In this paper, a stochastic model is formulated to describe the transmission dynamics of tuberculosis. The model incorporates vaccination and treatment in the intervention strategies. Firstly, sufficient conditions for persistence in mean and extinction of tuberculosis are provided. In addition, sufficient conditions are obtained for the existence of stationary distribution and ergodicity. Moreover, numerical simulations are given to illustrate these analytical results. The theoretical and numerical results show that large environmental disturbances can suppress the spread of tuberculosis.
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Transfer diagram of the ODE TB model
Trajectory of the solution of system (2) and its corresponding deterministic model (1)
Trajectory of the solution of system (2) and its corresponding deterministic model (1)
The pictures on the left are trajectories of the solution of system (2). The pictures on the right are the distribution density functions of system (2)