Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 184918, 19 pages
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.


An epidemiological model of TB with infectivity in latent period and imperfect treatment is introduced. As presented, sustained oscillations are not possible and the endemic proportions either approach the disease-free equilibrium or an endemic equilibrium. The expanded model that stratified the infectious individuals according to their time-since-infection θ is also carried out. The global asymptotic stability of the infection-free state is established as well as local asymptotic stability of the endemic equilibrium. At the end, numerical simulations are presented to illustrate the results.