We developed a model to simulate the dispersion of released anthrax spores; the infection of exposed persons; the progression of disease in infected persons; and symptomatic persons' use of the healthcare system, including blood culture testing in clinical settings. Using the simulation model, we generated outbreak signals and time until the first clinical diagnosis for 3 amounts of spores released. To incorporate into the model the uncertainty in parameter values, we used a Latin hypercube sampling design, which allows many parameter values to vary simultaneously (15). The 3,000 simulated signals generated with this sampling strategy were superimposed in turn onto baseline administrative records of ambulatory healthcare visits in the Norfolk, Virginia, area. These records are generated daily and similar types of records are used widely for syndromic surveillance (4,7,9). We assessed the usefulness of syndromic surveillance by modeling the healthcare system use that would occur after an anthrax attack and superimposing this use onto actual administrative data over 1-year period. Finally, we assessed, over a range of specificity, the sensitivity and timeliness of syndromic surveillance and the detection benefit of syndromic surveillance compared with clinical case finding for each simulated outbreak. We summarize our methods in the remainder of this section and refer readers to the Technical Appendix for additional details.

The simulation model builds on our previous work (16–18) and is composed of 4 components: dispersion, infection, disease, and healthcare system use. The dispersion model simulates the number of anthrax spores a person would inhale at locations throughout the region after release of aerosolized spores. We used the Hazard Prediction and Assessment Capability (HPAC) software developed by the Defense Threat Reduction Agency to simulate the dispersion of spores (19). The HPAC model accounts for factors such as atmospheric conditions and terrain. We simulated a point release of 3 amounts of anthrax spores: 1 kg, 0.1 kg, and 0.01 kg (Figure 1A).

The infection model simulates the number of persons infected, according to residential address and dispersion of spores (Figure 1B). The probability of infection given exposure to an amount of spores was modeled by using a probit regression model. The disease model uses a semi-Markov process to simulate the progression of infected persons through 3 discrete states of disease. Each infected person began in the incubation state and then progressed through the prodromal state and the fulminant state. The time in each state was sampled from a log normal distribution.

The healthcare use model uses a semi-Markov process to simulate the probability and timing of a symptomatic person seeking care and submission of blood for culture and culture results when care is sought. For persons in the prodromal or fulminant state of disease who sought care, the instantaneous probability of seeking care increased linearly over the duration of the state. For patients whose blood samples were cultured, the testing process was modeled as the transition through 2 discrete states: growth and isolation. The time spent in each of these states was modeled by using an exponential distribution.

The infection model used an infection function corresponding to the data reported by Glassman (20). This is a probit model with a 50% lethal dose (LD₅₀) of 8,600 spores and a slope of 0.67. Uncertainty exists about the values for many of the parameters in the disease and healthcare use models. To incorporate this uncertainty into our estimates, we used a Latin hypercube sampling approach to sample parameter values for random variables in our simulation model (15). This approach requires specifying equal probability bins for parameter values. We specified 3 bins for each parameter value, a narrow bin around the most likely estimate, and wider bins on either side of the estimate. Table 1 shows the bins we used for each parameter value, the probability distribution that each value parameterizes, and the sources that we used to define the bins.

We used previous work modeling anthrax for the distribution of time periods in each disease state (2,21,22). For the probability of seeking care while in the prodromal disease state, cross-sectional surveys indicate that 14%–30% of persons visit a physician at some point during an episode of upper respiratory tract illness (23,24). For the fulminant disease state, we estimated the probability of seeking care before death as 90%–95%, given the severity of the symptoms in that state.

After a person made a healthcare visit, we simulated the syndrome assigned to the person by using probabilities that reflect the distribution of clinical presentations for inhalational anthrax reported in the literature (25,26). Because we considered only respiratory syndromes for surveillance, we varied directly only the probability of being assigned a respiratory syndrome to persons in the prodromal disease state.

For visits from persons in either symptomatic disease state, the estimate of sensitivity from published studies of blood culture testing was 0.8–0.9 (27). For a visit in the prodromal state, we estimated the probability of a physician ordering a blood culture as 0.01–0.015 on the basis of data from the National Ambulatory Medical Care Survey (28). For a visit in the fulminant state of disease, we estimated the probability of a blood culture test as 0.9–0.95. After gram-positive rods grew in the blood culture, we estimated the probability of isolating the organism to be 0.8–0.9 (29). We modeled the time until growth and isolation as exponential (25,30).

We used records of ambulatory visits in the Norfolk, Virginia, region acquired from the TRICARE health maintenance organization as a baseline onto which we superimposed simulated outbreak records. The data covered the period 2001–2003, and the simulation region included 17 clinical facilities within an ≈160-km × 200-km area that encompasses 158 ZIP codes from 2 states. Over the 3 years of available data, 427,634 persons made >5 million visits. We classified the records into syndromes by using the International Classification of Diseases, 9th Revision, Clinical Modification (ICD-9-CM) to syndrome mapping defined by the ESSENCE system (7) and used only 351,749 records for which persons were classified as having a respiratory syndrome. The Human Subjects Panel at the Stanford School of Medicine approved the use of these data for this study. We examined 3 scenarios defined by the amount of spores released: 1 kg, 0.1 kg, and 0.01 kg. For each scenario, we performed 1,000 simulations.

The time to outbreak detection through clinical case finding for a simulated outbreak was calculated for each simulated outbreak as the time between exposure to spores and the first positive blood culture. To calculate time to outbreak detection through syndromic surveillance, we superimposed the simulated records for respiratory syndrome visits onto the authentic baseline data, beginning on a randomly selected date in 2003, and then applied the outbreak detection algorithm to the combined baseline and simulated data. The outbreak detection algorithm used a time-series model (31) to generate daily 1-step-ahead forecasts for the total number of respiratory syndrome visits (13) and then applied a cumulative sum (32) to the forecast residual. To vary the specificity of the detection algorithm, we varied the decision threshold of the cumulative sum.

To evaluate outbreak detection through syndromic surveillance, we calculated sensitivity, specificity, and timeliness at a range of decision thresholds. Timeliness is the duration between the release of anthrax spores and the first report of an outbreak. We also computed the detection benefit of syndromic surveillance relative to clinical case finding, and the proportion of runs with a detection benefit >0. Detection benefit is the potential time saved in detection from using syndromic surveillance compared with clinical case finding. The benefit is calculated as the difference in the timeliness between syndromic surveillance and clinical case finding in those simulations in which detection occurred first by syndromic surveillance. When an outbreak was not detected by syndromic surveillance, the detection benefit was 0. For a given release scenario, each of the 1,000 simulations integrated both randomness in the component model outputs as well as uncertainty in component model parameters. Each of the 1,000 simulations is a sample from the integrated distribution of possible outcomes. To indicate the spread of the integrated uncertainty distribution, we calculated the upper and lower deciles from the 1,000 simulations. For plots, we calculated 95% confidence intervals, which reflect finiteness of the simulation.

Because all outbreaks were ultimately detected by clinical case finding through routine blood culture, the sensitivity of this approach was 1.0 for the scenarios considered. Clinical case finding detected outbreaks from an average of 3.7 days to 4.1 days after release, with larger amounts of spores detected before smaller amounts (Table 2). Results from analyses of additional release scenarios (data not shown) suggested that the influence of amount released on time to detection was mediated, in part, through the number infected. Mean timeliness across the scenarios examined was associated with the mean number infected (Pearson's r -0.94, 95% confidence interval -0.98 to -0.79), and an increase of 10,000 infected persons resulted in a decrease in the time until detection of ≈4 hours.

The sensitivity and timeliness of syndromic surveillance were influenced by the release amount and by specificity. Table 3 shows this relationship over the release scenarios examined and 2 levels of specificity. At a specificity of 0.90, a 1-kg release was detected in 100% of our simulations (sensitivity 1.0) at a mean detection time of 3.1 days. For a release that was much smaller, 0.01 kg, sensitivity was 0.94, and the mean detection time increased to 3.6 days. Although the sensitivity of syndromic surveillance was high when we set specificity to 0.90, this specificity resulted in a false alarm (false-positive detection) ≈1 every 10 days. By increasing specificity to 0.975, we reduced the false alarm rate to ≈1 every 40 days (Table 3). However, with increased specificity, the sensitivity of syndromic surveillance decreased (from 0.98 to 0.82 depending on the size of the release) and the mean time until detection lengthened to 4.3 days for a 1-kg release and to 5.1 days for a 0.01-kg release (Table 3).

Results from analyses of additional release scenarios (data not shown) indicated that the trends in sensitivity and timeliness across release amount were mediated to some extent by the number infected. Sensitivity was a nonlinear function of the number of persons infected, with sensitivity increasing more quickly when fewer persons were infected. At a specificity of 0.975, an increase of 10,000 infected persons resulted in a decrease in time to detection of ≈6 hours.

The detection benefit of syndromic surveillance compared with clinical case finding was influenced by specificity and the release amount. Table 3 shows this relationship for the release amounts examined and 2 levels of specificity. When the specificity was 0.9, syndromic surveillance detected from 51% to 59% of outbreaks before clinical case finding, and the mean detection benefit was 1.0–1.1 days, but this specificity resulted in a false alarm every 10 days. At a specificity of 0.975, which reduced false alarms to 1 every 40 days, syndromic surveillance detected 19%–28% of outbreaks before clinical case finding and the mean detection benefit was 0.32–0.33 days, or ≈8 hours. Figure 2 shows that for the 0.01-kg and 1-kg release scenarios (results for the 0.1-kg release are similar, but are not shown), the proportion of outbreaks detected first by syndromic surveillance and the mean detection benefit of surveillance each increased as specificity decreased. Figure 2 also shows that the release amount had a strong effect on the proportion of outbreaks detected first by syndromic surveillance but that it did not have a strong effect on the mean detection benefit.

At a set specificity, syndromic surveillance tended to detect a higher proportion of outbreaks before clinical case finding with increasing release amount. The mean detection benefit, in contrast, tended to decrease when the amount of spores released increased. This decrease in average detection benefit occurred because even though syndromic surveillance detected more outbreaks before clinical case finding as the release amount increased, the detection benefit for the additional outbreaks was small, and the average detection benefit thus decreased.