The impact of migrant workers on the tuberculosis transmission: General models and a case study for
China
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School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023
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2.
Centre for Disease Modeling, York University, 4700 Keele Street, Toronto, ON M3J1P3
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3.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7
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Received:
01 October 2011
Accepted:
29 June 2018
Published:
01 October 2012
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MSC :
Primary: 34D23; Secondary: 92D30.
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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
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Abstract
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.
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