This thesis is based on the use of mathematical theories, modelling, and simulations to study the transmission dynamics of HIV/AIDS in the presence of PrEP (pre-exposure prophylaxis) in the MSM (men who have sex with men) population in the United States. A new deterministic model for HIV/AIDS that incorporates PrEP is designed and used to assess the population-level impact of the use of PrEP on the transmission dynamics within an MSM population. Conditions for the effective control (or elimination) and persistence of HIV/AIDS in the MSM population are determined by rigorously analyzing this model. Uncertainty and sensitivity analysis is carried out to determine the effect of the uncertainties in the parameter values on the response variable (the associated reproduction number) and to identify the top-five parameters that have the most effect on the disease transmission dynamics. Numerical simulations show that HIV burden decreases with increasing PrEP coverage. / October 2015