Positive recurrence of a stochastic heroin epidemic model with standard incidence and telegraph noise

Abstract

The heroin epidemic has posed a serious threat to public health and social stability. Understanding the dynamics of the heroin epidemic model is of great significance for formulating effective prevention and control strategies. In this paper, a stochastic heroin epidemic model with standard incidence and telegraph noise is considered. By constructing a suitable stochastic Lyapunov function with regime switching, we get sufficient conditions of positive recurrence of the solution for stochastic system, which may provide valuable insights for further research and control strategies related to heroin epidemics.