A stochastic SIQR epidemic model with Lévy jumps and three-time delays.

• The paper proposes the stochastic dynamics of SIQR model structure with Lévy jumps and three time delays. • The existence and uniqueness of the positive solution, the dynamic properties around the disease-free equilibrium and the endemic equilibrium are obtained by constructing some suitable Lyapunov functions. • The inuence of isolation and vaccination rate on the disease dynamics is also examined by sensitivity analysis. • The unknown parameters are estimated by the least-square method and the trend of COVID-19 epidemic was predicted. Isolation and vaccination are the two most effective measures in protecting the public from the spread of illness. The SIQR model with vaccination is widely used to investigate the dynamics of an infectious disease at population level having the compartments: susceptible, infectious, quarantined and recovered. The paper mainly aims to extend the deterministic model to a stochastic SQIR case with Lévy jumps and three-time delays, which is more suitable for modeling complex and instable environment. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. The dynamic properties of stochastic solution are studied around the disease-free and endemic equilibria of the deterministic model. Our results reveal that stochastic perturbation affect the asymptotic properties of the model. Numerical simulation shows the effects of interested parameters of theoretical results, including quarantine, vaccination and jump parameters. Finally, we apply both the stochastic and deterministic models to analyze the outbreak of mutant COVID-19 epidemic in Gansu Province, China. [ABSTRACT FROM AUTHOR]