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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 932186, 15 pages
http://dx.doi.org/10.1155/2014/932186
Research Article

A Mathematical Study of a TB Model with Treatment Interruptions and Two Latent Periods

1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
2College of Science, China University of Petroleum, Qingdao, Shandong 266580, China

Received 16 January 2014; Revised 21 March 2014; Accepted 23 April 2014; Published 22 May 2014

Academic Editor: Reinoud Maex

Copyright © 2014 Luju Liu and Yan Wang. 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. D. Bleed, C. Watt, and C. Dye, “World health report 2001: global tuberculosis control,” Tech. Rep., World Health Organization, 2001. View at Google Scholar
  2. World Health Organization, Global Tuberculosis Report 2013, WHO, Geneva, Switzerland, 2013.
  3. A. Kochi, “The global tuberculosis situation and the new control strategy of the World Health Organization. 1991,” Bulletin of the World Health Organization, vol. 79, no. 1, pp. 71–75, 2001. View at Google Scholar · View at Scopus
  4. W. Jakubowiak, E. Bogorodskaya, S. Borisov, I. Danilova, and E. Kourbatova, “Treatment interruptions and duration associated with default among new patients with tuberculosis in six regions of Russia,” International Journal of Infectious Diseases, vol. 13, no. 3, pp. 362–368, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. W.-C. Tsai, P.-T. Kung, M. Khan et al., “Effects of pay-for-performance system on tuberculosis default cases control and treatment in Taiwan,” Journal of Infection, vol. 61, no. 3, pp. 235–243, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. P. D. van Helden, P. R. Donald, T. C. Victor et al., “Antimicrobial resistance in tuberculosis: an international perspective,” Expert Review of Anti-Infective Therapy, vol. 4, no. 5, pp. 759–766, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. E. Ziv, C. L. Daley, and S. M. Blower, “Early therapy for latent tuberculosis infection,” American Journal of Epidemiology, vol. 153, no. 4, pp. 381–385, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. Z. Feng, M. Iannelli, and F. A. Milner, “A two-strain tuberculosis model with age of infection,” SIAM Journal on Applied Mathematics, vol. 62, no. 5, pp. 1634–1656, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. L. Liu, Y. Zhou, and J. Wu, “Global dynamics in a TB model incorporating case detection and two treatment stages,” Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1541–1559, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. L. liu, “Global stability in a tuberculosis model incorporating two latent periods,” International Journal of Biomathematics, vol. 2, pp. 357–362, 2009. View at Google Scholar
  11. L. liu and X. Gao, “Qualitative study for a multi-drug resistant TB model with exogenous reinfection and relapse,” International Journal of Biomathematics, vol. 5, no. 4, Article ID 1250031, 19 pages, 2012. View at Google Scholar
  12. H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, vol. 41 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1995.
  13. P. Van Den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Korobeinikov, “Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages,” Bulletin of Mathematical Biology, vol. 71, no. 1, pp. 75–83, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. C. C. McCluskey, “A strategy for constructing Lyapunov functions for non-autonomous linear differential equations,” Linear Algebra and Its Applications, vol. 409, no. 1–3, pp. 100–110, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. J. P. Lasalle, The Stability of Dynamical Systems, SIAM, Philadelphia, Pa, USA, 1976.
  17. C. Dye and B. G. William, “Criteria for the control of drug resistant tuber- culosis,” Proceedings of the National Academy of Sciences, vol. 97, pp. 8180–8185, 2000. View at Google Scholar