Publisher Summary According to the UNAIDS2003 report, more than 40 million people are currently living with human immunodeficiency virus (HIV) infection worldwide. Despite the efforts on educational campaigns and the development of potent antiretroviral drugs, the “acquired immunodeficiency syndrome” (AIDS) epidemic continues to spread. Developing a vaccine to prevent HIV infection is a priority, especially in developing countries where treatment costs are prohibitive. This chapter combines theory and data analysis to understand the rapid initial growth of virus in an infected individual. This approach is based on the estimation of the basic reproductive ratio R0. In untreated individuals, HIV spreads and establishes infection so that R0 > 1. The goal of a vaccine is to boost the immune response and drive R0 below 1 so that the virus can be eradicated following the infection. Refining estimates of R0—for instance, by measuring more accurately the key parameters—will quantify the impact the vaccine must have in terms of the drop in R0 necessary to successfully combat infection. At the same time, comparisons of estimates of R0 will establish the relative efficacies of different vaccines and protocols.