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We study two multigroup mathematical models of the spread of HIV. In the di!erential infectivity model, the infected population is divided into groups according to their infectious-ness, and HIV is primarily spread by a small, highly infectious, group of superspreaders. In the staged-progression model, every infected individual goes through a series of infection stages and the virus is primarily spread by individuals in an initial highly infectious stage or in the late stages of the disease. We demonstrate the importance of choosing appropriate initial condi-tions, and de"ne a new approach to distributing the initial population among the subgroups so as to minimize the arti"cial transients in the solutions due to unbalanced initial conditions. We demonstrate that the rate of removal in and out of a population is an important, yet often neglected, e!ect. We also illustrate the importance of distinguishing between the number of partners a person has and the number of contacts per partner. By assuming that people with many partners have fewer contacts per partner than people with few partners, we found that the epidemic is less sensitive to the partner acquisition rate than one might expect. However, because the probability of transmission of HIV per contact is low, the epidemic is very sensitive to the number of contacts per partner. Modeling this distinction is particularly important when estimating the impact of programs which encourage people to have fewer sexual partners. ( 2001 Academic Press 1