Estimating the location and spatial extent of a covert anthrax release

Abstract

Rapidly identifying the features of a covert release of an agent such as anthrax could help to inform the planning of public health mitigation strategies. Previous studies have sought to estimate the time and size of a bioterror attack based on the symptomatic onset dates of early cases. We extend the scope of these methods by proposing a method for characterizing the time, strength, and also the location of an aerosolized pathogen release. A back-calculation method is developed allowing the characterization of the release based on the data on the first few observed cases of the subsequent outbreak, meteorological data, population densities, and data on population travel patterns. We evaluate this method on small simulated anthrax outbreaks (about 25-35 cases) and show that it could date and localize a release after a few cases have been observed, although misspecifications of the spore dispersion model, or the within-host dynamics model, on which the method relies can bias the estimates. Our method could also provide an estimate of the outbreak's geographical extent and, as a consequence, could help to identify populations at risk and, therefore, requiring prophylactic treatment. Our analysis demonstrates that while estimates based on the first ten or 15 observed cases were more accurate and less sensitive to model misspecifications than those based on five cases, overall mortality is minimized by targeting prophylactic treatment early on the basis of estimates made using data on the first five cases. The method we propose could provide early estimates of the time, strength, and location of an aerosolized anthrax release and the geographical extent of the subsequent outbreak. In addition, estimates of release features could be used to parameterize more detailed models allowing the simulation of control strategies and intervention logistics.

Figure 1. Map of the risk of anthrax infection (attack rates) in each ward for all scenarios except scenario D.

The cross on the main map represents the location of all simulated releases. The inset map represents population-weighted ward centroids (crosses) and their Voronoi diagram (polygons).

Figure 2. Histograms of the release location (left column) and date (right column) estimates for the 40 simulated outbreaks with Reference scenario (Ref.) and scenarios A to E.

The release location is represented by the distance to the real source. For the date estimates, breaks were set at 9 AM and 7 PM and counts are represented by bar heights rather than bar surfaces. For two outbreaks of scenario D, the source location estimated with 5 observed cases was further than 12 kilometers (14.3 and 18.2 km). For scenario E, the source location estimated with 5 observed cases was further than 35 kilometers for two outbreaks (57 and 68 km), the source location estimated with 10 observed cases was further than 35 kilometers for one outbreak (57 km), the source location estimated with 15 observed cases was further than 35 kilometers for two outbreaks (45 km and 117 km).

Figure 3. Comparison of the estimates based on the standard model (M1) with estimates based on the model allowing for occasional movements during the day (M2).

Estimates of the height (A), strength (B) and location (C) of the source for outbreaks simulated with Scenario E, based on the first 5 (blue), 10 (red), 15 (green) observed cases. (D) Ratio of the number of individuals inaccurately targeted (IC) by the mitigation strategy for a risk threshold of 1/100,000 relative to the theoretical number of individuals at risk (%). Triangles indicate estimates for simulations in which there is no observed case infected during an occasional movement. Rectangles indicate estimates for simulations in which there is at least one observed case infected during an occasional movement. The horizontal and vertical lines indicate the true values. The third line is the bisector.

Figure 4. Performance of the back-calculation method to predict the outbreak size with Reference scenario (R) and scenarios A to E.

Each box-plot represents the distribution (minimum, maximum, percentiles 2.5,25,50,75,97.5) of the predicted outbreak size relative bias based on the 5, 10 and 15 first cases on 40 simulated outbreaks per scenario.

Figure 5. Impact of the targeting mitigation strategy with Reference scenario (R) and scenarios A to E.

(A) Ratio of the number of individuals missed by the targeting mitigation strategy for a risk threshold of 1/100,000 relative to the theoretical number of individuals at risk. (B) Ratio of the number of individuals inaccurately targeted by the mitigation strategy for a risk threshold of 1/100 000 relative to the theoretical number of individuals at risk. (C) Number of individuals at risk according to the model used to generate the data. (D) Impact of administrating treatments to individuals living or working in a ward exposed to a risk of at least 1/100 ,000 inhabitants: outbreak size when there is no treatment and when prophylactic treatment compliance and efficacy is 100% prior to the onset of symptoms and administered 4 days after the first 5, 10 or 15 cases occurred. Each box-plot represents the distribution (minimum, maximum, percentiles 2.5, 25, 50, 75, 97.5) of the total number of cases.