Global dynamics of a tuberculosis model with fast and slow progression and age-dependent latency and infection

ABSTRACT In this paper, a mathematical model describing tuberculosis transmission with fast and slow progression and age-dependent latency and infection is investigated. It is assumed in the model that infected individuals can develop tuberculosis by either of two pathogenic mechanisms: direct progression or endogenous reactivation. It is shown that the transmission dynamics of the disease is fully determined by the basic reproduction number. By analyzing corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, it is proved that the system is uniformly persistent when the basic reproduction number is greater than unity. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, it is verified that the global dynamics of the system is completely determined by the basic reproduction number