Model-based optimization of infectivity parameters: a study of the early epidemic in San Francisco

By combining dynamic modeling of human immunodeficiency virus (HIV) transmission with mathematical optimization techniques, we calculate values of epidemiological parameters characterizing the early epidemic (1978-1986) among homosexual and bisexual men in San Francisco. The seroconversion fraction data reported by the San Francisco hepatitis B vaccine trials cohort study for this period is accurately simulated by a model assuming varying infectivity among three stages of HIV infection (early antigen stage, HIV antibody-positive stage, and AIDS stage). Using optimization techniques, we generate curves of the annual number of new partners and the annual number of risk contacts as functions of time. We project future case rates using optimized parameter values, and we study the sensitivity of these projections to variations in parameters, including the population size and the incubation period.