AbstractChanges over time in the cumulative number of cases of AIDS depend in a complex way on several features of the epidemic, including the distribution of the induction time between infection with the human immunodeficiency virus (HIV) and onset of symptoms of AIDS, heterogeneity in such behaviours as sexual practices, selection of partners, and IV drug use, and changes over time in these behaviours. Consequently, the observed increase in the doubling time in cumulative AIDS incidence from 5 to 13 months, since AIDS was first recognized in 1982, demonstrates neither that the epidemic has begun to ‘run its course’ nor that behavioural changes have had a major impact in reducing incidence. Even in a homogeneous population with known induction distribution, AIDS incidence data currently are of little value in determining the number of persons infected with HIV unless additional information is available about the shape of cumulative incidence curve of HIV infect