Abstract
In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.
•A stochastic tuberculosis model with constant recruitment is studied.•We establish sufficient conditions for the existence of ergodic stationary distribution.•We establish sufficient conditions for the extinction of the disease.