A Measles Epidemic Threshold in a Highly Vaccinated Population
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{"title"=>"A measles epidemic threshold in a highly vaccinated population", "type"=>"journal", "authors"=>[{"first_name"=>"Jacco", "last_name"=>"Wallinga", "scopus_author_id"=>"7003807945"}, {"first_name"=>"Janneke C M", "last_name"=>"Heijne", "scopus_author_id"=>"23990865400"}, {"first_name"=>"Mirjam", "last_name"=>"Kretzschmar", "scopus_author_id"=>"7005173750"}], "year"=>2005, "source"=>"PLoS Medicine", "identifiers"=>{"issn"=>"15491277", "scopus"=>"2-s2.0-28444433814", "sgr"=>"28444433814", "pui"=>"41735783", "isbn"=>"1549-1676 (Electronic)", "pmid"=>"16218769", "doi"=>"10.1371/journal.pmed.0020316"}, "id"=>"5c820305-b562-3b76-a3a1-692c55a2e058", "abstract"=>"BACKGROUND: Mass vaccination against measles has successfully lowered the incidence of the disease and has changed the epidemic pattern from a roughly biennial cycle to an irregular sequence of outbreaks. A possible explanation for this sequence of outbreaks is that the vaccinated population is protected by solid herd immunity. If so, we would expect to see the fraction of susceptible individuals remaining below an epidemic threshold. An alternative explanation is the occurrence of occasional localised lapses in herd immunity that allow for major outbreaks in areas with a low vaccine coverage. In that case, we would expect the fraction of susceptible individuals to exceed an epidemic threshold before outbreaks occur. These two explanations for the irregular sequence of measles outbreaks can be tested against observations of both the fraction of susceptible individuals and infection attack rates. METHODS AND FINDINGS: We have estimated both the fraction of susceptible individuals at the start of each epidemic year and the infection attack rates for each epidemic year in the Netherlands over a 28-y period. During this period the vaccine coverage averaged 93%, and there was no sustained measles transmission. Several measles outbreaks occurred in communities with low vaccine coverage, and these ended without intervention. We show that there is a clear threshold value for the fraction of susceptible individuals, below which only minor outbreaks occurred, and above which both minor and major outbreaks occurred. A precise, quantitative relationship exists between the fraction of susceptible individuals in excess of this threshold and the infection attack rate during the major outbreaks. CONCLUSION: In populations with a high but heterogeneous vaccine coverage, measles transmission can be interrupted without establishing solid herd immunity. When infection is reintroduced, a major outbreak can occur in the communities with low vaccine coverage. During such a major outbreak, each additional susceptible individual in excess of the threshold is associated with almost two additional infections. This quantitative relationship offers potential for anticipating both the likelihood and size of future major outbreaks when measles transmission has been interrupted.", "link"=>"http://www.mendeley.com/research/measles-epidemic-threshold-highly-vaccinated-population", "reader_count"=>53, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>9, "Researcher"=>14, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>1, "Other"=>3, "Student > Master"=>7, "Student > Bachelor"=>5, "Lecturer > Senior Lecturer"=>2, "Professor"=>3}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>9, "Researcher"=>14, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>7, "Student > Postgraduate"=>1, "Other"=>3, "Student > Master"=>7, "Student > Bachelor"=>5, "Lecturer > Senior Lecturer"=>2, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>4, "Environmental Science"=>1, "Nursing and Health Professions"=>2, "Mathematics"=>5, "Agricultural and Biological Sciences"=>9, "Medicine and Dentistry"=>22, "Business, Management and Accounting"=>1, "Psychology"=>1, "Social Sciences"=>3, "Computer Science"=>2, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>22}, "Social Sciences"=>{"Social Sciences"=>3}, "Psychology"=>{"Psychology"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>9}, "Computer Science"=>{"Computer Science"=>2}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>2}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Mathematics"=>{"Mathematics"=>5}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>1}}, "reader_count_by_country"=>{"Belgium"=>1, "United States"=>3, "United Kingdom"=>1, "Australia"=>1, "India"=>1}, "group_count"=>5}

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  • {"month"=>"2", "year"=>"2017", "pdf_views"=>"13", "xml_views"=>"0", "html_views"=>"99"}
  • {"month"=>"3", "year"=>"2017", "pdf_views"=>"12", "xml_views"=>"0", "html_views"=>"125"}
  • {"month"=>"4", "year"=>"2017", "pdf_views"=>"5", "xml_views"=>"1", "html_views"=>"148"}
  • {"month"=>"5", "year"=>"2017", "pdf_views"=>"8", "xml_views"=>"2", "html_views"=>"79"}
  • {"month"=>"6", "year"=>"2017", "pdf_views"=>"3", "xml_views"=>"0", "html_views"=>"61"}
  • {"month"=>"7", "year"=>"2017", "pdf_views"=>"8", "xml_views"=>"1", "html_views"=>"46"}
  • {"month"=>"8", "year"=>"2017", "pdf_views"=>"7", "xml_views"=>"1", "html_views"=>"34"}
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  • {"month"=>"1", "year"=>"2018", "pdf_views"=>"5", "xml_views"=>"2", "html_views"=>"67"}
  • {"month"=>"2", "year"=>"2018", "pdf_views"=>"7", "xml_views"=>"0", "html_views"=>"60"}
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  • {"month"=>"4", "year"=>"2018", "pdf_views"=>"9", "xml_views"=>"0", "html_views"=>"66"}
  • {"month"=>"5", "year"=>"2018", "pdf_views"=>"34", "xml_views"=>"0", "html_views"=>"31"}
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  • {"month"=>"1", "year"=>"2019", "pdf_views"=>"2", "xml_views"=>"2", "html_views"=>"55"}
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  • {"month"=>"7", "year"=>"2019", "pdf_views"=>"14", "xml_views"=>"0", "html_views"=>"30"}
  • {"month"=>"8", "year"=>"2019", "pdf_views"=>"9", "xml_views"=>"0", "html_views"=>"32"}
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  • {"month"=>"10", "year"=>"2019", "pdf_views"=>"19", "xml_views"=>"0", "html_views"=>"74"}
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  • {"month"=>"12", "year"=>"2019", "pdf_views"=>"19", "xml_views"=>"1", "html_views"=>"49"}
  • {"month"=>"1", "year"=>"2020", "pdf_views"=>"17", "xml_views"=>"0", "html_views"=>"33"}
  • {"month"=>"2", "year"=>"2020", "pdf_views"=>"25", "xml_views"=>"0", "html_views"=>"23"}
  • {"month"=>"3", "year"=>"2020", "pdf_views"=>"35", "xml_views"=>"1", "html_views"=>"29"}
  • {"month"=>"4", "year"=>"2020", "pdf_views"=>"33", "xml_views"=>"0", "html_views"=>"19"}
  • {"month"=>"5", "year"=>"2020", "pdf_views"=>"43", "xml_views"=>"0", "html_views"=>"33"}
  • {"month"=>"6", "year"=>"2020", "pdf_views"=>"45", "xml_views"=>"0", "html_views"=>"19"}
  • {"month"=>"7", "year"=>"2020", "pdf_views"=>"5", "xml_views"=>"1", "html_views"=>"8"}

Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/960976"], "description"=>"<div><p>(A) The fraction of individuals susceptible to measles on 1 September of each year.</p>\n <p>(B) Infection attack rate of measles during each epidemic year from 1 September to 31 August.</p>\n <p>(C) Relation between fraction of susceptible individuals and attack rate.</p>\n <p>Dark blue markers correspond to major outbreaks; light blue markers correspond to minor outbreaks. Solid gray lines indicate the maximum likelihood values for infection attack rate; broken gray lines indicate the likelihood support region. The dotted yellow line in (A) and (C) indicates the threshold value for susceptible individuals below which solid herd immunity is achieved.</p></div>", "links"=>[], "tags"=>["measles", "outbreaks", "september", "1976", "31", "august"], "article_id"=>630978, "categories"=>["Biotechnology", "Infectious Diseases"], "users"=>["Jacco Wallinga", "Janneke C. M Heijne", "Mirjam Kretzschmar"], "doi"=>"https://dx.doi.org/10.1371/journal.pmed.0020316.g002", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Observed_Measles_Outbreaks_in_the_Netherlands_from_1_September_1976_to_31_August_2004_/630978", "title"=>"Observed Measles Outbreaks in the Netherlands, from 1 September 1976 to 31 August 2004", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:54:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/960915"], "description"=>"<div><p>(A) Expected infection attack rates during measles outbreaks in an idealised homogeneously mixing population.</p>\n <p>(B) Expected infection attack rates during measles outbreaks in a population protected by solid herd immunity.</p>\n <p>(C) Expected infection attack rates during measles outbreaks in a heterogeneous population consisting of a small community embedded in a larger population. The expectations are calculated for a stochastic “susceptible–exposed–infectious–recovered” (SEIR) model, with measles basic reproduction number <i>R</i><sub>0</sub> = 17 [<a href=\"http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020316#pmed-0020316-b02\" target=\"_blank\">2</a>], and ten imported measles cases per year. The population structure is as reported for the Netherlands, where a small community of 300 000 persons with a variable fraction of susceptible individuals exists in a larger population of 15 million persons with a fraction of susceptible individuals of 0.043 [<a href=\"http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020316#pmed-0020316-b21\" target=\"_blank\">21</a>].</p>\n <p>Dark blue markers correspond to major outbreaks; light blue markers correspond to minor outbreaks. The solid gray line indicates the approximation, near the threshold, of the infection attack rate: two infections occur per susceptible individual in excess of the threshold.</p></div>", "links"=>[], "tags"=>["Infectious diseases", "public health and epidemiology"], "article_id"=>630918, "categories"=>["Biotechnology", "Infectious Diseases"], "users"=>["Jacco Wallinga", "Janneke C. M Heijne", "Mirjam Kretzschmar"], "doi"=>"https://dx.doi.org/10.1371/journal.pmed.0020316.g001", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Epidemic_Threshold_Concept_/630918", "title"=>"The Epidemic Threshold Concept", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-22 08:53:36"}

PMC Usage Stats | Further Information

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  • {"month"=>"6", "scanned-page-browse"=>"0", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"2", "year"=>"2010", "pdf"=>"4", "unique-ip"=>"5", "figure"=>"0", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"scanned-page-browse"=>"0", "month"=>"7", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"6", "unique-ip"=>"13", "pdf"=>"11", "year"=>"2010", "figure"=>"0", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"month"=>"8", "scanned-page-browse"=>"0", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"2", "year"=>"2010", "pdf"=>"2", "unique-ip"=>"4", "figure"=>"0", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"scanned-page-browse"=>"0", "month"=>"9", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"9", "unique-ip"=>"14", "pdf"=>"11", "year"=>"2010", "figure"=>"0", "scanned-summary"=>"0", "supp-data"=>"0"}
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  • {"scanned-page-browse"=>"0", "month"=>"11", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"11", "unique-ip"=>"14", "pdf"=>"3", "year"=>"2010", "figure"=>"6", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"month"=>"12", "scanned-page-browse"=>"0", "cited-by"=>"0", "abstract"=>"1", "full-text"=>"4", "year"=>"2010", "pdf"=>"0", "unique-ip"=>"5", "figure"=>"2", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"scanned-page-browse"=>"0", "month"=>"1", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"8", "unique-ip"=>"7", "pdf"=>"0", "year"=>"2011", "figure"=>"1", "scanned-summary"=>"0", "supp-data"=>"0"}
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  • {"scanned-page-browse"=>"0", "month"=>"7", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"10", "unique-ip"=>"9", "pdf"=>"3", "year"=>"2011", "figure"=>"1", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"month"=>"8", "scanned-page-browse"=>"0", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"6", "year"=>"2011", "pdf"=>"3", "unique-ip"=>"7", "figure"=>"0", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"scanned-page-browse"=>"0", "month"=>"9", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"12", "unique-ip"=>"11", "pdf"=>"4", "year"=>"2011", "figure"=>"1", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"month"=>"10", "scanned-page-browse"=>"0", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"8", "year"=>"2011", "pdf"=>"0", "unique-ip"=>"9", "figure"=>"1", "scanned-summary"=>"0", "supp-data"=>"0"}
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  • {"scanned-page-browse"=>"0", "month"=>"2", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"4", "unique-ip"=>"6", "pdf"=>"1", "year"=>"2012", "figure"=>"2", "scanned-summary"=>"0", "supp-data"=>"0"}
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  • {"scanned-page-browse"=>"11", "month"=>"12", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"4", "unique-ip"=>"0", "pdf"=>"0", "year"=>"2005", "figure"=>"33", "scanned-summary"=>"18", "supp-data"=>"23"}
  • {"month"=>"1", "scanned-page-browse"=>"5", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "year"=>"2006", "pdf"=>"0", "unique-ip"=>"1", "figure"=>"23", "scanned-summary"=>"17", "supp-data"=>"17"}
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  • {"month"=>"3", "scanned-page-browse"=>"14", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "year"=>"2006", "pdf"=>"0", "unique-ip"=>"2", "figure"=>"41", "scanned-summary"=>"25", "supp-data"=>"26"}
  • {"scanned-page-browse"=>"7", "month"=>"4", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"2", "unique-ip"=>"3", "pdf"=>"0", "year"=>"2006", "figure"=>"38", "scanned-summary"=>"26", "supp-data"=>"22"}
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  • {"scanned-page-browse"=>"3", "month"=>"6", "cited-by"=>"1", "abstract"=>"0", "full-text"=>"1", "unique-ip"=>"1", "pdf"=>"0", "year"=>"2006", "figure"=>"22", "scanned-summary"=>"17", "supp-data"=>"17"}
  • {"month"=>"7", "scanned-page-browse"=>"6", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "year"=>"2006", "pdf"=>"0", "unique-ip"=>"1", "figure"=>"27", "scanned-summary"=>"20", "supp-data"=>"20"}
  • {"scanned-page-browse"=>"4", "month"=>"8", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"1", "unique-ip"=>"0", "pdf"=>"0", "year"=>"2006", "figure"=>"21", "scanned-summary"=>"16", "supp-data"=>"15"}
  • {"month"=>"9", "scanned-page-browse"=>"5", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"1", "year"=>"2006", "pdf"=>"0", "unique-ip"=>"0", "figure"=>"28", "scanned-summary"=>"22", "supp-data"=>"22"}
  • {"scanned-page-browse"=>"7", "month"=>"10", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"1", "unique-ip"=>"3", "pdf"=>"0", "year"=>"2006", "figure"=>"53", "scanned-summary"=>"42", "supp-data"=>"37"}
  • {"month"=>"11", "scanned-page-browse"=>"8", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"1", "year"=>"2006", "pdf"=>"0", "unique-ip"=>"2", "figure"=>"43", "scanned-summary"=>"32", "supp-data"=>"33"}
  • {"scanned-page-browse"=>"7", "month"=>"12", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "unique-ip"=>"0", "pdf"=>"0", "year"=>"2006", "figure"=>"33", "scanned-summary"=>"26", "supp-data"=>"22"}
  • {"month"=>"1", "scanned-page-browse"=>"7", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "year"=>"2007", "pdf"=>"0", "unique-ip"=>"1", "figure"=>"35", "scanned-summary"=>"27", "supp-data"=>"27"}
  • {"scanned-page-browse"=>"8", "month"=>"2", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "unique-ip"=>"1", "pdf"=>"0", "year"=>"2007", "figure"=>"32", "scanned-summary"=>"23", "supp-data"=>"23"}
  • {"month"=>"3", "scanned-page-browse"=>"16", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "year"=>"2007", "pdf"=>"0", "unique-ip"=>"10", "figure"=>"65", "scanned-summary"=>"39", "supp-data"=>"35"}
  • {"scanned-page-browse"=>"6", "month"=>"4", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"0", "unique-ip"=>"1", "pdf"=>"0", "year"=>"2007", "figure"=>"34", "scanned-summary"=>"27", "supp-data"=>"25"}
  • {"month"=>"5", "scanned-page-browse"=>"10", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"1", "year"=>"2007", "pdf"=>"0", "unique-ip"=>"2", "figure"=>"44", "scanned-summary"=>"31", "supp-data"=>"30"}
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Relative Metric

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