Abstract
•A stochastic tuberculosis model with antibiotic resistance is proposed and studied.•We establish sufficient conditions for the existence of a unique ergodic stationary distribution.•We obtain sufficient conditions for extinction of the disease.•The existence of a stationary distribution implies stochastic weak stability.
In this paper, we study a stochastic tuberculosis model with antibiotic resistance. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Moreover, we obtain sufficient conditions for extinction of the disease. The existence of a stationary distribution implies stochastic weak stability.