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 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.