An event-based model of superspreading in epidemics
Identifieur interne : 001170 ( Pmc/Checkpoint ); précédent : 001169; suivant : 001171An event-based model of superspreading in epidemics
Auteurs : Alex James [Nouvelle-Zélande] ; Jonathan W. Pitchford [Royaume-Uni] ; Michael J. Plank [Nouvelle-Zélande]Source :
- Proceedings of the Royal Society B: Biological Sciences [ 0962-8452 ] ; 2006.
Abstract
Many recent disease outbreaks (e.g. SARS, foot-and-mouth disease) exhibit superspreading, where relatively few individuals cause a large number of secondary cases. Epidemic models have previously treated this as a demographic phenomenon where each individual has an infectivity allocated at random from some distribution. Here, it is shown that superspreading can also be regarded as being caused by environmental variability, where superspreading events (SSEs) occur as a stochastic consequence of the complex network of interactions made by individuals. This interpretation based on SSEs is compared with data and its efficacy in evaluating epidemic control strategies is discussed.
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DOI: 10.1098/rspb.2006.0219
PubMed: 17255000
PubMed Central: 2197209
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">An event-based model of superspreading in epidemics</title><author><name sortKey="James, Alex" sort="James, Alex" uniqKey="James A" first="Alex" last="James">Alex James</name><affiliation wicri:level="1"><nlm:aff id="aff1"><institution>Department of Mathematics and Statistics, University of Canterbury</institution><addr-line>Christchurch 8140, New Zealand</addr-line></nlm:aff><country xml:lang="fr">Nouvelle-Zélande</country><wicri:regionArea>Christchurch 8140</wicri:regionArea></affiliation></author><author><name sortKey="Pitchford, Jonathan W" sort="Pitchford, Jonathan W" uniqKey="Pitchford J" first="Jonathan W" last="Pitchford">Jonathan W. Pitchford</name><affiliation wicri:level="1"><nlm:aff id="aff2"><institution>Department of Biology and York Centre for Complex Systems Analysis, University of York</institution><addr-line>PO Box 373, York YO10 5YW, UK</addr-line></nlm:aff><country xml:lang="fr">Royaume-Uni</country><wicri:regionArea>PO Box 373, York YO10 5YW</wicri:regionArea><wicri:noRegion>York YO10 5YW</wicri:noRegion></affiliation></author><author><name sortKey="Plank, Michael J" sort="Plank, Michael J" uniqKey="Plank M" first="Michael J" last="Plank">Michael J. Plank</name><affiliation wicri:level="1"><nlm:aff id="aff1"><institution>Department of Mathematics and Statistics, University of Canterbury</institution><addr-line>Christchurch 8140, New Zealand</addr-line></nlm:aff><country xml:lang="fr">Nouvelle-Zélande</country><wicri:regionArea>Christchurch 8140</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">17255000</idno><idno type="pmc">2197209</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2197209</idno><idno type="RBID">PMC:2197209</idno><idno type="doi">10.1098/rspb.2006.0219</idno><date when="2006">2006</date><idno type="wicri:Area/Pmc/Corpus">000D13</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000D13</idno><idno type="wicri:Area/Pmc/Curation">000D13</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">000D13</idno><idno type="wicri:Area/Pmc/Checkpoint">001170</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Checkpoint">001170</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">An event-based model of superspreading in epidemics</title><author><name sortKey="James, Alex" sort="James, Alex" uniqKey="James A" first="Alex" last="James">Alex James</name><affiliation wicri:level="1"><nlm:aff id="aff1"><institution>Department of Mathematics and Statistics, University of Canterbury</institution><addr-line>Christchurch 8140, New Zealand</addr-line></nlm:aff><country xml:lang="fr">Nouvelle-Zélande</country><wicri:regionArea>Christchurch 8140</wicri:regionArea></affiliation></author><author><name sortKey="Pitchford, Jonathan W" sort="Pitchford, Jonathan W" uniqKey="Pitchford J" first="Jonathan W" last="Pitchford">Jonathan W. Pitchford</name><affiliation wicri:level="1"><nlm:aff id="aff2"><institution>Department of Biology and York Centre for Complex Systems Analysis, University of York</institution><addr-line>PO Box 373, York YO10 5YW, UK</addr-line></nlm:aff><country xml:lang="fr">Royaume-Uni</country><wicri:regionArea>PO Box 373, York YO10 5YW</wicri:regionArea><wicri:noRegion>York YO10 5YW</wicri:noRegion></affiliation></author><author><name sortKey="Plank, Michael J" sort="Plank, Michael J" uniqKey="Plank M" first="Michael J" last="Plank">Michael J. Plank</name><affiliation wicri:level="1"><nlm:aff id="aff1"><institution>Department of Mathematics and Statistics, University of Canterbury</institution><addr-line>Christchurch 8140, New Zealand</addr-line></nlm:aff><country xml:lang="fr">Nouvelle-Zélande</country><wicri:regionArea>Christchurch 8140</wicri:regionArea></affiliation></author></analytic><series><title level="j">Proceedings of the Royal Society B: Biological Sciences</title><idno type="ISSN">0962-8452</idno><idno type="eISSN">1471-2954</idno><imprint><date when="2006">2006</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Many recent disease outbreaks (e.g. SARS, foot-and-mouth disease) exhibit superspreading, where relatively few individuals cause a large number of secondary cases. Epidemic models have previously treated this as a demographic phenomenon where each individual has an infectivity allocated at random from some distribution. Here, it is shown that superspreading can also be regarded as being caused by environmental variability, where superspreading events (SSEs) occur as a stochastic consequence of the complex network of interactions made by individuals. This interpretation based on SSEs is compared with data and its efficacy in evaluating epidemic control strategies is discussed.</p></div></front></TEI><pmc article-type="research-article"><pmc-comment>The publisher of this article does not allow downloading of the full text in XML form.</pmc-comment>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Proc Biol Sci</journal-id><journal-id journal-id-type="publisher-id">RSPB</journal-id><journal-title>Proceedings of the Royal Society B: Biological Sciences</journal-title><issn pub-type="ppub">0962-8452</issn><issn pub-type="epub">1471-2954</issn><publisher><publisher-name>The Royal Society</publisher-name><publisher-loc>London</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">17255000</article-id><article-id pub-id-type="pmc">2197209</article-id><article-id pub-id-type="publisher-id">rspb20060219</article-id><article-id pub-id-type="doi">10.1098/rspb.2006.0219</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title>An event-based model of superspreading in epidemics</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>James</surname><given-names>Alex</given-names></name><xref ref-type="aff" rid="aff1">1</xref></contrib><contrib contrib-type="author"><name><surname>Pitchford</surname><given-names>Jonathan W</given-names></name><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="corresp" rid="cor1">*</xref></contrib><contrib contrib-type="author"><name><surname>Plank</surname><given-names>Michael J</given-names></name><xref ref-type="aff" rid="aff1">1</xref></contrib></contrib-group><aff id="aff1"><label>1</label><institution>Department of Mathematics and Statistics, University of Canterbury</institution><addr-line>Christchurch 8140, New Zealand</addr-line></aff><aff id="aff2"><label>2</label><institution>Department of Biology and York Centre for Complex Systems Analysis, University of York</institution><addr-line>PO Box 373, York YO10 5YW, UK</addr-line></aff><author-notes><corresp id="cor1"><label>*</label>Author for correspondence (<email>jwp5@york.ac.uk</email>)</corresp></author-notes><pub-date pub-type="epub"><day>5</day><month>12</month><year>2006</year></pub-date><pub-date pub-type="ppub"><day>07</day><month>3</month><year>2007</year></pub-date><volume>274</volume><issue>1610</issue><fpage>741</fpage><lpage>747</lpage><history><date date-type="received"><day>28</day><month>9</month><year>2006</year></date><date date-type="accepted"><day>9</day><month>11</month><year>2006</year></date></history><permissions><copyright-statement>© 2006 The Royal Society</copyright-statement><copyright-year>2006</copyright-year></permissions><abstract><p>Many recent disease outbreaks (e.g. SARS, foot-and-mouth disease) exhibit superspreading, where relatively few individuals cause a large number of secondary cases. Epidemic models have previously treated this as a demographic phenomenon where each individual has an infectivity allocated at random from some distribution. Here, it is shown that superspreading can also be regarded as being caused by environmental variability, where superspreading events (SSEs) occur as a stochastic consequence of the complex network of interactions made by individuals. This interpretation based on SSEs is compared with data and its efficacy in evaluating epidemic control strategies is discussed.</p></abstract><kwd-group><kwd>superspreading</kwd><kwd>epidemiology</kwd><kwd>branching process</kwd><kwd>environmental stochasticity</kwd></kwd-group></article-meta></front><floats-wrap><fig id="fig1" position="float"><label>Figure 1</label><caption><p>The cumulative percentage of secondary cases caused by the most infectious individuals for a number of disease outbreaks. The vertical line shows the percentage of cases caused by the most infectious 20% of individuals; the horizontal line shows the percentage of individuals responsible for 80% of all infections. For the SARS and FMD outbreaks, the most infectious 20% of individuals caused more than 80% of all infections; for the other disease outbreaks, the most infectious 20% of individuals caused less than 80% of all infections. Abbreviations: before control (b.c.); after control (a.c.).</p></caption><graphic xlink:href="rspb20060219f01"></graphic></fig><fig id="fig2" position="float"><label>Figure 2</label><caption><p>The probability <italic>η</italic> of ultimate extinction (PUE) for different levels of superspreading: (<italic>r</italic>/<italic>R</italic><sub>0</sub>)=1 corresponds to simple Poisson infections (BP1); (<italic>r</italic>/<italic>R</italic><sub>0</sub>)=0 corresponds to spread purely by SSEs. (<italic>a</italic>) PUE against <italic>r</italic>/<italic>R</italic><sub>0</sub> for fixed <italic>R</italic><sub>0</sub> and <italic>λ</italic>=5. (<italic>b</italic>) PUE against <italic>r</italic>/<italic>R</italic><sub>0</sub> and <italic>λ</italic> for fixed <italic>R</italic><sub>0</sub>=2.</p></caption><graphic xlink:href="rspb20060219f02"></graphic></fig><fig id="fig3" position="float"><label>Figure 3</label><caption><p>(<italic>a</italic>) Probability of extinction (<italic>p</italic><sub><italic>n</italic></sub>) against generation number (<italic>n</italic>) for different levels of superspreading. (<italic>b</italic>) Expected trajectory E(<italic>X</italic>) and average observed trajectories for different levels of superspreading. <italic>R</italic><sub>0</sub>=1.1 and <italic>λ</italic>=3.</p></caption><graphic xlink:href="rspb20060219f03"></graphic></fig><fig id="fig4" position="float"><label>Figure 4</label><caption><p>Offspring distributions for the SARS outbreaks before control: (<italic>a</italic>) Singapore, 2003; (<italic>b</italic>) Beijing, 2003. <italic>P</italic>(<italic>Z</italic>) is the probability of an infected individual causing <italic>Z</italic> secondary infections during his/her infectious lifetime, according to data (bars) and the CP and LS models (points). The logarithmic scale highlights the occurrence of rare SSEs (which are all counts of 1 or 2).</p></caption><graphic xlink:href="rspb20060219f04"></graphic></fig><table-wrap id="tbl1" position="float"><label>Table 1</label><caption><p>Maximum log-likelihood estimates of CP parameters <italic>r</italic>, <italic>ρ</italic> and <italic>λ</italic>. (<italic>N</italic> is the total number of infected individuals in the dataset; <italic>R</italic><sub>0</sub> is the average number of secondary cases per infected individual. <inline-formula><inline-graphic xlink:href="rspb20060219e02.jpg" alternate-form-of="M2"></inline-graphic><mml:math id="M2"><mml:mrow><mml:msubsup><mml:mrow><mml:mtext>AIC</mml:mtext></mml:mrow><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> is the modified Akaike information criterion for the best-fit parameter values for model <italic>i</italic>; <italic>K</italic> is the number of parameters associated with each model. The ‘<italic>α</italic> (% SSE)’ column indicates the percentage of infections that are caused by SSEs resulting in two or more cases according to the fitted parameters. Abbreviations: before control (b.c.); after control (a.c.); FMD, foot-and-mouth disease.)</p></caption><table frame="hsides" rules="groups"><tr><th align="left" rowspan="1" colspan="1">outbreak</th><th rowspan="1" colspan="1"><italic>N</italic></th><th rowspan="1" colspan="1"><italic>R</italic><sub>0</sub></th><th rowspan="1" colspan="1"><italic>r</italic></th><th rowspan="1" colspan="1"><italic>ρ</italic></th><th rowspan="1" colspan="1"><italic>λ</italic></th><th rowspan="1" colspan="1"><italic>α</italic> (% SSE)</th><th align="left" rowspan="1" colspan="1">AIC<sub>c</sub><sup>CP</sup><italic>K</italic>=3</th><th align="left" rowspan="1" colspan="1">AIC<sub>c</sub><sup>BP1</sup><italic>K</italic>=1</th><th align="left" rowspan="1" colspan="1">AIC<sub>c</sub><sup>BP2</sup><italic>K</italic>=1</th><th align="left" rowspan="1" colspan="1">AIC<sub>c</sub><sup>LS</sup><italic>K</italic>=2</th><th align="left" rowspan="1" colspan="1">references</th></tr><tr><td rowspan="1" colspan="1">SARS Beijing 2003 b.c.</td><td rowspan="1" colspan="1">34</td><td align="char" rowspan="1" colspan="1">1.88</td><td align="char" rowspan="1" colspan="1">0.41</td><td align="char" rowspan="1" colspan="1">0.12</td><td align="char" rowspan="1" colspan="1">12.0</td><td rowspan="1" colspan="1">78</td><td rowspan="1" colspan="1">110</td><td rowspan="1" colspan="1">281</td><td rowspan="1" colspan="1">129</td><td rowspan="1" colspan="1">97</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib15">Shen <italic>et al</italic>. (2004)</xref></td></tr><tr><td rowspan="1" colspan="1">SARS Beijing 2003 a.c.</td><td rowspan="1" colspan="1">43</td><td align="char" rowspan="1" colspan="1">0.28</td><td align="char" rowspan="1" colspan="1">0.00</td><td align="char" rowspan="1" colspan="1">0.02</td><td align="char" rowspan="1" colspan="1">12.0</td><td rowspan="1" colspan="1">100</td><td rowspan="1" colspan="1">20</td><td rowspan="1" colspan="1">97</td><td rowspan="1" colspan="1">60</td><td rowspan="1" colspan="1">22</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib15">Shen <italic>et al</italic>. (2004)</xref></td></tr><tr><td rowspan="1" colspan="1">SARS Singapore 2003 b.c.</td><td rowspan="1" colspan="1">57</td><td align="char" rowspan="1" colspan="1">1.63</td><td align="char" rowspan="1" colspan="1">0.48</td><td align="char" rowspan="1" colspan="1">0.05</td><td align="char" rowspan="1" colspan="1">21.9</td><td rowspan="1" colspan="1">70</td><td rowspan="1" colspan="1">151</td><td rowspan="1" colspan="1">411</td><td rowspan="1" colspan="1">201</td><td rowspan="1" colspan="1">160</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib9">Leo <italic>et al</italic>. (2003)</xref></td></tr><tr><td rowspan="1" colspan="1">SARS Singapore 2003 a.c.</td><td rowspan="1" colspan="1">114</td><td align="char" rowspan="1" colspan="1">0.68</td><td align="char" rowspan="1" colspan="1">0.22</td><td align="char" rowspan="1" colspan="1">0.03</td><td align="char" rowspan="1" colspan="1">17.2</td><td rowspan="1" colspan="1">67</td><td rowspan="1" colspan="1">187</td><td rowspan="1" colspan="1">491</td><td rowspan="1" colspan="1">260</td><td rowspan="1" colspan="1">178</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib9">Leo <italic>et al</italic>. (2003)</xref></td></tr><tr><td rowspan="1" colspan="1">FMD UK 2001</td><td rowspan="1" colspan="1">78</td><td align="char" rowspan="1" colspan="1">0.99</td><td align="char" rowspan="1" colspan="1">0.33</td><td align="char" rowspan="1" colspan="1">0.06</td><td align="char" rowspan="1" colspan="1">11.2</td><td rowspan="1" colspan="1">67</td><td rowspan="1" colspan="1">181</td><td rowspan="1" colspan="1">380</td><td rowspan="1" colspan="1">217</td><td rowspan="1" colspan="1">169</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib12">Matthews & Woolhouse (2005)</xref></td></tr><tr><td rowspan="1" colspan="1">Measles MA 1984</td><td rowspan="1" colspan="1">27</td><td align="char" rowspan="1" colspan="1">0.89</td><td align="char" rowspan="1" colspan="1">0.29</td><td align="char" rowspan="1" colspan="1">0.38</td><td align="char" rowspan="1" colspan="1">1.59</td><td rowspan="1" colspan="1">32</td><td rowspan="1" colspan="1">77</td><td rowspan="1" colspan="1">79</td><td rowspan="1" colspan="1">73</td><td rowspan="1" colspan="1">75</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib14">Nkowane <italic>et al</italic>. (1987)</xref></td></tr><tr><td rowspan="1" colspan="1">Pneumonic plague 1907–1933</td><td rowspan="1" colspan="1">74</td><td align="char" rowspan="1" colspan="1">1.32</td><td align="char" rowspan="1" colspan="1">0.13</td><td align="char" rowspan="1" colspan="1">1.26</td><td align="char" rowspan="1" colspan="1">0.94</td><td rowspan="1" colspan="1">22</td><td rowspan="1" colspan="1">240</td><td rowspan="1" colspan="1">252</td><td rowspan="1" colspan="1">237</td><td rowspan="1" colspan="1">239</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib7">Gani & Leach (2004)</xref></td></tr><tr><td rowspan="1" colspan="1">Ebola HF Uganda 2000</td><td rowspan="1" colspan="1">13</td><td align="char" rowspan="1" colspan="1">1.50</td><td align="char" rowspan="1" colspan="1">0.00</td><td align="char" rowspan="1" colspan="1">3.18</td><td align="char" rowspan="1" colspan="1">0.48</td><td rowspan="1" colspan="1">8</td><td rowspan="1" colspan="1">51</td><td rowspan="1" colspan="1">45</td><td rowspan="1" colspan="1">47</td><td rowspan="1" colspan="1">48</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib5">Francesconi <italic>et al</italic>. (2003)</xref></td></tr><tr><td rowspan="1" colspan="1">Hantavirus Argentina 1996</td><td rowspan="1" colspan="1">20</td><td align="char" rowspan="1" colspan="1">0.70</td><td align="char" rowspan="1" colspan="1">0.48</td><td align="char" rowspan="1" colspan="1">0.12</td><td align="char" rowspan="1" colspan="1">1.81</td><td rowspan="1" colspan="1">17</td><td rowspan="1" colspan="1">53</td><td rowspan="1" colspan="1">49</td><td rowspan="1" colspan="1">48</td><td rowspan="1" colspan="1">51</td><td rowspan="1" colspan="1"><xref ref-type="bibr" rid="bib16">Wells <italic>et al</italic>. (1997)</xref></td></tr></table></table-wrap></floats-wrap></pmc><affiliations><list><country><li>Nouvelle-Zélande</li><li>Royaume-Uni</li></country></list><tree><country name="Nouvelle-Zélande"><noRegion><name sortKey="James, Alex" sort="James, Alex" uniqKey="James A" first="Alex" last="James">Alex James</name></noRegion><name sortKey="Plank, Michael J" sort="Plank, Michael J" uniqKey="Plank M" first="Michael J" last="Plank">Michael J. Plank</name></country><country name="Royaume-Uni"><noRegion><name sortKey="Pitchford, Jonathan W" sort="Pitchford, Jonathan W" uniqKey="Pitchford J" first="Jonathan W" last="Pitchford">Jonathan W. Pitchford</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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