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

Comparison of dose-response models.

<p>Our best fit exponential model <b>B4</b> based on Brachman data (shaded region = 95% confidence range) is compared to selected other models from <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat-1003555-t001" target="_blank">Table 1</a>. Models <b>E3</b>, <b>E4</b>, and <b>E5</b> fall entirely within the shaded region. Model <b>B2</b> falls just below the lower boundary of the shaded region and is visually indistinguishable from it. We omit the curve for model <b>D2</b> in this figure, as our fit of the exponential model to the Druett <i>et al.</i> data set (<b>D3</b>) replaces the fit done by Haas (<b>D2</b>).</p

Cumulative distribution function for time from exposure to death.

<p>Assuming exposure to ID₁, solid curve is the distribution produced by our model <b>B4</b> (shaded area is the 95% confidence region). Dashed curve is produced by model <b>B2</b>. Points are from autopsy-confirmed anthrax deaths after the Sverdlovsk release.</p

Estimated relationship between duration of prophylaxis and subsequent chance of infection.

<p>Relationship between duration of prophylaxis (days, post-exposure) and the estimated chance of infection after antibiotics are no longer taken, at doses of 100, 1,000, and 10,000 spores. We assume the probability-per-day for clearance of spores from the lung, <i>θ</i>, is 0.07, and shaded areas are the confidence regions based on the 95% confidence interval for model <b>B4</b>'s fitted parameter <i>r</i> (probability of one spore germinating before being cleared).</p