This thesis focuses on understanding the fundamentals of compartmental models in epidemiology and the role that di↵erential equations play within this field of mathematics. Specifically, this thesis goes through the derivation and stability analyses of equilibrium points to systems following variants of the Basic SIR Model. Finally, the core part of this thesis focuses on studying the SLIT Model, a compartmental model developed by Castillo-Chavez and Feng, and the works of others, for modelling and understanding the dynamics of Tuberculosis (TB). It was found through rigorous proof that there exists a disease-free equilibrium point, and a unique TB-endemic equilibrium point within the SLIT Model. These results indicate that models based on a simple one-strain TB still provide useful insight in understanding how TB spreads within a population in reality.