@article{He2024, 
author = {Ying He and Bo Bi},
title = {Conditions for extinction and ergodicity of a stochastic Mycobacterium tuberculosis model with Markov switching},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30686-30709},
keywords = {Mycobacterium tuberculosis, Markov switching, stationary distribution, extinction},
url = {https://www.sciopen.com/article/10.3934/math.20241482},
doi = {10.3934/math.20241482},
abstract = {This paper is concerned with a stochastic Mycobacterium tuberculosis model, which is perturbed by both white noise and colored noise. First, we prove that the stochastic model has a unique global positive solution. Second, we derive an important condition  R0∗ depending on environmental noise for this stochastic model. We construct an appropriate Lyapunov function, and show that the model possesses a unique ergodic stationary distribution when  R0∗<0, in other words, it indicates the long-term persistence of the disease. Finally, we investigate the related conditions of extinction.}
}