Modeling the AIDS epidemic in Mexico City.

To study the future course of the AIDS epidemic in Mexico City, we use an open compartmental model to forecast new AIDS cases among homosexual and bisexual males and among heterosexual males and females. For each group three compartments are defined: uninfected persons, infected but asymptomatic persons, and persons diagnosed with AIDS. It is assumed that the AIDS epidemic will follow the propagation of infectious disease model, where spread of infection is proportional to the product of the number of healthy persons and the number of infected ones. The compartmental model is represented by a system of nonlinear differential equations describing the rate of change in the number of persons in each compartment. The impact of preventive measures is explored by decreasing the probability of HIV transmission, which is one of the model parameters representing behavioral patterns. By April 1989, 491 AIDS cases had been reported in Mexico City and classified as sexually related. Our model predicts that the AIDS incidence will continue to rise in Mexico City for the foreseeable future and will spread among the heterosexual population. Decreasing the transmission probability by 10% in all groups (through education programs) will result in a decrease of 18.1% in the number of accumulated cases over a 5-year period. A 20% decrease would prevent more than 31% of the cases. We conclude that mathematical models can be valuable in predicting the spread of the AIDS epidemic and the impact of behavioral change on its spread.