An AIDS model with distributed incubation and variable infectiousness: applications to i.v. drug users in Latium, Italy

A mathematical model for Chagas disease with infection-age-dependent infectivity

In this paper we develop a mathematical model for Chagas disease with infection-age-dependent infectivity. The effects of vector and blood transfusion transmission are considered, and the infected population is structured by the infection age (the time elapsed from infection). The authors identify the basic reproduction ratio R0 and show that the disease can invade into the susceptible population and unique endemic steady state exists if R0 > 1, whereas the disease dies out if R0 is small enough. We show that depending on parameters, backward bifurcation of endemic steady state can occur, so even if R0 < 1, there could exist endemic steady states. We also discuss local and global stability of steady states.

HIV Infection and Drug Use in the Netherlands: The Course of the Epidemic

The introduction of human immunodeficiency virus (HIV) among injecting drug users (IDUs) in the Netherlands has been traced back to 1982, whereas the first case of the acquired immunodeficiency syndrome (AIDS) in an IDU was diagnosed in 1985. By the end of December 1995, 438 AIDS cases among IDUs had been reported to the surveillance system, 53% of whom were Amsterdam residents, making the capital the epicenter of the national HIV epidemic. After a rapid spread of HIV during the first half of the 1980s, HIV prevalence stabilized at about 30% during the second half of that decade in Amsterdam. Since 1984, a variety of preventive measures have been implemented, including needle and syringe exchange programs. These measures have contributed to large reductions in HIV risk behavior. However, an important residual of HIV risk behavior remains and new infections of HIV continue to occur. In recent years, new HIV infections have been outnumbered by the increasing number of deaths occurring among HIV-infected IDUs. A large fraction of these deaths have occurred without an AIDS diagnosis. By 1994, an estimated 1,400 HIV-infected IDUs remained in the country who were still alive and AIDS-free and this number is expected to decrease further in the near future.

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.