Abstract
This paper proposes a stochastic intestinal chemostat model considering microbial migration, intraspecific competition and stochastic perturbation. First, the extinction and persistence in mean of the intestinal microbe of the chemostat model are investigated by constructing the appropriate Lyapunov functions. Second, we explore and obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the model by using ergodic theory. The results show stochastic interference has a critical impact on the extinction and sustainable survival of the intestinal microbe. Eventually, numerical simulations are carried out to verify the theoretical results.