Abstract: This study considers a Mathematical model of the dynamical behaviour of tuberculosis disease in the Upper East region of the Northern part of Ghana. The equilibrium points of the model system are found and their stability is investigated. The model exhibits two equilibria namely, the disease-free and the endemic equilibrium. Using stability theory and computer simulation, it is observed that population determine the infection rate of tuberculosis hence the higher the population density, the greater the risk of instability of the disease free equilibrium.