Global stability of two tuberculosis models with treatment and self-cure

Two tuberculosis (TB) models with treatment and self-cure are investigated.It is assumed that the treated individuals may reenter either the latent compartment due to the remainder of Mycobacterium tuberculosis or the infectious compartment due to the treatment failure.On the other hand, infectious individuals with mild symptoms may reenter the latent compartment due to self-cure.After investigating a simple model with one latent compartment, a TB model with two latent compartments is studied to describe the slow and fast progression of the exposed individuals.The basic reproduction numbers of those two models are defined, and their epidemiological interpretation is given.Similar threshold dynamics is obtained for those two models: the disease dies out ultimately when the basic reproduction number is less than or equal to one; the unique endemic equilibrium is globally stable when the basic reproduction number is greater than one.The influence of treatment failure and self-cure on the basic reproduction number is also discussed.