The Stages of HIV Infection: Waiting Times and Infection Transmission Probabilities

Abstract

Robert Horsburgh, Jr. AIDS Program, Centers for Disease Control Atlanta, GA 30333 We use stochastic models to estimate the waiting time distributions for progressive stages of HIV infection and to estimate stage-specific infection transmission probabilities between exposed and infected persons. We partition the infection period into four progressive stages: 1. infected but antibody negative; 2. antibody positive but asymptomatic; 3. pre-AIDS symptoms and/or abnormal hematologic indicator; and 4. clinical AIDS. We also define a fifth stage, death due to AIDS. A time-dependent Markov model is fitted to data on 45 persons with known time of HIV exposure to estimate the waiting time in stage I, i.e., the pre-HIV-antibody period. The mean pre-HIV-antibody period is estimated to be 2.6 ± 0.2 months. A time-homogeneous Markov model was previously used to estimate the waiting time distributions for stages 2-3 from data on a sample of 513 homosexual and bisexual men from San Francisco. By combining this model with the model for stage I, we estimate the mean AIDS incubation period, i.e., the waiting time in stages 1-3, as 9.8 ± 0.7 years. The estimated mean HIV infectious period, i.e., the waiting time in stages 1-4, is 11.8 ± 0.8 years. The estimated AIDS incubation period distribution is combined with a stochastic transmission model to estimate the stage-specific infection transmission rates from a sample of 45 heterosexual sex partners of persons with AIDS. The probability that an exposed person will be infected by a single sexual contact with an C. Castillo-Chavez (ed.), Mathematical and Statistical Approaches to AIDS Epidemiology © Springer-Verlag Berlin Heidelberg 1989 112 infected person in stage 4 is estimated to be 0.0057 ± 0.0016. For stage 3. this probability is estimated to be 0.0007 ± 0.0002. and it is estimated to be very near to 0 for stage 2. Thus. an exposed person is about eight times more likely to be infected by a person who has AIDS than by one who has pre-AIDS symptoms {p < 0.001}. The stochastic models that we developed can be extended to assess the risk of HIV transmission for different levels of important risk factors when more detailed data become available.