Unraveling the Transmission Ecology of Polio
Publication Date
June 19, 2015
Journal
PLOS Biology
Authors
Micaela Martinez Bakker, Aaron A. King & Pejman Rohani
Volume
13
Issue
6
Pages
e1002172
DOI
https://dx.plos.org/10.1371/journal.pbio.1002172
Publisher URL
http://journals.plos.org/plosbiology/article?id=10.1371%2Fjournal.pbio.1002172
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/26090784
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4474890
Europe PMC
http://europepmc.org/abstract/MED/26090784
Web of Science
000357339600011
Scopus
84934761918
Mendeley
http://www.mendeley.com/research/unraveling-transmission-ecology-polio
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Mendeley | Further Information

{"title"=>"Unraveling the transmission ecology of polio", "type"=>"journal", "authors"=>[{"first_name"=>"Micaela", "last_name"=>"Martinez-Bakker", "scopus_author_id"=>"35781897200"}, {"first_name"=>"Aaron A.", "last_name"=>"King", "scopus_author_id"=>"7403373719"}, {"first_name"=>"Pejman", "last_name"=>"Rohani", "scopus_author_id"=>"7004381613"}], "year"=>2015, "source"=>"PLoS Biology", "identifiers"=>{"issn"=>"15457885", "doi"=>"10.1371/journal.pbio.1002172", "sgr"=>"84934761918", "scopus"=>"2-s2.0-84934761918", "isbn"=>"1545-7885", "pmid"=>"26090784", "pui"=>"605059973"}, "id"=>"0cbf4c0c-3a8a-3f3e-b74a-eef24675ec2e", "abstract"=>"Sustained and coordinated vaccination efforts have brought polio eradication within reach. Anticipating the eradication of wild poliovirus (WPV) and the subsequent challenges in preventing its re-emergence, we look to the past to identify why polio rose to epidemic levels in the mid-20th century, and how WPV persisted over large geographic scales. We analyzed an extensive epidemiological dataset, spanning the 1930s to the 1950s and spatially replicated across each state in the United States, to glean insight into the drivers of polio's historical expansion and the ecological mode of its persistence prior to vaccine introduction. We document a latitudinal gradient in polio's seasonality. Additionally, we fitted and validated mechanistic transmission models to data from each US state independently. The fitted models revealed that: (1) polio persistence was the product of a dynamic mosaic of source and sink populations; (2) geographic heterogeneity of seasonal transmission conditions account for the latitudinal structure of polio epidemics; (3) contrary to the prevailing \"disease of development\" hypothesis, our analyses demonstrate that polio's historical expansion was straightforwardly explained by demographic trends rather than improvements in sanitation and hygiene; and (4) the absence of clinical disease is not a reliable indicator of polio transmission, because widespread polio transmission was likely in the multiyear absence of clinical disease. As the world edges closer to global polio eradication and continues the strategic withdrawal of the Oral Polio Vaccine (OPV), the regular identification of, and rapid response to, these silent chains of transmission is of the utmost importance.", "link"=>"http://www.mendeley.com/research/unraveling-transmission-ecology-polio", "reader_count"=>55, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>5, "Researcher"=>18, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>12, "Student > Postgraduate"=>1, "Student > Master"=>8, "Other"=>2, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>5, "Researcher"=>18, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>12, "Student > Postgraduate"=>1, "Student > Master"=>8, "Other"=>2, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Unspecified"=>6, "Engineering"=>1, "Environmental Science"=>8, "Biochemistry, Genetics and Molecular Biology"=>2, "Medicine and Dentistry"=>16, "Agricultural and Biological Sciences"=>16, "Social Sciences"=>1, "Computer Science"=>2, "Immunology and Microbiology"=>1, "Earth and Planetary Sciences"=>1, "Linguistics"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>16}, "Social Sciences"=>{"Social Sciences"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>16}, "Computer Science"=>{"Computer Science"=>2}, "Linguistics"=>{"Linguistics"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>2}, "Unspecified"=>{"Unspecified"=>6}, "Environmental Science"=>{"Environmental Science"=>8}}, "reader_count_by_country"=>{"Saudi Arabia"=>1, "United States"=>5, "Brazil"=>1, "United Kingdom"=>1, "Israel"=>1, "France"=>2, "Portugal"=>1}, "group_count"=>1}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2127540"], "description"=>"<p>(A) Example of simulated infections and cases for Wisconsin. Months absent of reported cases are indicated in green. During periods when the disease is absent, WPV infections are often silently transmitted in the population. In this simulation, there were two instances (indicated by arrows) when the local chain of transmission was broken and WPV went locally extinct but quickly rebounded due to reintroduction. This example illustrates the two polio persistence mechanisms observed throughout the US, which are (i) local WPV persistence via unbroken chains of transmission and (ii) WPV extinction and reintroduction. (B) Distributions of mean monthly silent infections during periods absent of reported disease. (C) Distributions of cumulative silent infections during periods absent of disease. Distributions in B and C are 10%–90% quantiles and the median, based on 500 simulations per state. Silent infections are those that occur in the absence of reported cases and highlight the unobservable dynamics of polio. (D) Simulated cases surrounding WPV extinction events. Distributions show 10%–90% quantiles and the median number of cases observed up to 6 mo preceding and 6 mo following an extinction event. Generally, fewer than 5 cases/mo are reported 2 mo to either side of an extinction event. However, it is unclear whether 5 mo, each with less than 5 cases, is a reliable signal of extinction. The data used to make this figure can be found in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s005\" target=\"_blank\">S4 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s006\" target=\"_blank\">S5 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s007\" target=\"_blank\">S6 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s008\" target=\"_blank\">S7 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s014\" target=\"_blank\">S13 Data</a>, and <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s015\" target=\"_blank\">S14 Data</a>.</p>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455456, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.1002172.g006", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Persistence_mechanisms_/1455456", "title"=>"Persistence mechanisms.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-19 04:02:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/2127528"], "description"=>"<p>(A) Linear regression of state population size versus simulated trough infections, both on a log<sub>10</sub> scale. Trough infections are those shown in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.g004\" target=\"_blank\">Fig 4E</a>. (B) Residuals from the regression of population size versus trough infections were used as the dependent variable in the multiple regression model, where the predictors were: the state’s seasonal minimum reproductive ratio, the immigration rate, and the seasonal amplitude of the reproductive ratio, measured as half the peak–trough difference in the reproductive ratio. Plot shows on the <i>y</i>-axis, the residuals, <i>r</i><sub><i>i</i></sub>, from panel A, along with the prediction of the residuals based on the multiple regression </p><p></p><p></p><p></p><p><mi>r</mi><mi>i</mi></p><mo>=</mo><p><mi>b</mi><mn>0</mn></p><mo>+</mo><p><mi>b</mi><mn>1</mn></p>min<mo stretchy=\"false\">(</mo><p><mi>R</mi><mi>t</mi><mi>i</mi></p><mo stretchy=\"false\">)</mo><mo>+</mo><p><mi>b</mi><mn>2</mn></p><p></p><p>max<mo stretchy=\"false\">(</mo></p><p><mi>R</mi><mi>t</mi><mi>i</mi></p><mo stretchy=\"false\">)</mo><mo>−</mo>min<mo stretchy=\"false\">(</mo><p><mi>R</mi><mi>t</mi><mi>i</mi></p><mo stretchy=\"false\">)</mo><p></p><mn>2</mn><p></p><mo>+</mo><p><mi>b</mi><mn>3</mn></p><p><mi>ψ</mi><mi>i</mi></p><p></p><p></p><p></p>, where <p></p><p></p><p></p><p><mi>R</mi><mi>t</mi><mi>i</mi></p><p></p><p></p><p></p> is the reproductive ratio, <i>ψ</i><sub><i>i</i></sub> is the immigration rate, and <i>i</i> indicates the state. Taken together, panels A and B demonstrate that the predictors of a source versus sink are: the population size, the minimum reproductive ratio, the amplitude of the reproductive ratio, and the immigration rate. (C) Map of the seasonal minimum reproductive ratio showing geographic clustering. (D) The residuals, <i>r</i><sub><i>i</i></sub>, versus the seasonal amplitude of the reproductive ratio (i.e., the transmission amplitude), point size and color indicate the immigration rate, <i>ψ</i><sub><i>i</i></sub>. (E) The residuals, <i>r</i><sub><i>i</i></sub>, versus the seasonal minimum reproductive ratio, point size and color indicate the immigration rate, <i>ψ</i><sub><i>i</i></sub>. The data used to make this figure can be found in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s004\" target=\"_blank\">S3 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s005\" target=\"_blank\">S4 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s006\" target=\"_blank\">S5 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s007\" target=\"_blank\">S6 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s008\" target=\"_blank\">S7 Data</a>, and <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s009\" target=\"_blank\">S8 Data</a>.<p></p>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455454, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.1002172.g005", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Source_sink_population_predictors_/1455454", "title"=>"Source-sink population predictors.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-19 04:02:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/2127525"], "description"=>"<p>(A) Births enter the first susceptible infant class, </p><p></p><p></p><p></p><p><mi>S</mi><mn>1</mn><mi>B</mi></p><p></p><p></p><p></p>. Susceptible infants of age 0–6 mo, <p></p><p></p><p></p><p><mi>S</mi></p><p><mn>1</mn><mo>−</mo><mn>6</mn></p><mi>B</mi><p></p><p></p><p></p><p></p>, are susceptible to infection but are protected from symptomatic disease by maternal antibodies. Susceptible individuals over 6 months of age are in the <i>S</i><sup><i>O</i></sup> class. Infected infants and noninfant infections are in <i>I</i><sup><i>B</i></sup> and <i>I</i><sup><i>O</i></sup>, respectively. Infected individuals over 6 months of age, <i>I</i><sup><i>O</i></sup>, can have symptomatic illness and subsequently be reported as a clinical case with mean probability <i>ρ</i><sub><i>t</i></sub>. <i>ρ</i><sub><i>t</i></sub> is a composite parameter that represents the probability of symptoms and reporting. (B) Likelihood profile for the report rate, <i>ρ</i><sub><i>t</i></sub>, of noninfant infections and the immigration rate, <i>ψ</i>, for the state of Wisconsin. Maximum likelihood estimate (MLE) indicated by green asterisk. The report rate for Wisconsin was constant through time. The data used to make this figure can be found in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s011\" target=\"_blank\">S10 Data</a>.<p></p>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455451, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.1002172.g002", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_schematic_and_example_likelihood_profile_/1455451", "title"=>"Model schematic and example likelihood profile.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-19 04:02:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/2127524"], "description"=>"<p>(A) Total monthly case reports, 1931–1954, color-coded by per capita incidence. (B) Log-transformed per capita incidence by state, ranked top-to-bottom by population size. (C) Disease fadeout frequency as a function of state population size, during the pre-baby boom and baby boom eras. The lines represent fitted negative exponential curves, which tended toward zero. (D) Pairwise epidemic synchrony between states during the pre-baby boom and the baby boom. Mean and 95% bootstrap confidence envelope shown. (E, F) Relative timing of polio epidemic peaks during the (E) pre-baby boom and (F) baby boom eras. Color indicates mean rank of each state across years; lower rank indicates earlier epidemic peak. Below each map, relative timing is regressed on latitude. Lower latitude states had significantly earlier epidemic peaks. The data used to make this figure can be found in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s002\" target=\"_blank\">S1 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s003\" target=\"_blank\">S2 Data</a>, and <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s004\" target=\"_blank\">S3 Data</a>.</p>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455450, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.1002172.g001", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spatiotemporal_patterns_in_polio_incidence_/1455450", "title"=>"Spatiotemporal patterns in polio incidence.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-19 04:02:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/2127578", "https://ndownloader.figshare.com/files/2127579", "https://ndownloader.figshare.com/files/2127580", "https://ndownloader.figshare.com/files/2127581", "https://ndownloader.figshare.com/files/2127582", "https://ndownloader.figshare.com/files/2127583", "https://ndownloader.figshare.com/files/2127584", "https://ndownloader.figshare.com/files/2127585", "https://ndownloader.figshare.com/files/2127586", "https://ndownloader.figshare.com/files/2127587", "https://ndownloader.figshare.com/files/2127588", "https://ndownloader.figshare.com/files/2127589", "https://ndownloader.figshare.com/files/2127590", "https://ndownloader.figshare.com/files/2127591", "https://ndownloader.figshare.com/files/2127592"], "description"=>"<div><p>Sustained and coordinated vaccination efforts have brought polio eradication within reach. Anticipating the eradication of wild poliovirus (WPV) and the subsequent challenges in preventing its re-emergence, we look to the past to identify why polio rose to epidemic levels in the mid-20th century, and how WPV persisted over large geographic scales. We analyzed an extensive epidemiological dataset, spanning the 1930s to the 1950s and spatially replicated across each state in the United States, to glean insight into the drivers of polio’s historical expansion and the ecological mode of its persistence prior to vaccine introduction. We document a latitudinal gradient in polio’s seasonality. Additionally, we fitted and validated mechanistic transmission models to data from each US state independently. The fitted models revealed that: (1) polio persistence was the product of a dynamic mosaic of source and sink populations; (2) geographic heterogeneity of seasonal transmission conditions account for the latitudinal structure of polio epidemics; (3) contrary to the prevailing “disease of development” hypothesis, our analyses demonstrate that polio’s historical expansion was straightforwardly explained by demographic trends rather than improvements in sanitation and hygiene; and (4) the absence of clinical disease is not a reliable indicator of polio transmission, because widespread polio transmission was likely in the multiyear absence of clinical disease. As the world edges closer to global polio eradication and continues the strategic withdrawal of the Oral Polio Vaccine (OPV), the regular identification of, and rapid response to, these silent chains of transmission is of the utmost importance.</p></div>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455486, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>["https://dx.doi.org/10.1371/journal.pbio.1002172.s001", "https://dx.doi.org/10.1371/journal.pbio.1002172.s002", "https://dx.doi.org/10.1371/journal.pbio.1002172.s003", "https://dx.doi.org/10.1371/journal.pbio.1002172.s004", "https://dx.doi.org/10.1371/journal.pbio.1002172.s005", "https://dx.doi.org/10.1371/journal.pbio.1002172.s006", "https://dx.doi.org/10.1371/journal.pbio.1002172.s007", "https://dx.doi.org/10.1371/journal.pbio.1002172.s008", "https://dx.doi.org/10.1371/journal.pbio.1002172.s009", "https://dx.doi.org/10.1371/journal.pbio.1002172.s010", "https://dx.doi.org/10.1371/journal.pbio.1002172.s011", "https://dx.doi.org/10.1371/journal.pbio.1002172.s012", "https://dx.doi.org/10.1371/journal.pbio.1002172.s013", "https://dx.doi.org/10.1371/journal.pbio.1002172.s014", "https://dx.doi.org/10.1371/journal.pbio.1002172.s015"], "stats"=>{"downloads"=>7, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Unraveling_the_Transmission_Ecology_of_Polio_/1455486", "title"=>"Unraveling the Transmission Ecology of Polio", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-06-19 04:02:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/2127527"], "description"=>"<p>(A) Annual number of infected individuals in contrast to the small number of reported cases. Annual infections were reconstructed for the US using particle filtering means. The particle filtering mean is the expected value at time <i>t</i>, given the data up to time <i>t</i>. (B) Annual infections in the US represented as the percent of the population. Reconstructed infections show an increase in infection incidence that accompanies (C) the increase in the birth rate. (D) Simulated WPV extinction probability. The probability of extinction measured as the mean annual probability of observing an extinction during the off-season (December–May). “Sink\" populations are those states with a high extinction probability. (E) Simulated trough infections. Trough infections indicate the minimum number of infections during off-seasons. For each US state, the median was taken across simulations and averaged across years. “Source\" populations are those that maintain a high number of infections. Panels D–E were constructed using the 500 stochastic simulations for each state. The data used to make this figure can be found in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s002\" target=\"_blank\">S1 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s005\" target=\"_blank\">S4 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s006\" target=\"_blank\">S5 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s007\" target=\"_blank\">S6 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s008\" target=\"_blank\">S7 Data</a>, and <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s010\" target=\"_blank\">S9 Data</a>.</p>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455453, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.1002172.g004", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Epidemic_emergence_and_source_sink_dynamics_/1455453", "title"=>"Epidemic emergence and source-sink dynamics.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-19 04:02:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/2127526"], "description"=>"<p>(A) Observed data (black, shown for Wisconsin) and three stochastic simulations from the MLE (blue and green) highlight that both observed and simulated polio epidemics have a large amount of interannual variation in size but a narrow seasonal window. Fitted and out-of-fit data regions are indicated by blue and green, respectively. (B) Model validation showing observed log<sub>10</sub>(cases) versus expected log<sub>10</sub>(cases) for fitted data and (C) out-of-fit predictions for all 49 states. Expected cases are one-step-ahead predictions from the fitted models. Insets show observed cases (black) and expected cases (blue and green) for Wisconsin. Fitted data include May 1932–January 1953 for all states except South Dakota and Texas, whose covariate data limited our inference to begin in May 1933 and 1934, respectively; out-of-fit data spanned January 1953–December 1954. The generalized <i>R</i><sup>2</sup> = 0.76 for the fitted data and <i>R</i><sup>2</sup> = 0.61 for out-of-fit data, calculated on the natural scale, while data are plotted on a log scale for visualization. (D) Observed versus simulated mean rank of epidemic timing based on ten realizations of the fitted models. Inset shows the latitudinal gradient from one simulation; colors match Fig <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.g001\" target=\"_blank\">1E</a> and <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.g001\" target=\"_blank\">1F</a>. (E) Monthly polio cases in Texas and Wisconsin and (F) the MLE transmission rates. Epidemics occured earlier in southern states than northern states because the seasonal peak in transmission occured earlier at lower latitudes. (G) MLEs of the seasonal transmission rate for each state organized by geographic region; in our models, this represents the reproductive ratio. The reproductive ratio varies both seasonally and geographically, with some states having a reproductive ratio less than 1 during the wintertime off-season. The data used to make this figure can be found in <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s002\" target=\"_blank\">S1 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s005\" target=\"_blank\">S4 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s009\" target=\"_blank\">S8 Data</a>, <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s012\" target=\"_blank\">S11 Data</a>, and <a href=\"http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002172#pbio.1002172.s013\" target=\"_blank\">S12 Data</a>.</p>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455452, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.1002172.g003", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Fitted_model_and_seasonality_/1455452", "title"=>"Fitted model and seasonality.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-19 04:02:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/2127541"], "description"=>"<p>Local persistence of polio—within a state, region, or country—occurs when WPV overwinters during the off-season and the transmission chain is unbroken year-round. In contrast, local extinction and reintroduction occurs when WPV goes extinct during the off-season, breaking the chain of transmission; a new transmission chain begins when WPV is reintroduced from elsewhere. Discriminating among these scenarios is necessary for planning eradication strategies in endemic regions.</p><p>Four scenarios for the relationship between WPV infections and clinical disease.</p>", "links"=>[], "tags"=>["Oral Polio Vaccine", "polio eradication", "transmission conditions account", "opv", "polio transmission", "WPV"], "article_id"=>1455457, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Micaela Martinez-Bakker", "Aaron A. King", "Pejman Rohani"], "doi"=>"https://dx.doi.org/10.1371/journal.pbio.1002172.t001", "stats"=>{"downloads"=>6, "page_views"=>25, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Four_scenarios_for_the_relationship_between_WPV_infections_and_clinical_disease_/1455457", "title"=>"Four scenarios for the relationship between WPV infections and clinical disease.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-06-19 04:02:08"}

PMC Usage Stats | Further Information

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{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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