Dynamical behavior of a stochastic non-autonomous distributed delay heroin epidemic model with regime-switching

Motivated by the global impact of heroin addiction and the challenges associated with relapse rates among users, this paper investigates a stochastic non-autonomous distributed delay heroin epidemic model with regime-switching. Precisely, we first verify that this system has a unique global positive solution. Then, we presents some criteria for the extinction and persistence in mean of heroin users with this stochastic framework. Additionally, we establish the existence of a unique ergodic stationary distribution of this system by means of Lyapunov inequality. Finally, numerical simulations not only reinforces the theoretical findings but also demonstrates the practical implications of this system in various scenarios. •Extinction, persistence and stationary distribution are given.•Simulations is given.