[The dynamics of HIV-AIDS in Cali]. / Dinámica del VIH-SIDA en Cali.

ABSTRACT

The classical Kermack-Mckendric SIR model for infectious disease transmission was used for studying the dynamics of HIV-AIDS in the city of Cali; individuals were classified as being susceptible, infected or recovered (SIR) on the assumption that sexual transmission would be the only means of transmission and that individuals would not recover or die. The model's parameters and basic reproductive numbers were estimated using information supplied by the Santiago de Cali Municipal Secretariat of Health, the Colombian Statistics Bureau (DANE) and the Municipal Planning department. Some scenarios were simulated to establish long-term disease trends. The system's equilibrium points were estimated and stability conditions analyzed finding that the current system had two equilibrium points unstable, disease-free (E1) and stable, endemically asymptotic (E2). Taking information from 2008 as initial conditions, it was observed that the disease would tend towards equilibrium after a 100 year endemic. Simulations suggested that the disease would tend towards endemic equilibrium more slowly by reducing the probability of contact between susceptible and infected individuals and that the maximum number of infected and recovered could also become reduced.