Determination of the spread of HIV from the AIDS incidence history.

The relation between the incidence of HIV in the general population, the number of AIDS cases, and the incubation period for the disease is examined. The number of AIDS cases can be expressed in terms of a convolution integral over the incubation period distribution and the temporal history of HIV incidence. In order to determine the level of HIV incidence it is necessary to invert the convolution. In this manner, it is possible to determine the spread of HIV up to the present time from knowledge of the AIDS incidence history and the incubation period. We describe the inversion of the convolution in terms of a Laplace transform technique that is applicable for any given incubation period distribution. Substantial simplifications in the technique are found in the case of an Erlang distribution for the probability density. The spread of HIV infections in the United States is charted through 1988 using AIDS incidence data that are corrected for both the revised AIDS case definition and reporting time delays. The results are consistent with current estimates of the HIV incidence in the United States and show no evidence of saturation in the rate of new infections. Indeed, the rate of new infections still appears to be climbing as of that date. While the technique is unable to predict the future course of the epidemic, it may provide a useful benchmark for comparison with mathematical models of the epidemic. The techniques are conceptually applicable to diseases other than AIDS.