<p>Given the heterogeneity of the infected populations, an increasing number of scholars are turning their attention to multi-group models. Among these studies, research on multi-group SAIRS models is relatively scarce. In this context, our paper primarily investigates a multi-group SAIRS epidemic model with log-normal standard Ornstein-Uhlenbeck process and vaccination. For multi-group models, we employ graph-theoretic methods to ascertain the asymptotic stability of local equilibrium points by proving the global stability of the corresponding linearized systems. For the stochastic system, we demonstrate the existence and uniqueness of global positive solutions. Furthermore, by constructing appropriate Lyapunov functions, we provide sufficient conditions for disease extinction and the existence of a stationary distribution. Finally, some examples and numerical simulations are used to illustrate our theoretical results.</p>