Quantitative Models of the Dose-Response and Time Course of Inhalational Anthrax in Humans

Anthrax poses a community health risk due to accidental or intentional aerosol release. Reliable quantitative dose-response analyses are required to estimate the magnitude and timeline of potential consequences and the effect of public health intervention strategies under specific scenarios. Analyses of available data from exposures and infections of humans and non-human primates are often contradictory. We review existing quantitative inhalational anthrax dose-response models in light of criteria we propose for a model to be useful and defensible. To satisfy these criteria, we extend an existing mechanistic competing-risks model to create a novel Exposure–Infection–Symptomatic illness–Death (EISD) model and use experimental non-human primate data and human epidemiological data to optimize parameter values. The best fit to these data leads to estimates of a dose leading to infection in 50% of susceptible humans (ID50) of 11,000 spores (95% confidence interval 7,200–17,000), ID10 of 1,700 (1,100–2,600), and ID1 of 160 (100–250). These estimates suggest that use of a threshold to human infection of 600 spores (as suggested in the literature) underestimates the infectivity of low doses, while an existing estimate of a 1% infection rate for a single spore overestimates low dose infectivity. We estimate the median time from exposure to onset of symptoms (incubation period) among untreated cases to be 9.9 days (7.7–13.1) for exposure to ID50, 11.8 days (9.5–15.0) for ID10, and 12.1 days (9.9–15.3) for ID1. Our model is the first to provide incubation period estimates that are independently consistent with data from the largest known human outbreak. This model refines previous estimates of the distribution of early onset cases after a release and provides support for the recommended 60-day course of prophylactic antibiotic treatment for individuals exposed to low doses.Author Summary: Anthrax poses a potential community health risk due to accidental or intentional aerosol release. We address the need for a transparent and defensible quantitative dose-response model for inhalational anthrax that is useful for risk assessors in estimating the magnitude and timeline of potential public health consequences should a release occur. Our synthesis of relevant data and previous modeling efforts identifies areas of improvement among many commonly cited dose-response models and estimates. To address those deficiencies, we provide a new model that is based on clear, transparent assumptions and published data from human and non-human primate exposures. Our resulting estimates provide important insight into the infectivity to humans of low inhaled doses of anthrax spores and the timeline of infections after an exposure event. These insights are critical to assessment of the impacts of delays in responding to a large scale aerosol release, as well as the recommended course of antibiotic administration to those potentially exposed.