Quantitative Models of the Dose-Response and Time Course of Inhalational Anthrax in Humans
Publication Date
August 15, 2013
Journal
PLOS Pathogens
Authors
Damon J. A. Toth, Adi V. Gundlapalli, Wiley A. Schell, Kenneth Bulmahn, et al
Volume
9
Issue
8
Pages
e1003555
DOI
https://dx.plos.org/10.1371/journal.ppat.1003555
Publisher URL
http://journals.plos.org/plospathogens/article?id=10.1371%2Fjournal.ppat.1003555
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/24058320
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3744436
Europe PMC
http://europepmc.org/abstract/MED/24058320
Web of Science
000323888200045
Scopus
84883417733
Mendeley
http://www.mendeley.com/research/quantitative-models-doseresponse-time-course-inhalational-anthrax-humans
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Mendeley | Further Information

{"title"=>"Quantitative Models of the Dose-Response and Time Course of Inhalational Anthrax in Humans", "type"=>"journal", "authors"=>[{"first_name"=>"Damon J.A.", "last_name"=>"Toth", "scopus_author_id"=>"55844256200"}, {"first_name"=>"Adi V.", "last_name"=>"Gundlapalli", "scopus_author_id"=>"6506223668"}, {"first_name"=>"Wiley A.", "last_name"=>"Schell", "scopus_author_id"=>"7102288462"}, {"first_name"=>"Kenneth", "last_name"=>"Bulmahn", "scopus_author_id"=>"55842211100"}, {"first_name"=>"Thomas E.", "last_name"=>"Walton", "scopus_author_id"=>"57201507391"}, {"first_name"=>"Christopher W.", "last_name"=>"Woods", "scopus_author_id"=>"7202272125"}, {"first_name"=>"Catherine", "last_name"=>"Coghill", "scopus_author_id"=>"55843056700"}, {"first_name"=>"Frank", "last_name"=>"Gallegos", "scopus_author_id"=>"55842918100"}, {"first_name"=>"Matthew H.", "last_name"=>"Samore", "scopus_author_id"=>"7004341520"}, {"first_name"=>"Frederick R.", "last_name"=>"Adler", "scopus_author_id"=>"7006492816"}], "year"=>2013, "source"=>"PLoS Pathogens", "identifiers"=>{"pui"=>"369735832", "sgr"=>"84883417733", "issn"=>"15537366", "pmid"=>"24058320", "scopus"=>"2-s2.0-84883417733", "doi"=>"10.1371/journal.ppat.1003555", "isbn"=>"1553-7374"}, "id"=>"b48f3b1d-53cb-3eee-a8a9-4f00685852ec", "abstract"=>"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.", "link"=>"http://www.mendeley.com/research/quantitative-models-doseresponse-time-course-inhalational-anthrax-humans", "reader_count"=>36, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Researcher"=>8, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>9, "Student > Postgraduate"=>4, "Other"=>4, "Student > Master"=>1, "Student > Bachelor"=>5, "Lecturer"=>2, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Researcher"=>8, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>9, "Student > Postgraduate"=>4, "Other"=>4, "Student > Master"=>1, "Student > Bachelor"=>5, "Lecturer"=>2, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>2, "Environmental Science"=>1, "Biochemistry, Genetics and Molecular Biology"=>3, "Mathematics"=>7, "Agricultural and Biological Sciences"=>7, "Medicine and Dentistry"=>9, "Design"=>1, "Pharmacology, Toxicology and Pharmaceutical Science"=>2, "Social Sciences"=>1, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Design"=>{"Design"=>1}, "Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>9}, "Social Sciences"=>{"Social Sciences"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>7}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Mathematics"=>{"Mathematics"=>7}, "Unspecified"=>{"Unspecified"=>2}, "Environmental Science"=>{"Environmental Science"=>1}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>2}}, "reader_count_by_country"=>{"Sweden"=>1, "United States"=>3, "Brazil"=>1, "Portugal"=>1}, "group_count"=>2}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1172289"], "description"=>"<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>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax", "dose-response"], "article_id"=>774461, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_dose_response_models_/774461", "title"=>"Comparison of dose-response models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-08-15 05:12:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/1172290"], "description"=>"<p>Our best fit exponential model <b>B4</b> based on the Brachman data (shaded region = 95% confidence range) is compared to other models fit to the same data set. Dashed line = Mayer <i>et al.. </i><a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Mayer1\" target=\"_blank\">[35]</a> extended exponential model <b>B3</b> (<i>α</i> = 0.90, <i>r</i> = 1.87×10<sup>−5</sup>); solid line = Mayer <i>et al.. </i><a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Mayer1\" target=\"_blank\">[35]</a> exponential model <b>B2</b> (<i>r</i> = 3.95×10<sup>−5</sup>); dotted line = Haas <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Haas1\" target=\"_blank\">[18]</a> exponential model <b>B1</b> (<i>r</i> = 2.6×10<sup>−5</sup>). The Haas curve would shift very close to the Mayer exponential curve if the correct cumulative dose is applied (see <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555.s006\" target=\"_blank\">Table S5</a>).</p>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax", "dose-response", "brachman"], "article_id"=>774462, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_dose_response_models_fit_to_the_Brachman_data_/774462", "title"=>"Comparison of dose-response models fit to the Brachman data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-08-15 05:12:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/1172291"], "description"=>"<p>Assuming exposure to ID<sub>1</sub>, 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>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax"], "article_id"=>774463, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cumulative_distribution_function_for_time_from_exposure_to_death_/774463", "title"=>"Cumulative distribution function for time from exposure to death.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-08-15 05:12:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/1172293"], "description"=>"<p>The curves show the probability that a given incubation period (time from exposure to symptoms) among those infected by the ID<sub>1</sub> would be less than the given number of days post-exposure. Solid line represents the estimate produced by model <b>B4</b> and the shaded area spans the 95% confidence bounds; dashed line is the curve produced by the model of Brookmeyer et al. <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Brookmeyer1\" target=\"_blank\">[32]</a>; dotted line is the curve produced by the model of Wilkening <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Wilkening2\" target=\"_blank\">[37]</a>; points are data from 30 autopsy-confirmed anthrax cases after the Sverdlovsk release <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Abramova1\" target=\"_blank\">[36]</a>. Inset: comparison of our model <b>B4</b> with the model proposed for use by the IOM <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-IOM1\" target=\"_blank\">[12]</a> for the anthrax incubation period distribution over the first 8 days after exposure (dash-dotted line).</p>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax", "functions", "incubation", "infected"], "article_id"=>774464, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cumulative_distribution_functions_for_the_incubation_period_among_those_infected_by_a_low_dose_/774464", "title"=>"Cumulative distribution functions for the incubation period among those infected by a low dose.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-08-15 05:12:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/1172294"], "description"=>"<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>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax", "duration", "prophylaxis"], "article_id"=>774465, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Estimated_relationship_between_duration_of_prophylaxis_and_subsequent_chance_of_infection_/774465", "title"=>"Estimated relationship between duration of prophylaxis and subsequent chance of infection.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-08-15 05:12:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/1172295"], "description"=>"<p>This depicts the assumptions made under the time-dose-response model <b>B4</b>, developed for this paper. After a dose of a given size is inhaled, a competing risks process determines whether infection occurs and the distribution of the time between exposure and infection (initial spore germination) if it does occur. We assume a fixed delay between initial spore germination and the onset of symptoms and a gamma-distributed delay between the onset of symptoms and death among untreated cases.</p>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax", "timeline"], "article_id"=>774466, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_of_the_determination_of_infection_and_the_infection_timeline_for_anthrax_/774466", "title"=>"Schematic of the determination of infection and the infection timeline for anthrax.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-08-15 05:12:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/1172296"], "description"=>"<p>Model formulas and parameter value definitions are described in detail in the <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#s4\" target=\"_blank\">Materials and Methods</a> section. ID estimates for age-dependent models rely on estimates of the age distribution of the United States population from the 2010 census. Criteria used to evaluate the models are 1) the parameter values are derived from dose-response data; 2) the shape of the dose-response curve is consistent with Sverdlovsk data; 3) the model is derived from mechanistic assumptions; and 4) the model estimates the incubation period.</p>a<p>Papers <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Isukapalli1\" target=\"_blank\">[11]</a>, <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Wilkening1\" target=\"_blank\">[15]</a> citing model <b>J</b> instead used ID<sub>50</sub> = 8,600, which is just within the 95% confidence limits reported in <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Glassman1\" target=\"_blank\">[26]</a>.</p>b<p>Models <b>B2</b> and <b>B3</b> estimate the time from exposure to infection take-off and death, but not the incubation period (time from exposure to onset of symptoms).</p>c<p>Papers <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Isukapalli1\" target=\"_blank\">[11]</a>, <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Wilkening1\" target=\"_blank\">[15]</a> citing model <b>E1</b> instead used ID<sub>50</sub> = 8,600, which is within the range reported in the original paper.</p>d<p>For model <b>E5</b>, the original paper <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Brookmeyer1\" target=\"_blank\">[32]</a> estimated the time-dependent parameter <i>θ</i> from data and did not specify an estimate for <i>r</i>, but papers applying this model <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Isukapalli1\" target=\"_blank\">[11]</a>, <a href=\"http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003555#ppat.1003555-Wilkening1\" target=\"_blank\">[15]</a> used the <i>r</i> value given above under an assumption of ID<sub>50</sub> = 8,600, comparable to other models based on expert opinion.</p>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax", "dose-response"], "article_id"=>774467, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_anthrax_dose_response_models_/774467", "title"=>"Summary of anthrax dose-response models.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-08-15 05:12:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/1172297", "https://ndownloader.figshare.com/files/1172298", "https://ndownloader.figshare.com/files/1172301", "https://ndownloader.figshare.com/files/1172303", "https://ndownloader.figshare.com/files/1172304", "https://ndownloader.figshare.com/files/1172306"], "description"=>"<div><p>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 (ID<sub>50</sub>) of 11,000 spores (95% confidence interval 7,200–17,000), ID<sub>10</sub> of 1,700 (1,100–2,600), and ID<sub>1</sub> 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 ID<sub>50</sub>, 11.8 days (9.5–15.0) for ID<sub>10</sub>, and 12.1 days (9.9–15.3) for ID<sub>1</sub>. 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.</p></div>", "links"=>[], "tags"=>["Computational biology", "Population modeling", "Infectious disease modeling", "Infectious diseases", "Bacterial diseases", "anthrax", "dose-response", "inhalational"], "article_id"=>774468, "categories"=>["Medicine", "Biological Sciences"], "users"=>["Damon J. A. Toth", "Adi V. Gundlapalli", "Wiley A. Schell", "Kenneth Bulmahn", "Thomas E. Walton", "Christopher W. Woods", "Catherine Coghill", "Frank Gallegos", "Matthew H. Samore", "Frederick R. Adler"], "doi"=>["https://dx.doi.org/10.1371/journal.ppat.1003555.s001", "https://dx.doi.org/10.1371/journal.ppat.1003555.s002", "https://dx.doi.org/10.1371/journal.ppat.1003555.s003", "https://dx.doi.org/10.1371/journal.ppat.1003555.s004", "https://dx.doi.org/10.1371/journal.ppat.1003555.s005", "https://dx.doi.org/10.1371/journal.ppat.1003555.s006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Quantitative_Models_of_the_Dose_Response_and_Time_Course_of_Inhalational_Anthrax_in_Humans_/774468", "title"=>"Quantitative Models of the Dose-Response and Time Course of Inhalational Anthrax in Humans", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-08-15 05:12:37"}

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Relative Metric

{"start_date"=>"2013-01-01T00:00:00Z", "end_date"=>"2013-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Immunology", "average_usage"=>[266, 466, 591, 701, 799, 887, 982, 1067, 1155, 1237, 1317, 1395, 1458]}, {"subject_area"=>"/Biology and life sciences/Veterinary science", "average_usage"=>[313, 571, 709, 825, 944, 1048, 1145, 1261, 1354, 1434, 1524, 1599, 1684]}, {"subject_area"=>"/Medicine and health sciences", "average_usage"=>[264, 460, 584, 692, 794, 887, 978, 1067, 1154, 1241, 1328, 1408, 1474]}, {"subject_area"=>"/Medicine and health sciences/Infectious diseases", "average_usage"=>[297, 523, 655, 765, 866, 971, 1070, 1159, 1256, 1337, 1424, 1496, 1568]}, {"subject_area"=>"/Medicine and health sciences/Pathology and laboratory medicine", "average_usage"=>[267, 466, 592, 709, 806, 901, 989, 1075, 1162, 1254, 1342, 1424, 1486]}]}
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