Impact of treatment duration on tuberculosis dynamics in a population

This study develops a time-delay SEITS model to analyze how treatment duration influences tuberculosis transmission dynamics. The basic reproduction number [Formula: see text] is derived as an epidemic threshold. Theoretical analysis shows that while the endemic equilibrium is generally stable, introducing treatment delay alone can induce sustained periodic oscillations through Hopf bifurcation. However, concurrent latent delay suppresses this oscillatory behavior. Numerical simulations further suggest that, under [Formula: see text], sufficiently large values of [Formula: see text] may drive the system back into a Hopf bifurcation region and generate persistent oscillations. These findings highlight that shortening treatment duration is crucial not only for reducing transmission but also for stabilizing disease dynamics and improving the precision of public health interventions.