摘要：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.
