We use these formulas and numerical simulations to examine the relative importance of di erent stages of infection and di erent chronic levels of virus to the spreading of the disease

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 infectiousness. In the ®rst model, we account for dierent levels of virus between 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 equilibria. We show that formulas for both models can be put into a standard form, which allows for a clear interpretation. We de®ne the relative impact of each group as the fraction of infections being caused by that group. * Corresponding author. Tel.: +1-256 890 6470; fax: +1-256 890 6173 1 This research was supported by the Department of Energy under contracts W-7405-ENG-36 and the Applied Mathematical Sciences Program KC-07-01-01. 2 The authors thank John Jacquez and an anonymous referee for their valuable comments. 0025-5564/99/$ ± see front matter Ó 1999 Published by Elsevier Science Inc. All rights reserved. PII: S 0 0 2 5 5 5 6 4 ( 9 8 ) 1 0 0 5 7 3 Mathematical Biosciences 155 (1999) 77±109 We use these formulas and numerical simulations to examine the relative importance of dierent stages of infection and dierent chronic levels of virus to the spreading of the disease. The acute stage and the most infectious group both appear to have a disproportionate eect, 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. Ó 1999 Published by Elsevier Science Inc. All rights reserved.

对感染个体的HIV RNA的最新研究表明，随着时间的流逝，在同一个体中，病毒率在慢性阶段越来越差异。解释艾滋病毒传播研究的难题结果，并表明一小部分感染者可能导致不成比例感染的数量。我们使用两个简单的模型来研究感染性的变化。随着病毒载荷下降的辅助工具。在当前的疾病阶段，我们得出了两个模型的阈值条件，并比较了它们的内粒等值的明确公式®每组的相对影响是由该组引起的。在合同下的能源部W-7405-ENG-36和应用数学科学计划KC-07-01-01 /$±参见Elsevier Science Inc. 1999数学生物科学155（1999）77±109我们使用这些公式和数值模拟来检查不同感染阶段的相对重要性和不同的慢性病毒水平与疾病的扩散。具有不成比例的ECT，尤其是在早期的流行病上。 Elsevier Science Inc.出版的1999年保留所有权利。