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Discrete Dynamics in Nature and Society
Volume 2012, Article ID 184918, 19 pages
http://dx.doi.org/10.1155/2012/184918
Research Article

A TB Model with Infectivity in Latent Period and Imperfect Treatment

Department of Mathematics, Xinyang Normal University, Xinyang 464000, China

Received 12 October 2011; Revised 29 December 2011; Accepted 7 January 2012

Academic Editor: Zhen Jin

Copyright © 2012 Juan Wang 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. B. Song, C. Castillo-Chavez, and J. P. Aparicio, “Tuberculosis models with fast and slow dynamics: the role of close and casual contacts,” Mathematical Biosciences, vol. 180, pp. 187–205, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. C. Dye, K. Floyd, and M. Uplekar, “World health report: global tuber-culosis control: surveillance, planning, financing,” WHO/HTM/TB/ 2008.393, World Health organization, 2008. View at Google Scholar
  3. C. Castillo-Chavez and Z. Feng, “To treat or not to treat: the case of tuberculosis,” Journal of Mathematical Biology, vol. 35, no. 6, pp. 629–656, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. 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 Google Scholar
  5. C. P. Bhunu, W. Garira, and Z. Mukandavire, “Modeling HIV/AIDS and tuberculosis coinfection,” Bulletin of Mathematical Biology, vol. 71, no. 7, pp. 1745–1780, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. M. Blower and T. Chou, “Modeling the emergence of the “hot zones”: tuberculosis and the amplification dynamics of drug resistance,” Nature Medicine, vol. 10, no. 10, pp. 1111–1116, 2004. View at Publisher · View at Google Scholar
  7. T. Cohen and M. Murray, “Modeling epidemics of multidrug-resistant tuberculosis of heterogeneous fitness,” Nature Medicine, vol. 10, no. 10, pp. 1117–1121, 2004. View at Publisher · View at Google Scholar
  8. P. Rodrigues, M. G.M. Gomes, and C. Rebelo, “Drug resistance in tuberculosis-a reinfection model,” Theoretical Population Biology, vol. 71, no. 2, pp. 196–212, 2007. View at Publisher · View at Google Scholar
  9. E. Vynnycky and P. E.M. Fine, “The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection,” Epidemiology and Infection, vol. 119, no. 2, pp. 183–201, 1997. View at Publisher · View at Google Scholar
  10. C. P. Bhunu, W. Garira, Z. Mukandavire, and M. Zimba, “Tuberculosis transmission model with chemoprophylaxis and treatment,” Bulletin of Mathematical Biology, vol. 70, no. 4, pp. 1163–1191, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. O. Sharomi, C. N. Podder, A. B. Gumel, and B. Song, “Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment,” Mathematical Biosciences and Engineering, vol. 5, no. 1, pp. 145–174, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. L.-I.W. Roeger, Z. Feng, and C. Castillo-Chavez, “Modeling TB and HIV co-infections,” Mathematical Biosciences and Engineering, vol. 6, no. 4, pp. 815–837, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. N. Bacaër, R. Ouifki, C. Pretorius, R. Wood, and B. Williams, “Modeling the joint epidemics of TB and HIV in a South African township,” Journal of Mathematical Biology, vol. 57, no. 4, pp. 557–593, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Y. Zhou, K. Khan, Z. Feng, and J. Wu, “Projection of tuberculosis incidence with increasing immigration trends,” Journal of Theoretical Biology, vol. 254, no. 2, pp. 215–228, 2008. View at Publisher · View at Google Scholar
  15. S. Akhtar and H. G. H. H. Mohammad, “Seasonality in pulmonary tuberculosis among migrant workers entering Kuwait,” BMC Infectious Diseases, vol. 8, 2008. View at Publisher · View at Google Scholar
  16. 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
  17. D. E. Snider, M. Raviglione, and A. Kochi, “Global burden of tuberculosis,” in Tuberculosis Pathogenisis and Control, B. Bloom, Ed., ASM, Washington, DC, USA, 1994. View at Google Scholar
  18. A. S. Douglas, D. P. Strachan, and J. D. Maxwell, “Seasonality of tuberculosis: the reverse of other respiratory diseases in the UK,” Thorax, vol. 51, no. 9, pp. 944–946, 1996. View at Google Scholar
  19. 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 Zentralblatt MATH
  20. B. Fang and X. Z. Li, “Stability of an age-structured MSEIS epidemic model with infectivity in latent period,” Acta Mathematicae Applicatae Sinica, vol. 31, no. 1, pp. 110–125, 2008. View at Google Scholar · View at Zentralblatt MATH
  21. L. Guihua and J. Zhen, “Global stability of an SEI epidemic model,” Chaos, Solitons and Fractals, vol. 21, no. 4, pp. 925–931, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. G. Li and J. Zhen, “Global stability of an SEI epidemic model with general contact rate,” Chaos, Solitons and Fractals, vol. 23, no. 3, pp. 997–1004, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. G. Li and Z. Jin, “Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period,” Chaos, Solitons and Fractals, vol. 25, no. 5, pp. 1177–1184, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. T. J. Case, An Illustrated Guide to Theoretical Ecology, Oxford University, New York, NY, USA, 2000.
  25. H. R. Thieme, “Uniform weak implies uniform strong persistence for non-autonomous semiflows,” Proceedings of the American Mathematical Society, vol. 127, no. 8, pp. 2395–2403, 1999. View at Publisher · View at Google Scholar
  26. H. R. Thieme, Y. Takeuchi, Y. Iwasa, and K. Sato, “Pathogen competition and coexistence and the evolution of virulence,” in Mathematics for Life Sciences and Medicine, vol. 123, 2007. View at Google Scholar