2012, 9(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

1. 

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China

2. 

Centre for Disease Modeling, York University, 4700 Keele Street, Toronto, ON M3J1P3, Canada

3. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7

Received  October 2011 Revised  July 2012 Published  October 2012

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 for China. Mathematical Biosciences & Engineering, 2012, 9 (4) : 785-807. doi: 10.3934/mbe.2012.9.785
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Y. Zhou, K. Khan, Z. Feng, et al., Projection of tuberculosis incidence with increasing immigration trends,, J. Theor. Biol., 254 (2008), 215.  doi: 10.1016/j.jtbi.2008.05.026.  Google Scholar

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E. Ziv, C. L. Daley and S. M. Blower, Early therapy for latent tuberculosis infection,, Am. J. Epidemiol., 153 (2001), 381.  doi: 10.1093/aje/153.4.381.  Google Scholar

show all references

References:
[1]

L. Aggarwal, Tuberculosis-diagnosis and investigation,, Hospital Pharmacist, 13 (2006), 73.   Google Scholar

[2]

, http://www.agri.gov.cn/, ., ().   Google Scholar

[3]

S. Akhtar and H. G. Mohammad, Seasonality in pulmonary tuberculosis among migrant workers entering Kuwait,, BMC Infect Dis., 8 (2008).  doi: 10.1186/1471-2334-8-3.  Google Scholar

[4]

S. M. Blower, P. M. Small and P. C. Hopewell, Control strategies for tuberculosis epidemics: New models for old problems,, Science, 273 (1996), 497.  doi: 10.1126/science.273.5274.497.  Google Scholar

[5]

S. M. Blower and T. Chou, Modeling the emergence of the 'hot zones': tuberculosis and the amplification dynamics of drug resistance,, Nat. Med., 10 (2004), 1111.  doi: 10.1038/nm1102.  Google Scholar

[6]

F. Brauer and P. van den Driessche, Models for transmission of disease with immigration of infectives,, Math. Biosci., 171 (2001), 143.  doi: 10.1016/S0025-5564(01)00057-8.  Google Scholar

[7]

K. P. Cain, S. R. Benoit, C. A. Winston, et al., Tuberculosis among foreign-born persons in the United States,, JAMA., 300 (2008), 405.  doi: 10.1001/jama.300.4.405.  Google Scholar

[8]

C. Castillo-Chavez and Z. Feng, To treat or not to treat: the case of tuberculosis,, J. Math. Biol., 35 (1997), 629.  doi: 10.1007/s002850050069.  Google Scholar

[9]

C. Castillo-Chavez and Z. Feng, Global stability of an age-structure model for TB and its application to optimal vaccination strategies,, Math. Biosci., 151 (1998), 135.  doi: 10.1016/S0025-5564(98)10016-0.  Google Scholar

[10]

C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications,, Math. Biosci. Eng., 1 (2004), 361.   Google Scholar

[11]

, http://www.lm.gov.cn/gb/employment/2005-09/14/content_85850.htm, ., ().   Google Scholar

[12]

, http://www.lm.gov.cn/gb/faqs/2007-07/23/content_187192.htm, ., ().   Google Scholar

[13]

, http://www.chinadaily.com.cn/bw/2007-06/04/content_886147.htm, ., ().   Google Scholar

[14]

T. Cohen and M. Murry, Modeling epidemics of multidrug-resistant M.tuberculosis of heterogeneous fitness,, Nature Med., 10 (2004), 1117.  doi: 10.1038/nm1110.  Google Scholar

[15]

P. D. O. Davies, Tuberculosis and migration,, J. R. Coll. Physicians Lond., 29 (1995), 113.   Google Scholar

[16]

, http://www.chinadaily.com.cn/china/2006-09/12/content_686676.htm, ., ().   Google Scholar

[17]

M. G. Farah, H. E. meyer, R. Selmer, et al., long-term risk of tuberculosis among immigrants in Norway,, Int. J. Epidemiol., 34 (2005), 1005.  doi: 10.1093/ije/dyi058.  Google Scholar

[18]

Z. Feng, C. Castillo-Chavez and A. F. Capurro, A model for tuberculosis with exogenous reinfection,, Theor. Popul. Biol., 57 (2000), 235.  doi: 10.1006/tpbi.2000.1451.  Google Scholar

[19]

Z. Feng, W. Huang and C. Castillo-Chavez, On the role of variable latent periods in mathematical models for tuberculosis,, J. Dyn. Diff. Equations, 13 (2001), 425.  doi: 10.1023/A:1016688209771.  Google Scholar

[20]

Z. Feng, M. Iannelli and F. A. Milner, A two-strain tuberculosis model with age of infection,, SIAM J. Appl. Math., 62 (2002), 1634.  doi: 10.1137/S003613990038205X.  Google Scholar

[21]

J. R. Glynn, Resurgence of tuberculosis and the impact of HIV infection,, Br. Med. Bull., 54 (1998), 579.  doi: 10.1093/oxfordjournals.bmb.a011712.  Google Scholar

[22]

H. Guo and M. Y. Li, Global dynamics to a three-population TB model with immigration and cross-infectin,, preprint., ().   Google Scholar

[23]

S. Howie, L. Voss, M. Baker, et al., Tuberculosis in New Zealand, 1992-2001: a resurgence,, Arch. Dis. Child., 90 (2005), 1157.  doi: 10.1136/adc.2004.066415.  Google Scholar

[24]

Z. Jia, X. Jia, Y. Liu, et al., Spatial analysis of tuberculosis cases in migrants and permanent residents, Beijing, 2000-2006,, Emerg. Infec. Dis., 14 (2008), 1413.  doi: 10.3201/1409.071543.  Google Scholar

[25]

D. Kelly and X. Luo, SARS and China's rural migrant labour: roots of a government crisis,, in, (2006), 389.   Google Scholar

[26]

, http://www.kscein.gov.cn/Information/information_view.aspx?contentid=6981, ., ().   Google Scholar

[27]

C. C. McCluskey and P. van den Driessche, Global analysis of two tuberculosis models,, J. Dyn. Diff. Equations, 16 (2004), 139.  doi: 10.1023/B:JODY.0000041283.66784.3e.  Google Scholar

[28]

M. T. McKenna, E. McCray and I. Onorato, The epidemiology of tuberculosis among foreign-born persons in the United States, 1986 to 1993,, N. Engl. J. Med., 332 (1995), 1071.  doi: 10.1056/NEJM199504203321606.  Google Scholar

[29]

B. M. Murphy, B. H. Singer, S. Anderson, et al., Comparing epidemic tuberculosis in demographically distinct heterogeneous populations,, Math. Biosci., 180 (2002), 161.  doi: 10.1016/S0025-5564(02)00133-5.  Google Scholar

[30]

The Ministry of Health of the People's Republic of China, Report on nationwide random survey for the epidemiology of tuberculosis in 2000,, Beijing: The Ministry of Health of The People's Republic of China, (2002).   Google Scholar

[31]

, http://www.molss.gov.cn/index/, ., ().   Google Scholar

[32]

, http://www.stats.gov.cn/, ., ().   Google Scholar

[33]

C. Parry and P. D. O. Davies, The resurgence of tuberculosis,, J. Applied. Bacteriol., 81 (1996).  doi: 10.1111/j.1365-2672.1996.tb04829.x.  Google Scholar

[34]

T. C. Porco and S. M. Blower, Quantifying the intrinsic transmission dynamics of tuberculosis,, Theor. Popul. Biol., 54 (1998), 117.  doi: 10.1006/tpbi.1998.1366.  Google Scholar

[35]

A. Saltelli, K. Chan and M. Scott, "Sensitivity Analysis,", Probability and Statistics series. John Wiley & Sons: New York, (2000).   Google Scholar

[36]

E. Schneider, M. Moore and K. G. Castro, Epidemiology of tuberculosis in the United States,, Clin. Chest. Med., 26 (2005), 183.  doi: 10.1016/j.ccm.2005.02.007.  Google Scholar

[37]

O. Sharomi, C. N. Podder, A. B. Gumel, et al., Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment,, Math. Biosci. Eng., 5 (2008), 145.   Google Scholar

[38]

A. C. Sleigh, Health-system reforms to control tuberculosis in China,, Lancet., 369 (2007), 626.  doi: 10.1016/S0140-6736(07)60292-X.  Google Scholar

[39]

H. L. Smith, "Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Cystems,", Mathematical Surveys and Monographs, (1995).   Google Scholar

[40]

H. L. Smith and P. Walman, "The Theory of the Chemostat,", Cambridge Univ. Press, (1995).   Google Scholar

[41]

H. R. Thieme, Convergence results and a Poincaré-Bendison trichotomy for asymptotical autonomous differential equations,, J. Math. Biol., 30 (1992), 755.  doi: 10.1007/BF00173267.  Google Scholar

[42]

P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[43]

L. Wang, J. Liu, and D. P. Chin, Progress in tuberculosis control and the evolving public-health system in China,, Lancet., 369 (2007), 691.  doi: 10.1016/S0140-6736(07)60316-X.  Google Scholar

[44]

World health report 1998: WHO report on the global tuberculosis epidemic 1998., World Health Organization., , ().   Google Scholar

[45]

, http://www.who.int/tb/en/, ., ().   Google Scholar

[46]

WHO, Tuberculosis Fact Sheet. 2007., (, ().   Google Scholar

[47]

L. Zhang, D. Tu, Y. An, et al., The impact of migrants on the epidemiology of tuberculosis in Beijing, China,, Int. J. Tuberc. Dis., 10 (2006), 959.   Google Scholar

[48]

X.-Q. Zhao, "Dynamical Systems in Population Biology,", Springer-Verlag, (2003).   Google Scholar

[49]

Y. Zhou, K. Khan, Z. Feng, et al., Projection of tuberculosis incidence with increasing immigration trends,, J. Theor. Biol., 254 (2008), 215.  doi: 10.1016/j.jtbi.2008.05.026.  Google Scholar

[50]

E. Ziv, C. L. Daley and S. M. Blower, Early therapy for latent tuberculosis infection,, Am. J. Epidemiol., 153 (2001), 381.  doi: 10.1093/aje/153.4.381.  Google Scholar

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