Modeling the incidence of Acquired Immunodeficiency Syndrome (AIDS) in San Francisco, Los Angeles, and New York

Abstract

By November, 1985, reported AIDS cases in New York, San Francisco, and Los Angeles totaled over 4980, 1403, and 1315, respectively. Although the cumulative number of cases diagnosed doubled in these cities in the 10–11 months before July, 1984, the incidence of AIDS will not necessarily continue to increase at this rate. A discrete, nonlinear model is presented and used to explore underlying biological and sociological characteristics of the AIDS outbreak and to forecast the number of new cases. The model's structure assumes that AIDS is sexually transmitted and that other forms of transmission mimic sexual transmission. Its parameters reflect (1) how long AIDS takes to develop from exposure to diagnosis, (2) when during this development individuals are contagious, and (3) how changes in sexual behavior and saturation— the removal of susceptible individuals through infection—affect the incidence of AIDS. As indices of behavioral changes, the model uses trends in gonorrhea diagnosed at a San Francisco clinic, where anal/rectal cases have dropped from a monthly average of 411 in 1979–1981 to 59 in 1985, and, urethral cases, similarly, from 863 to 248. Judged by the least residual sum of squares of the model's fit to observations, the drop in anal/rectal gonorrhea better reflects the decline in sexual contact rates in the San Francisco population at risk to AIDS than does the drop in urethral gonorrhea. Furthermore, the parameter values that best fit the model to the incidence data from Los Angeles, New York, and San Francisco currently suggest in general that AIDS takes 35–47 months to develop from exposure to diagnosis, and, that individuals are most infectious in the 3–16 months immediately following exposure to the agent. Although forecasts for each of these three cities suggest that the incidence of AIDS could level off or even decline from present levels before 1987, the model shows that there may currently be insufficient data to choose, using the sum of squares criterion, between radically different forecasts. Two parameter sets that fit the model to Los Angeles AIDS incidence by linking it to the drop in anal/rectal gonorrhea, for example, give similar residual sum of squares of 806 and 808 but different forecasts of 3271 and 2230 total cases diagnosed in Los Angeles before 1987. These results suggest that more data are needed before conclusive parameter values can be chosen. Nevertheless, the model is used in conjunction with anal/rectal gonorrhea rates from San Francisco to generate preliminary forecasts of AIDS incidence. By the end of 1986, it forecasts a range for the total cumulative number of diagnosed cases in Los Angeles of 2200–3300, in New York of 6800–8900, and in San Francisco of 2100–4200, with the model's best fits to observed incidence suggesting that there will be at least 2400, 7200, and 2500 cummulative cases in these cities, respectively.