Dynamical analysis of a stochastic delayed epidemic model with lévy jumps and regime switching

•Study of the epidemic model for SARS-CoV-2 virus spread in a stochastic framework.•Transmission rate satisfies the mean-reverting Ornstain-Uhlenbeck process.•Dynamics of model that contains white and telegraph noise, Lévy jump and time delay.•Mathematical tool for constructing strategies for the control of diseases.•Numerical simulations based on the real data illustrate the main theoretical results. In this paper a delayed stochastic SLVIQR epidemic model, which can be applied for modeling the new coronavirus COVID-19 after a calibration, is derived. Model is constructed by assuming that transmission rate satisfies the mean-reverting Ornstain-Uhlenbeck process and, besides a standard Brownian motion, another two driving processes are considered: a stationary Poisson point process and a continuous finite-state Markov chain. For the constructed model, the existence and uniqueness of positive global solution is proven. Also, sufficient conditions under which the disease would lead to extinction or be persistent in the mean are established and it is shown that constructed model has a richer dynamic analysis compared to existing models. In addition, numerical simulations are given to illustrate the theoretical results.