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Computational and Mathematical Methods in Medicine
Volume 2016, Article ID 3410320, 10 pages
http://dx.doi.org/10.1155/2016/3410320
Research Article

A Dynamic Model of Human and Livestock Tuberculosis Spread and Control in Urumqi, Xinjiang, China

1Department of Public Health, Xinjiang Medical University, Urumqi 830011, China
2Urumqi Animal Disease Control and Diagnosis Center, Urumqi 830063, China
3Department of Mathematics, Yuncheng University, Yuncheng 044000, China
4Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China

Received 18 February 2016; Accepted 12 June 2016

Academic Editor: Konstantin Blyuss

Copyright © 2016 Shan Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. WHO, “Global tuberculosis report 2015,” Global Tuberculosis Report, 2015. View at Google Scholar
  2. A. Z. Guo and H. C. Chen, “The epidemiological characterization and control strategy of bovine tuberculosis,” China Dairy Cattle, no. 11, pp. 38–45, 2010. View at Google Scholar
  3. C. H. Lei, D. L. Ran, J. L. Yu, L. Jiang, Y. Liu, and Y. S. Zhang, “Monitoring and analysis of bovine tuberculosis,” Xinjiang Agricultural Sciences, vol. 49, no. 1, pp. 150–154, 2012. View at Google Scholar
  4. H. Jia, T. Xin, X. Y. Guo, W. F. Yuan, S. H. Hou, and H. F. Zhu, “Bovine tuberculosis impacts on human health and its diagnostic methods,” Journal of Microbes and Infections, vol. 9, no. 1, pp. 6–13, 2014. View at Google Scholar
  5. Y. X. Shi, Q. Y. Yang, L. I. Ai-Qiao, and C. S. Zhang, “Preliminary approach to tactics of cattle TB prevention and control in xinjiang,” Grass-Feeding Livestock, no. 1, pp. 76–77, 2010. View at Google Scholar
  6. W. X. Wang, G. L. Sun, and A. Q. Li, “Characteristic of epidemiology about tuberculosis in the Urumqi,” Grass-Feeding Livestock, no. 2, pp. 74–76, 2011. View at Google Scholar
  7. X. Jin, “The epidemic state of tuberculosis and its control strategies in xinjiang from 1979 to 2000,” Endemic Diseases Bulletin, no. 1, pp. 50–52, 2003. View at Google Scholar
  8. S. M. Blower, A. R. McLean, T. C. Porco et al., “The intrinsic transmission dynamics of tuberculosis epidemics,” Nature Medicine, vol. 1, no. 8, pp. 815–821, 1995. View at Publisher · View at Google Scholar · View at Scopus
  9. S. M. Blower, P. M. Small, and P. C. Hopewell, “Control strategies for tuberculosis epidemics: new models for old problems,” Science, vol. 273, no. 5274, pp. 497–500, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. T. C. Porco and S. M. Blower, “Quantifying the intrinsic transmission dynamics of tuberculosis,” Theoretical Population Biology, vol. 54, no. 2, pp. 117–132, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Mehra, N. Cossrow, C. Kambili, R. Underwood, R. Makkar, and R. Potluri, “Assessment of tuberculosis burden in China using a dynamic disease simulation model,” International Journal of Tuberculosis and Lung Disease, vol. 17, no. 9, pp. 1186–1194, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Whang, S. Choi, and E. Jung, “A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea,” Journal of Theoretical Biology, vol. 279, no. 1, pp. 120–131, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. E. Brooks-Pollock, G. O. Roberts, and M. J. Keeling, “A dynamic model of bovine tuberculosis spread and control in Great Britain,” Nature, vol. 511, no. 7508, pp. 228–231, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. J. G. Yang and L. W. Zhang, “Stability of an age-structured epidemic model with latent period,” Journal of Xuchang University, vol. 29, no. 5, pp. 4–8, 2010. View at Google Scholar
  15. L. Liu, X.-Q. Zhao, and Y. Zhou, “A tuberculosis model with seasonality,” Bulletin of Mathematical Biology, vol. 72, no. 4, pp. 931–952, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. L. Liu and Y. Wang, “A mathematical study of a TB model with treatment interruptions and two latent periods,” Computational and Mathematical Methods in Medicine, vol. 2014, Article ID 932186, 15 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. Y. Yang, J. Li, Z. Ma, and L. Liu, “Global stability of two models with incomplete treatment for tuberculosis,” Chaos, Solitons & Fractals, vol. 43, no. 1–12, pp. 79–85, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. L. Liu, Y. Wu, and G. You, “Global dynamics for a tb model incorporating case detection and noninfectious tb cases,” Far East Journal of Mathematical Sciences, vol. 2, no. 2, pp. 157–180, 2012. View at Google Scholar
  19. A. Q. Li, J. G. Zhao, and D. J. Hu, “Epidemiological investigation and control of dairy cow tuberculosis in urumqi,” China Animal Quarantine, no. 10, pp. 52–53, 2012. View at Google Scholar
  20. S. H. Lin, “Investigation on the production management of dairy farms in the Xinjiang in 2011,” China Dairy, no. 9, pp. 18–21, 2012. View at Google Scholar
  21. H. P. Chen, “Investigation report on the status of the dairy farm workers in 2011,” China Dairy, no. 8, pp. 6–11, 2012. View at Google Scholar
  22. Y. Q. Feng and H. P. Chen, “Investigation report on the production management of dairy farms in 21 provinces of China in 2011,” China Dairy, no. 6, pp. 10–18, 2012. View at Google Scholar
  23. Y. Q. Feng and H. P. Chen, “Investigation report on the production management of dairy farms in 21 provinces of China in 2011,” China Dairy, no. 9, pp. 22–25, 2012. View at Google Scholar
  24. O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  25. P. V. D. Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, “Global dynamics of a SEIR model with varying total population size,” Mathematical Biosciences, vol. 160, no. 2, pp. 191–213, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus