Mathematical Biosciences and Engineering (MBE)

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

Pages: 785 - 807, Volume 9, Issue 4, October 2012      doi:10.3934/mbe.2012.9.785

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Luju Liu - School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China (email)
Jianhong Wu - Centre for Disease Modeling, York University, 4700 Keele Street, Toronto, ON M3J1P3, Canada (email)
Xiao-Qiang Zhao - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada (email)

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.

Keywords:  Migrant workers, basic reproduction number, uniform persistence, global attractivity.
Mathematics Subject Classification:  Primary: 34D23; Secondary: 92D30.

Received: October 2011;      Accepted: July 2012;      Available Online: October 2012.