Asymptotic behavior of an SIQR epidemic model driven by Levy jumps on scale-free networks

To investigate the effect of information transmission, Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic, a stochastic SIQR epidemic model with non-monotone incidence rate and Levy jumps on scale-free networks is constructed. At first, the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions. Then the stochastic model is made in accordance with the ecological significance, the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested. Next, by constructing suitable stochastic Lyapunov functions and applying Ito formula with jump, the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked. At last, the correctness of the analytical results is verified by numerical simulations.