A methodological study of a nonlinear stochastic model of the AIDS epidemic in Philadelphia

A nonlinear stochastic model with heterogeneous risk behavior and recruitment is fitted to Philadelphia public health data adjusted for delays in reporting. Nonlinear difference equations embedded in a stochastic population process are used in computer intensive searches through the parameter space of time homogeneous factor and level combinations to fit projections for cumulative new AIDS cases to data for whites and blacks. Time inhomogeneous factors are applied in efforts to improve the fits and compute confidence bounds for the projections by Monte Carlo simulation, which measures central tendency for the random functions of the process. The model partitions the population into the risk categories of homosexual, bisexual, or heterosexual male, and prostitute or nonprostitute female. Each is further partitioned by intravenous or non-intravenous drug use, a low or high level of needle sharing and sexual contact, and state of HIV disease. The epidemics are seeded by high risk homosexual and bisexual males with recruitment of susceptibles based on census and behavioral data. The Philadelphia public health data covers 1981 to 1992 with a sharp upturn in AIDS cases in 1987 corresponding to a change in the definition of AIDS. The various combinations of factors providing good fits to the data for individual risk categories suggest that several different epidemics exist. Further, for white and black male homosexual/bisexual non-intravenous drug users, the largest data risk categories, the better fitting confidence bounds are achieved with the probabilities of infection per sexual contact decreasing over time. This could suggest an increased awareness of HIV transmission and the use of condoms to prevent infection. For white male homosexual/bisexual non-intravenous drug users, the fit suggests that recruits may be decreasing over time as well.