The Di erential Infectivity and Staged ProgressionModels for the Transmission of HIV yJames

Recent studies of HIV RNA in infected individuals show that viral levels vary widely between individuals and within the same individual over time. Individuals with higher viral loads during the chronic phase tend to develop AIDS more rapidly. If RNA levels are correlated with infectiousness, these variations explain puzzling results from HIV transmission studies and suggest that a small subset of infected people may be responsible for a disproportionate number of infections. We use two simple models to study the impact of variations in in-fectiousness. In the rst model, we account for diierent levels of virus between 1 individuals during the chronic phase of infection, and the increase in the average time from infection to AIDS that goes along with a decreased viral load. The second model follows the more standard hypothesis that infected individuals progress through a series of infection stages, with the infectiousness of a person depending upon his current disease stage. We derive and compare threshold conditions for the two models and nd explicit formulas of their endemic equi-libria. We show that formulas for both models can be put into a standard form, which allows for a clear interpretation. We deene the relative impact of each group as the fraction of infections being caused by that group. We use these formulas and numerical simulations to examine the relative importance of different stages of infection and diierent chronic levels of virus to the spreading of the disease. The acute stage and the most infectious group both appear to have a disproportionate eeect, especially on the early epidemic. Contact tracing to identify superspreaders and alertness to the symptoms of acute HIV infection may both be needed to contain this epidemic.