AbstractStatistical models of the HIV infection epidemic in the U.S. which account for the observed incidence of AIDS cases in the years 1978–1987 are considered. The models assume a known distribution of times from infection to AIDS. The best model estimates that there were approximately 563,000 to 1,110,000 individuals infected in the U.S. in April 1987. These estimates do not take into account underreporting of AIDS cases.The sensitivity of the conclusions to the model's assumptions is ascertained by investigating a variety of parametric models for the infection epidemic, a variety of likely distributions for the time from infection to AIDS, and some plausible alternatives for the history of AIDS cases in the U.S. It is concluded that there is too much uncertainty in the data and the models to be able to give highly accurate predictions of the number of people currently infected in the U.S., however, the results from the best fitting models suggest that there are less than the 1 to 1·5 million infected as estimated by the Centers for Disease Control. A Bayesian scheme is suggested for incorporating the uncertainty in the mode