Abstract
In this paper, we study a multi-group stochastic alcoholism model with public health education, which is formulated as a piecewise deterministic Markov process. Through a rigorous analysis, we firstly show that the solution of the stochastic model is positive and global. Then we obtain sufficient conditions for the extinction of alcohol problems. In addition, sufficient conditions for the persistence in the mean of alcoholism are derived. Specifically, in the case of persistence, we prove the existence of positive recurrence of the solution to the model by employing suitable stochastic Lyapunov functions.