In this study, we analyse models of TB dynamics in the literature and present a model of our own. We conduct global stability analysis of equilibrium states of the model. Our results show that the basic reproduction number R₀ is a threshold parameter of the disease dynamics. In particular, either all positive solutions approach the disease-free equilibrium (R₀≤1) or a unique endemic equilibrium (R₀>1) . The Disease- Free Equilibrium (DFE) is shown to be Globally Asymptotically Stable (GAS) if R₀≤1 and we investigate the endemic global stability using Lyapunov functions and Volterra-Lyapunov matrix properties.