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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.