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Estimating the location and spatial extent of a covert anthrax release.

Legrand J, Egan JR, Hall IM, Cauchemez S, Leach S, Ferguson NM - PLoS Comput. Biol. (2009)

Bottom Line: 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.In addition, estimates of release features could be used to parameterize more detailed models allowing the simulation of control strategies and intervention logistics.

View Article: PubMed Central - PubMed

Affiliation: MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Diseases Epidemiology, Imperial College London, London, United Kingdom. jlegrand@imperial.ac.uk

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.

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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.
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pcbi-1000356-g005: 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.

Mentions: Regarding mitigation policies, key is how many people might be missed by a risk-targeted strategy guided by the model estimates, and how many would be inaccurately considered at risk. Both of these numbers varied substantially from one simulated outbreak to another (see Figure 5). For a risk threshold of 1 case per 100,000 inhabitants and estimates based on 5 observed cases, the median proportion of at-risk individuals missed by targeting was less than 8%, for any scenario, with 3rd quartiles under 20% for all scenarios (see Figure 5a). The location of those exposed wards missed by the targeting strategy and those wards inaccurately considered at risk is shown in Text S1. For any scenario other than E and estimates based on 10 or 15 observed cases, the median number of individuals inaccurately considered at risk was about 5–8% of those actually at risk (see Figure 5b) but was larger when the simulated outbreaks included local occasional movements (see scenario E, estimates based on 15 cases). Most of the wards inaccurately considered as exposed with scenario E estimates are in the west of the exposed area (see Text S1). Figure 5c shows the actual numbers at risk as a function of the risk threshold used. For Scenario E, using a model which took account of occasional movements decreased the number of individuals inaccurately considered at risk (see Figure 3d).


Estimating the location and spatial extent of a covert anthrax release.

Legrand J, Egan JR, Hall IM, Cauchemez S, Leach S, Ferguson NM - PLoS Comput. Biol. (2009)

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.
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2663800&req=5

pcbi-1000356-g005: 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.
Mentions: Regarding mitigation policies, key is how many people might be missed by a risk-targeted strategy guided by the model estimates, and how many would be inaccurately considered at risk. Both of these numbers varied substantially from one simulated outbreak to another (see Figure 5). For a risk threshold of 1 case per 100,000 inhabitants and estimates based on 5 observed cases, the median proportion of at-risk individuals missed by targeting was less than 8%, for any scenario, with 3rd quartiles under 20% for all scenarios (see Figure 5a). The location of those exposed wards missed by the targeting strategy and those wards inaccurately considered at risk is shown in Text S1. For any scenario other than E and estimates based on 10 or 15 observed cases, the median number of individuals inaccurately considered at risk was about 5–8% of those actually at risk (see Figure 5b) but was larger when the simulated outbreaks included local occasional movements (see scenario E, estimates based on 15 cases). Most of the wards inaccurately considered as exposed with scenario E estimates are in the west of the exposed area (see Text S1). Figure 5c shows the actual numbers at risk as a function of the risk threshold used. For Scenario E, using a model which took account of occasional movements decreased the number of individuals inaccurately considered at risk (see Figure 3d).

Bottom Line: 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.In addition, estimates of release features could be used to parameterize more detailed models allowing the simulation of control strategies and intervention logistics.

View Article: PubMed Central - PubMed

Affiliation: MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Diseases Epidemiology, Imperial College London, London, United Kingdom. jlegrand@imperial.ac.uk

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.

Show MeSH
Related in: MedlinePlus