a stochastic SEIQR epidemic model driven by Lévy noise. Based on the relevant theory of stochastic differential equations, we proved the existence and uniqueness of the global positive solution of the stochastic SEIQR epidemic model by using the Lyapunov analysis method, and discussed the asymptotic behavior of the solutions for stochastic system at the disease-free equilibrium point and the endemic equilibrium point of the corresponding deterministic model respectively by constructing the appropriate Lyapunov functions.

Key words: Lévy noise, stochastic SEIQR epidemic model, Lyapunov function, existence and uniqueness of positive solution, asymptotic behavior