The initialization and sensitivity of multigroup models for the transmission of HIV

We study two multigroup mathematical models of the spread of HIV. In the di fferential infectivity model, the infected population is divided into group s according to their infectiousness, and HIV is primarily spread by a small , highly infectious, group of superspreaders. In the staged-progression mod el, every infected individual goes through a series of infection stages and the virus is primarily spread by individuals in an initial highly infectio us stage or in the late stages of the disease. We demonstrate the importanc e of choosing appropriate initial conditions, and define a new approach to distributing the initial population among the subgroups so as to minimize t he artificial transients in the solutions due to unbalanced initial conditi ons. We demonstrate that the rate of removal in and out of a population is an important, yet often neglected, effect. We also illustrate the importanc e of distinguishing between the number of partners a person has and the num ber of contacts per partner. By assuming that people with many partners hav e fewer contacts per partner than people with few partners, we found that t he epidemic is less sensitive to the partner acquisition rate than one migh t expect. However, because the probability of transmission of HIV per conta ct is low, the epidemic is very sensitive to the number of contacts per par tner. Modeling this distinction is particularly important when estimating t he impact of programs which encourage people to have fewer sexual partners. (C) 2001 Academic Press.