# American Institute of Mathematical Sciences

June  2019, 24(6): 2923-2939. doi: 10.3934/dcdsb.2018292

## Global analysis of a stochastic TB model with vaccination and treatment

 School of Science, Nanjing University of Science and Technology, Nanjing 210094, China

* Corresponding author: Zhipeng Qiu

Received  September 2017 Revised  February 2018 Published  October 2018

Fund Project: Z. Qiu is supported by the National Natural Science Foundation of China (NSFC) grant No. 11671206, T. Feng is supported by the Scholarship Foundation of China Scholarship Council grant No. 201806840120, the Postgraduate Research & Practice Innovation Program of Jiangsu Province grant No. KYCX18 0370 and the Fundamental Research Funds for the Central Universities grant No. 30918011339.

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.

Citation: Tao Feng, Zhipeng Qiu. Global analysis of a stochastic TB model with vaccination and treatment. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2923-2939. doi: 10.3934/dcdsb.2018292
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##### References:
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)
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