The HIV/AIDS epidemics among drug injectors: a study of contact structure through a mathematical model

Numerical results of a model with variable infectivity for the dynamics of HIV/AIDS (human immunodeficiency virus/acquired immune deficiency syndrome) have been compared with the data of AIDS cases among intravenous drug users in Italy, especially in the Latium region. We examined several hypotheses about the dynamics of the epidemics; for each we obtained, mainly through a least-square approach but also minimizing a different quantity, a best-fit estimate of the parameters. In the simplest model, the population is assumed to be homogeneous, and we estimate contact rate and year of start of the epidemics, obtaining a good fit up to 1989, less so after. A substantial increase in fit is obtained in assuming either a decrease of the contact rate over time or a heterogeneous population with a smaller active group. We have also compared models with different infectivity curves during the incubation period: the assumption of constant infectivity is untenable, whereas the often suggested hypothesis of a peak in infectivity shortly after infection seems to be in agreement with data.