Dynamics of a tuberculosis model with treatment and self-cure

Abstract

A tuberculosis (TB) model with treatment and self-cure is investigated. The basic reproduction number is found and its epidemiological interpretation is given. It has been shown that the dynamics of the model is determined by its basic reproductive number. If the basic reproduction number is less than or equal to one, there exists only the disease-free equilibrium which is globally asymptotically stable, and the disease dies out eventually. When the basic reproduction number exceeds one, there exists a unique endemic equilibrium which is uniformly persistent. At last, some measures to control the spread of TB are discussed. © 2011 Springer-Verlag.