Rocky Mountain Journal of Mathematics

Global Dynamics in a TB Model Incorporating Case Detection And Two Treatment Stages

Luju Liu, Yicang Zhou, and Jianhong Wu

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Rocky Mountain J. Math., Volume 38, Number 5 (2008), 1541-1559.

First available in Project Euclid: 22 September 2008

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TB model case detection relapse treatment M. tuberculosis


Liu, Luju; Zhou, Yicang; Wu, Jianhong. Global Dynamics in a TB Model Incorporating Case Detection And Two Treatment Stages. Rocky Mountain J. Math. 38 (2008), no. 5, 1541--1559. doi:10.1216/RMJ-2008-38-5-1541.

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  • American Thoracic Society, Treatment of tuberculosis and tuberculosis infection in adults and children,, Amer. J. Respiratory Critical Care Med. 149 (1994), 1359-1374.
  • D. Bleed, C. Watt and C. Dye, World health report 2001: Global tuberculosis control, (Technical Report, World Health Organization, 2001, WHO/CDS/TB/2001.287.
  • B.R. Bloom, Tuberculosis: Pathogenesis, protection and control, ASM Press, Washington, DC, 1994.
  • S.M. Blower and T. Chou, Modeling the emergence of the `hot zones': Tuberculosis and the amplification dynamics of drug resistance, Nature Med. 10 (2004), 1111-1116.
  • S.M. Blower, A.R. McLean, T.C. Porco, et al., The intrinsic transmission dynamics of tuberculosis epidemics, Nature Med. 1 (1995), 815-821.
  • C. Castillo-Chavez and Z. Feng, To treat or not to treat: The case of tuberculosis, J. Math. Biol. 6 (1997), 629-656.
  • T. Cohen and M. Murry, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nature Med. 10 (2004), 1117-1121.
  • Z. Feng, M. Iannelli and F.A. Milner, A Two-strain tuberculosis model with age of infection, SIAM J. Appl. Math. 62 (2002), 1634-1656.
  • J. Gittler, Controlling resurgent tuberculosis: Public health agencies, public policy, and law, J. Health Policy 19 (1994), 107-147.
  • M.G.M. Gomes, L.J. White and G.F. Medley, Infection, reinfection, and vaccination under suboptimal immune protection: Epidemiological perspectives, J. Theoret. Biol. 228 (2004), 539-549.
  •, /2006/2084.html.
  • D. Kirschner, Dynamics of co-infection with M. tuberculosis and HIV-1, Theoret. Popul. Biol. 55 (1999), 94-109.
  • A. Korobeinikov and P.K. Maini, A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Math. Biosci. Engineering 1 (2004), 57-60.
  • J.P. LaSalle, The stability of dynamical systems, SIAM, Philadelphia, 1976.
  • C.C. Mccluskey, Lyapunov functions for tuberculosis models with fast and slow progression, Math. Biosci. Engineering 3 (2006), 603-614.
  • People's Republic of China Medical Department, The material assembly of epidemiological sample investigation of national TB in 2000, People's Medical Press, 2003.
  • P. Rodrigues, M.G.M. Gomes and C. Rebelo, Drug resistance in tuberculosisa reinfection model, Theoret. Popul. Biol. 71 (2007), 196-212.
  • D.E. Snider, Jr., M. Raviglione and A. Kochi, in, Tuberculosis: Pathogenesis, protection and control, B.R. Bloom, ed., ASM Press, Washington, DC, 1994.
  • P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29-48.
  • World Health Organization Global Tuberculosis Programme, WHO, Report on the Tuberculosis epidemic 1997, W.H.O. Geneva, 1997.
  • E. Ziv, C.L. Daley and S.M. Blower, Amer. J. Epidemiology, Early therapy for latent tuberculosis infection 153 (2001), 381-385.