In many parts of the world, drugs of abuse, specifically opiates, are one of the leading causes of HIV transmission. Morphine, a metabolite of common opiates, affects the expression of receptors on the surface of target cells (CD4+ T-cell) of HIV leading to a higher risk of acquiring HIV for individuals under drugs of abuse. In this study, we incorporate the difference in T-cell expression into the model to compute the risk of infection initiation and infection persistence for drug abusers. We quantify how morphine conditioning causes a heightened risk of infection, depending on the relative timings of virus exposure and morphine intake. With a better understanding of the viral dynamics and the increased risk of infection for these individuals, we further evaluate how preventive therapies, such as pre- and post-exposure prophylaxis, reduce the risk of infection for drug abusers. We also extend the plasma model to include the viral dynamics in the brain, a lesser known viral reservoir. Our novel mathematical model is consistent with experimental data from SIV infection of morphine addicted macaques and predicts HIV dynamics in the brain along with the plasma. These results are helpful for health professionals to better create treatment protocols to overcome the several obstacles that those under drugs of abuse face.