Dynamics analysis and numerical simulations of a stochastic delayed epidemic model with double disease driven by Lévy noise

This paper investigates a stochastic delayed $S{I}_1{I}_2$ epidemic model with double epidemic and saturated incidence rate driven by Lévy noise. First, we used the stopping time theory to establish sufficient conditions for the existence of a unique positive solution. Furthermore, by the Lyapunov method and stochastic differential equation theory, we analyze the asymptotic properties of the stochastic delayed system around each equilibrium point. In addition, we show that both Lévy noise and time delay can affect the dynamics of the epidemic system. Finally, we use the Euler–Maruyama method to discretize the equations and perform numerical simulations to illustrate thetheoretical results.