### Mathematical Biosciences and Engineering

2012, Issue 4: 785-807. doi: 10.3934/mbe.2012.9.785

# The impact of migrant workers on the tuberculosis transmission: General models and a case study for China

• Received: 01 October 2011 Accepted: 29 June 2018 Published: 01 October 2012
• MSC : Primary: 34D23; Secondary: 92D30.

• A tuberculosis (TB) transmission model involving migrant workers is proposed and investigated. The basic reproduction number $\mathcal{R}_{0}$ is calculated, and is shown to be a threshold parameter for the disease to persist or become extinct in the population. The existence and global attractivity of an endemic equilibrium, if $\mathcal{R}_{0}>1$, is also established under some technical conditions. A case study, based on the TB epidemiological and other statistical data in China, indicates that the disease spread can be controlled if effective measures are taken to reduce the reactivation rate of exposed/latent migrant workers. Impact of the migration rate and direction, as well as the duration of home visit stay, on the control of disease spread is also examined numerically.

Citation: Luju Liu, Jianhong Wu, Xiao-Qiang Zhao. The impact of migrant workers on the tuberculosis transmission: General models and a case study forChina[J]. Mathematical Biosciences and Engineering, 2012, 9(4): 785-807. doi: 10.3934/mbe.2012.9.785

### Related Papers:

• A tuberculosis (TB) transmission model involving migrant workers is proposed and investigated. The basic reproduction number $\mathcal{R}_{0}$ is calculated, and is shown to be a threshold parameter for the disease to persist or become extinct in the population. The existence and global attractivity of an endemic equilibrium, if $\mathcal{R}_{0}>1$, is also established under some technical conditions. A case study, based on the TB epidemiological and other statistical data in China, indicates that the disease spread can be controlled if effective measures are taken to reduce the reactivation rate of exposed/latent migrant workers. Impact of the migration rate and direction, as well as the duration of home visit stay, on the control of disease spread is also examined numerically.

###### 通讯作者: 陈斌, bchen63@163.com
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沈阳化工大学材料科学与工程学院 沈阳 110142

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