A class of four linear and nonlinear di®erential equations models is given to describe the detection of HIV-positive individuals in Cuba through random screening and contact tracing. The basic reproduction number is obtained for each of the four models. Cuban HIV data from 1986 to 2002 are used to ¯t the models for the purpose of comparison. We also use the models to gauge the di®erence in detection time through random screening and contact tracing. Remarks on the implications for intervention measures and treatment of people living with HIV in Cuba are also given.