An operational research approach to estimating the age distribution of residence time in an HIV/AIDS core group

An operational research approach is used to estimate the age distribution of residence time in an HIV/AIDS core group of gay men, employing only good public health data for administration, planning and decision-making. Any HIV/AIDS modelling involving a high-activity high-risk core group must allow for a restricted but variable residence time in the group. An earlier steady-state approximation by Bailey assumed an arrival process with negligible departures, followed by a departure process with negligible arrivals. That conjecture naturally overestimated the average residence time. An improved model, using age-dependent public health data on AIDS for some 4129 cases in gay men in San Francisco, has now been reanalysed to present the distribution of age at a fixed point of time close to the peak of the underlying HIV epidemic. It is important to note that these data, at any rate, have no appreciable age-dependence in the observed incubation periods. We have adopted the underlying infection dynamics of Jacquez et al. that recognizes an initial concentrated period of high infectivity in all HIV positives leading to a well-marked primary HIV epidemic. Maximum-likelihood estimation has been used to identify five major parameters with small standard errors. The residence model as a whole gives a good fit to the reanalysed data with chi(2)(4)=2.83.