All over the world, tuberculosis is a public health problem in prisons due to the fact that many inmates come from communities at high risk of TB, to their living conditions in prisons and to the insufficiencies of prisons health services. In this paper, a simple mathematical model is used to gain insights on tuberculosis transmission in prison settings. A threshold parameter known as the reproductive number is derived. Latin hypercube sampling has been used to estimate the correlation between the reproductive number and the model parameters which forms the reproductive number. Finally, the study highlights the need for attention and, indeed, resources to control tuberculosis transmission dynamics amongst prisoners.