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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Superspreading and the effect of individual variation on disease emergence</title><author><name sortKey="Lloyd Smith, J O" sort="Lloyd Smith, J O" uniqKey="Lloyd Smith J" first="J. O." last="Lloyd-Smith">J. O. Lloyd-Smith</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Department of Environmental Science,</institution><institution>Policy and Management, University of California,</institution></institution-wrap>140 Mulford Hall, California 94720-3114 Berkeley, USA</nlm:aff></affiliation><affiliation><nlm:aff id="Aff2"><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Biophysics Graduate Group,</institution><institution>University of California,</institution></institution-wrap>California 94720-3200 Berkeley, USA</nlm:aff></affiliation></author><author><name sortKey="Schreiber, S J" sort="Schreiber, S J" uniqKey="Schreiber S" first="S. J." last="Schreiber">S. J. Schreiber</name><affiliation><nlm:aff id="Aff3"><institution-wrap><institution-id institution-id-type="GRID">grid.264889.9</institution-id><institution-id institution-id-type="ISNI">0000 0001 1940 3051</institution-id><institution>Department of Mathematics,</institution><institution>The College of William and Mary,</institution></institution-wrap>Virginia 23187-8975 Williamsburg, USA</nlm:aff></affiliation></author><author><name sortKey="Kopp, P E" sort="Kopp, P E" uniqKey="Kopp P" first="P. E." last="Kopp">P. E. Kopp</name><affiliation><nlm:aff id="Aff4"><institution-wrap><institution-id institution-id-type="GRID">grid.9481.4</institution-id><institution-id institution-id-type="ISNI">0000 0004 0412 8669</institution-id><institution>Centre for Mathematics,</institution><institution>University of Hull,</institution></institution-wrap>HU6 7RX Hull, UK</nlm:aff></affiliation></author><author><name sortKey="Getz, W M" sort="Getz, W M" uniqKey="Getz W" first="W. M." last="Getz">W. M. Getz</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Department of Environmental Science,</institution><institution>Policy and Management, University of California,</institution></institution-wrap>140 Mulford Hall, California 94720-3114 Berkeley, USA</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">16292310</idno><idno type="pmc">7094981</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7094981</idno><idno type="RBID">PMC:7094981</idno><idno type="doi">10.1038/nature04153</idno><date when="2005">2005</date><idno type="wicri:Area/Pmc/Corpus">000449</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000449</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Superspreading and the effect of individual variation on disease emergence</title><author><name sortKey="Lloyd Smith, J O" sort="Lloyd Smith, J O" uniqKey="Lloyd Smith J" first="J. O." last="Lloyd-Smith">J. O. Lloyd-Smith</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Department of Environmental Science,</institution><institution>Policy and Management, University of California,</institution></institution-wrap>140 Mulford Hall, California 94720-3114 Berkeley, USA</nlm:aff></affiliation><affiliation><nlm:aff id="Aff2"><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Biophysics Graduate Group,</institution><institution>University of California,</institution></institution-wrap>California 94720-3200 Berkeley, USA</nlm:aff></affiliation></author><author><name sortKey="Schreiber, S J" sort="Schreiber, S J" uniqKey="Schreiber S" first="S. J." last="Schreiber">S. J. Schreiber</name><affiliation><nlm:aff id="Aff3"><institution-wrap><institution-id institution-id-type="GRID">grid.264889.9</institution-id><institution-id institution-id-type="ISNI">0000 0001 1940 3051</institution-id><institution>Department of Mathematics,</institution><institution>The College of William and Mary,</institution></institution-wrap>Virginia 23187-8975 Williamsburg, USA</nlm:aff></affiliation></author><author><name sortKey="Kopp, P E" sort="Kopp, P E" uniqKey="Kopp P" first="P. E." last="Kopp">P. E. Kopp</name><affiliation><nlm:aff id="Aff4"><institution-wrap><institution-id institution-id-type="GRID">grid.9481.4</institution-id><institution-id institution-id-type="ISNI">0000 0004 0412 8669</institution-id><institution>Centre for Mathematics,</institution><institution>University of Hull,</institution></institution-wrap>HU6 7RX Hull, UK</nlm:aff></affiliation></author><author><name sortKey="Getz, W M" sort="Getz, W M" uniqKey="Getz W" first="W. M." last="Getz">W. M. Getz</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Department of Environmental Science,</institution><institution>Policy and Management, University of California,</institution></institution-wrap>140 Mulford Hall, California 94720-3114 Berkeley, USA</nlm:aff></affiliation></author></analytic><series><title level="j">Nature</title><idno type="ISSN">0028-0836</idno><idno type="eISSN">1476-4687</idno><imprint><date when="2005">2005</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><title>Coughs and sneezes...</title><p id="Par1">From Typhoid Mary to SARS, it has long been known that some people spread disease more than others. But for diseases transmitted via casual contact, contagiousness arises from a plethora of social and physiological factors, so epidemiologists have tended to rely on population averages to assess a disease's potential to spread. A new analysis of outbreak data shows that individual differences in infectiousness exert powerful influences on the epidemiology of ten deadly diseases. SARS and measles (and perhaps avian influenza) show strong tendencies towards ‘superspreading events’ that can ignite explosive epidemics — but this same volatility makes outbreaks more likely to fizzle out. Smallpox and pneumonic plague, two potential bioterrorism agents, show steadier growth but still differ markedly from the traditional average-based view. These findings are relevant to how emerging diseases are detected and controlled.</p><sec><title>Supplementary information</title><p>The online version of this article (doi:10.1038/nature04153) contains supplementary material, which is available to authorized users.</p></sec></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Levin, Sa" uniqKey="Levin S">SA Levin</name></author><author><name sortKey="Grenfell, B" uniqKey="Grenfell B">B Grenfell</name></author><author><name sortKey="Hastings, A" uniqKey="Hastings A">A Hastings</name></author><author><name sortKey="Perelson, As" uniqKey="Perelson A">AS Perelson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Becker, Ng" uniqKey="Becker N">NG Becker</name></author><author><name sortKey="Britton, T" uniqKey="Britton T">T Britton</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Anderson, Rm" uniqKey="Anderson R">RM Anderson</name></author><author><name sortKey="May, Rm" uniqKey="May R">RM May</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Diekmann, O" uniqKey="Diekmann O">O Diekmann</name></author><author><name sortKey="Heesterbeek, Jap" uniqKey="Heesterbeek J">JAP Heesterbeek</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Leo, Ys" uniqKey="Leo Y">YS Leo</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Shen, Z" uniqKey="Shen Z">Z Shen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Dye, C" uniqKey="Dye C">C Dye</name></author><author><name sortKey="Gay, N" uniqKey="Gay N">N Gay</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lipsitch, M" uniqKey="Lipsitch M">M Lipsitch</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Riley, S" uniqKey="Riley S">S Riley</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bauch, Ct" uniqKey="Bauch C">CT Bauch</name></author><author><name sortKey="Lloyd Smith, Jo" uniqKey="Lloyd Smith J">JO Lloyd-Smith</name></author><author><name sortKey="Coffee, M" uniqKey="Coffee M">M Coffee</name></author><author><name sortKey="Galvani, Ap" uniqKey="Galvani A">AP Galvani</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Koopman, J" uniqKey="Koopman J">J Koopman</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="May, Rm" uniqKey="May R">RM May</name></author><author><name sortKey="Anderson, Rm" uniqKey="Anderson R">RM Anderson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Woolhouse, Mej" uniqKey="Woolhouse M">MEJ Woolhouse</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lloyd Smith, Jo" uniqKey="Lloyd Smith J">JO Lloyd-Smith</name></author><author><name sortKey="Getz, Wm" uniqKey="Getz W">WM Getz</name></author><author><name sortKey="Westerhoff, Hv" uniqKey="Westerhoff H">HV Westerhoff</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Anderson, Rm" uniqKey="Anderson R">RM Anderson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Gani, R" uniqKey="Gani R">R Gani</name></author><author><name sortKey="Leach, S" uniqKey="Leach S">S Leach</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Becker, N" uniqKey="Becker N">N Becker</name></author><author><name sortKey="Marschner, I" uniqKey="Marschner I">I Marschner</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Becker, N" uniqKey="Becker N">N Becker</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bailey, Ntj" uniqKey="Bailey N">NTJ Bailey</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Keeling, Mj" uniqKey="Keeling M">MJ Keeling</name></author><author><name sortKey="Grenfell, Bt" uniqKey="Grenfell B">BT Grenfell</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lloyd, Al" uniqKey="Lloyd A">AL Lloyd</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Meyers, La" uniqKey="Meyers L">LA Meyers</name></author><author><name sortKey="Pourbohloul, B" uniqKey="Pourbohloul B">B Pourbohloul</name></author><author><name sortKey="Newman, Mej" uniqKey="Newman M">MEJ Newman</name></author><author><name sortKey="Skowronski, Dm" uniqKey="Skowronski D">DM Skowronski</name></author><author><name sortKey="Brunham, Rc" uniqKey="Brunham R">RC Brunham</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Boswell, Mt" uniqKey="Boswell M">MT Boswell</name></author><author><name sortKey="Patil, Gp" uniqKey="Patil G">GP Patil</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Burnham, Kp" uniqKey="Burnham K">KP Burnham</name></author><author><name sortKey="Anderson, Dr" uniqKey="Anderson D">DR Anderson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lloyd Smith, Jo" uniqKey="Lloyd Smith J">JO Lloyd-Smith</name></author><author><name sortKey="Galvani, Ap" uniqKey="Galvani A">AP Galvani</name></author><author><name sortKey="Getz, Wm" uniqKey="Getz W">WM Getz</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wallinga, J" uniqKey="Wallinga J">J Wallinga</name></author><author><name sortKey="Teunis, P" uniqKey="Teunis P">P Teunis</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ha, Ld" uniqKey="Ha L">LD Ha</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Park, Bj" uniqKey="Park B">BJ Park</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ferguson, Nm" uniqKey="Ferguson N">NM Ferguson</name></author><author><name sortKey="Fraser, C" uniqKey="Fraser C">C Fraser</name></author><author><name sortKey="Donnelly, Ca" uniqKey="Donnelly C">CA Donnelly</name></author><author><name sortKey="Ghani, Ac" uniqKey="Ghani A">AC Ghani</name></author><author><name sortKey="Anderson, Rm" uniqKey="Anderson R">RM Anderson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Farrington, Cp" uniqKey="Farrington C">CP Farrington</name></author><author><name sortKey="Kanaan, Mn" uniqKey="Kanaan M">MN Kanaan</name></author><author><name sortKey="Gay, Nj" uniqKey="Gay N">NJ Gay</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Nature</journal-id><journal-id journal-id-type="iso-abbrev">Nature</journal-id><journal-title-group><journal-title>Nature</journal-title></journal-title-group><issn pub-type="ppub">0028-0836</issn><issn pub-type="epub">1476-4687</issn><publisher><publisher-name>Nature Publishing Group UK</publisher-name><publisher-loc>London</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">16292310</article-id><article-id pub-id-type="pmc">7094981</article-id><article-id pub-id-type="publisher-id">BFnature04153</article-id><article-id pub-id-type="doi">10.1038/nature04153</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Superspreading and the effect of individual variation on disease emergence</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name><surname>Lloyd-Smith</surname><given-names>J. O.</given-names></name><address><email>jls@nature.berkeley.edu</email></address><xref ref-type="aff" rid="Aff1">1</xref><xref ref-type="aff" rid="Aff2">2</xref></contrib><contrib contrib-type="author"><name><surname>Schreiber</surname><given-names>S. J.</given-names></name><xref ref-type="aff" rid="Aff3">3</xref></contrib><contrib contrib-type="author"><name><surname>Kopp</surname><given-names>P. E.</given-names></name><xref ref-type="aff" rid="Aff4">4</xref></contrib><contrib contrib-type="author"><name><surname>Getz</surname><given-names>W. M.</given-names></name><xref ref-type="aff" rid="Aff1">1</xref></contrib><aff id="Aff1"><label>1</label><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Department of Environmental Science,</institution><institution>Policy and Management, University of California,</institution></institution-wrap>140 Mulford Hall, California 94720-3114 Berkeley, USA</aff><aff id="Aff2"><label>2</label><institution-wrap><institution-id institution-id-type="GRID">grid.47840.3f</institution-id><institution-id institution-id-type="ISNI">0000 0001 2181 7878</institution-id><institution>Biophysics Graduate Group,</institution><institution>University of California,</institution></institution-wrap>California 94720-3200 Berkeley, USA</aff><aff id="Aff3"><label>3</label><institution-wrap><institution-id institution-id-type="GRID">grid.264889.9</institution-id><institution-id institution-id-type="ISNI">0000 0001 1940 3051</institution-id><institution>Department of Mathematics,</institution><institution>The College of William and Mary,</institution></institution-wrap>Virginia 23187-8975 Williamsburg, USA</aff><aff id="Aff4"><label>4</label><institution-wrap><institution-id institution-id-type="GRID">grid.9481.4</institution-id><institution-id institution-id-type="ISNI">0000 0004 0412 8669</institution-id><institution>Centre for Mathematics,</institution><institution>University of Hull,</institution></institution-wrap>HU6 7RX Hull, UK</aff></contrib-group><pub-date pub-type="ppub"><year>2005</year></pub-date><volume>438</volume><issue>7066</issue><fpage>355</fpage><lpage>359</lpage><history><date date-type="received"><day>1</day><month>3</month><year>2005</year></date><date date-type="accepted"><day>22</day><month>8</month><year>2005</year></date></history><permissions><copyright-statement>© Nature Publishing Group 2005</copyright-statement><license><license-p>This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.</license-p></license></permissions><abstract id="Abs1" abstract-type="LongSummary"><title>Coughs and sneezes...</title><p id="Par1">From Typhoid Mary to SARS, it has long been known that some people spread disease more than others. But for diseases transmitted via casual contact, contagiousness arises from a plethora of social and physiological factors, so epidemiologists have tended to rely on population averages to assess a disease's potential to spread. A new analysis of outbreak data shows that individual differences in infectiousness exert powerful influences on the epidemiology of ten deadly diseases. SARS and measles (and perhaps avian influenza) show strong tendencies towards ‘superspreading events’ that can ignite explosive epidemics — but this same volatility makes outbreaks more likely to fizzle out. Smallpox and pneumonic plague, two potential bioterrorism agents, show steadier growth but still differ markedly from the traditional average-based view. These findings are relevant to how emerging diseases are detected and controlled.</p><sec><title>Supplementary information</title><p>The online version of this article (doi:10.1038/nature04153) contains supplementary material, which is available to authorized users.</p></sec></abstract><abstract id="Abs2"><p id="Par2">Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups<sup><xref ref-type="bibr" rid="CR1">1</xref>,<xref ref-type="bibr" rid="CR2">2</xref></sup>. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, <italic>R</italic><sub>0</sub>, which is defined as the mean number of infections caused by an infected individual in a susceptible population<sup><xref ref-type="bibr" rid="CR3">3</xref>,<xref ref-type="bibr" rid="CR4">4</xref></sup>. Population estimates of <italic>R</italic><sub>0</sub> can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous ‘superspreading events’ in which certain individuals infected unusually large numbers of secondary cases<sup><xref ref-type="bibr" rid="CR5">5</xref>,<xref ref-type="bibr" rid="CR6">6</xref>,<xref ref-type="bibr" rid="CR7">7</xref>,<xref ref-type="bibr" rid="CR8">8</xref>,<xref ref-type="bibr" rid="CR9">9</xref>,<xref ref-type="bibr" rid="CR10">10</xref></sup>. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear<sup><xref ref-type="bibr" rid="CR2">2</xref>,<xref ref-type="bibr" rid="CR10">10</xref>,<xref ref-type="bibr" rid="CR11">11</xref></sup>. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around <italic>R</italic><sub>0</sub> is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.</p><sec><title>Supplementary information</title><p>The online version of this article (doi:10.1038/nature04153) contains supplementary material, which is available to authorized users.</p></sec></abstract><custom-meta-group><custom-meta><meta-name>issue-copyright-statement</meta-name><meta-value>© Springer Nature Limited 2005</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="Sec1"><title>Main</title><p id="Par3">For sexually transmitted and vector-borne diseases, host contact rates have long served as surrogates for individual infectiousness<sup><xref ref-type="bibr" rid="CR3">3</xref>,<xref ref-type="bibr" rid="CR12">12</xref>,<xref ref-type="bibr" rid="CR13">13</xref>,<xref ref-type="bibr" rid="CR14">14</xref></sup>, leading to the assertion of a general ‘20/80 rule’ (whereby 20% of cases cause 80% of transmission<sup><xref ref-type="bibr" rid="CR13">13</xref></sup>) and to the influential concept of high-risk ‘core groups’<sup><xref ref-type="bibr" rid="CR3">3</xref>,<xref ref-type="bibr" rid="CR12">12</xref>,<xref ref-type="bibr" rid="CR13">13</xref></sup>. For directly transmitted infections, however, the overall infectiousness of each case—that is, the number of other individuals infected during the infectious lifetime of a single individual—arises from a complex mixture of host, pathogen and environmental factors (see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>). Consequently, the degree of infectiousness is distributed continuously in any population<sup><xref ref-type="bibr" rid="CR4">4</xref>,<xref ref-type="bibr" rid="CR7">7</xref>,<xref ref-type="bibr" rid="CR11">11</xref>,<xref ref-type="bibr" rid="CR15">15</xref>,<xref ref-type="bibr" rid="CR16">16</xref></sup> and, crucially, distinct risk groups often cannot be defined <italic>a priori</italic><sup><xref ref-type="bibr" rid="CR2">2</xref>,<xref ref-type="bibr" rid="CR11">11</xref></sup>. This impedes the conventional approach to adding heterogeneity to epidemic models, in which populations are divided into homogeneous subgroups<sup><xref ref-type="bibr" rid="CR2">2</xref>,<xref ref-type="bibr" rid="CR3">3</xref>,<xref ref-type="bibr" rid="CR4">4</xref>,<xref ref-type="bibr" rid="CR17">17</xref></sup>. Research on continuous individual variation in infectiousness for directly transmitted infections has been largely restricted to within-household transmission<sup><xref ref-type="bibr" rid="CR18">18</xref>,<xref ref-type="bibr" rid="CR19">19</xref></sup>, or to variation in infectious period<sup><xref ref-type="bibr" rid="CR20">20</xref>,<xref ref-type="bibr" rid="CR21">21</xref></sup> or social network<sup><xref ref-type="bibr" rid="CR22">22</xref></sup>. Some recent studies have used contact tracing data to investigate specific questions in light of observed variation<sup><xref ref-type="bibr" rid="CR8">8</xref>,<xref ref-type="bibr" rid="CR16">16</xref></sup>, but a broad understanding of the role of individual variation in outbreak dynamics is lacking.</p><p id="Par4">As a theoretical basis, we introduce the ‘individual reproductive number’, <italic>ν</italic>, as a random variable representing the expected number of secondary cases caused by a particular infected individual. Values for <italic>ν</italic> are drawn from a continuous probability distribution with population mean <italic>R</italic><sub>0</sub> that encodes all variation in infectious histories of individuals, including properties of the host and pathogen and environmental circumstances. In this framework, superspreading events (SSEs) are not exceptional events<sup><xref ref-type="bibr" rid="CR9">9</xref></sup>, but important realizations from the right-hand tail of a distribution of <italic>ν</italic> (refs <xref ref-type="bibr" rid="CR7">7</xref>, <xref ref-type="bibr" rid="CR15">15</xref>). Stochastic effects in transmission are modelled using a Poisson process<sup><xref ref-type="bibr" rid="CR4">4</xref></sup>, so that the number of secondary infections caused by each case, <italic>Z</italic>, is described by an ‘offspring distribution’ Pr(<italic>Z</italic> = <italic>k</italic>) where <italic>Z</italic>∼Poisson(<italic>ν</italic>).</p><p id="Par5">By considering three possible distributions of <italic>ν</italic>, we generate three candidate models for the offspring distribution: (1) in generation-based models neglecting individual variation, <italic>ν</italic> = <italic>R</italic><sub>0</sub> for all cases, yielding <italic>Z</italic>∼Poisson(<italic>R</italic><sub>0</sub>); (2) in differential-equation models with homogeneous transmission and constant recovery rates, <italic>ν</italic> is exponentially distributed, yielding <italic>Z</italic>∼geometric(<italic>R</italic><sub>0</sub>); (3) in a more general formulation, we let <italic>ν</italic> be gamma-distributed with mean <italic>R</italic><sub>0</sub> and dispersion parameter <italic>k</italic>, yielding <italic>Z</italic>∼negative binomial(<italic>R</italic><sub>0</sub>,<italic>k</italic>) (ref. <xref ref-type="bibr" rid="CR23">23</xref>). The negative binomial model includes the conventional Poisson (<italic>k</italic> → ∞) and geometric (<italic>k</italic> = 1) models as special cases. It has variance <italic>R</italic><sub>0</sub>(1 + <italic>R</italic><sub>0</sub>/<italic>k</italic>), so smaller values of <italic>k</italic> indicate greater heterogeneity.</p><p id="Par6">We gathered empirical offspring distributions from detailed contact tracing or surveillance data sets, and challenged the candidate models using model selection techniques<sup><xref ref-type="bibr" rid="CR24">24</xref></sup> (see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>). For SARS outbreaks in Singapore and Beijing, the negative binomial model is unequivocally favoured (<xref rid="Fig1" ref-type="fig">Fig. 1a</xref> and <xref rid="MOESM1" ref-type="media">Supplementary Table 1</xref>). Conventional models assuming homogeneity cannot reproduce the observed transmission patterns. For the Singapore outbreak, the maximum-likelihood estimate <italic>k̂</italic> is 0.16 (90% confidence interval 0.11–0.64), indicating an underlying distribution of <italic>ν</italic> that is highly overdispersed (<xref rid="Fig1" ref-type="fig">Fig. 1a</xref>, inset). According to this analysis, the great majority of SARS cases in Singapore were barely infectious (73% had <italic>ν</italic> < 1) but a small proportion were highly infectious (6% had <italic>ν</italic> > 8). This is consistent with field reports from SARS-afflicted regions<sup><xref ref-type="bibr" rid="CR5">5</xref>,<xref ref-type="bibr" rid="CR6">6</xref></sup> but contrasts with published SARS models<sup><xref ref-type="bibr" rid="CR9">9</xref>,<xref ref-type="bibr" rid="CR10">10</xref>,<xref ref-type="bibr" rid="CR25">25</xref>,<xref ref-type="bibr" rid="CR26">26</xref></sup>.<fig id="Fig1"><label>Figure 1</label><caption><title><bold>Evidence for variation in individual reproductive number </bold><bold><italic>ν</italic></bold>.</title><p><bold>a</bold>, Transmission data from the SARS outbreak in Singapore in 2003 (ref. 5). Bars show observed frequency of <italic>Z</italic>, the number of individuals infected by each case. Lines show maximum-likelihood fits for <italic>Z</italic>∼Poisson (squares), <italic>Z</italic>∼geometric (triangles), and <italic>Z</italic>∼negative binomial (circles). Inset, probability density function (solid) and cumulative distribution function (dashed) for gamma-distributed <italic>ν</italic> (corresponding to <italic>Z</italic>∼negative binomial) estimated from Singapore SARS data. <bold>b</bold>, Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all <italic>ν</italic> = <italic>R</italic><sub>0</sub>), this relation is linear. For five directly transmitted infections (based on <italic>k̂</italic> values in Supplementary Table 1), the line is concave owing to variation in <italic>ν</italic>. <bold>c</bold>, Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population. <bold>d</bold>, Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number <italic>R</italic> (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of <italic>Z</italic>∼Poisson(<italic>R</italic>), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. <italic>R</italic> is not shown for ‘other’ diseases, and is off-scale for monkeypox. See Supplementary Notes for details.</p></caption><graphic xlink:href="41586_2005_Article_BFnature04153_Fig1_HTML" id="d29e665"></graphic></fig></p><p id="Par7">Comparing results for eight directly transmitted infections reveals the differing degree of individual variation among diseases and outbreak settings (<xref rid="Fig1" ref-type="fig">Fig. 1b</xref>, <xref rid="Fig1" ref-type="fig">c</xref> and <xref rid="MOESM1" ref-type="media">Supplementary Tables 1, 2</xref>). The Poisson offspring distribution is almost always strongly rejected. The geometric model has considerable support for several data sets, which indicates significant individual variation in transmission rates because real infectious periods are less dispersed than the exponential distribution<sup><xref ref-type="bibr" rid="CR20">20</xref>,<xref ref-type="bibr" rid="CR21">21</xref></sup>. The negative binomial model is selected decisively for several data sets, and enables comparative study of diseases through the dispersion parameter. Like SARS, measles in highly vaccinated populations shows high variation in two surveillance data sets, with narrow confidence intervals excluding the conventional models (note that heterogeneous vaccination coverage is an important environmental factor contributing to this pattern). Monkeypox and smallpox viruses show intermediate variation, consistent across multiple data sets, and pneumonic plague transmission is slightly less variable. Data limitations prevent definitive conclusions for other diseases. Comparing our findings to the 20/80 rule proposed for sexually transmitted and vector-borne diseases<sup><xref ref-type="bibr" rid="CR13">13</xref></sup>, no general rule emerges but the core principle of heterogeneous transmission is certainly supported (<xref rid="Fig1" ref-type="fig">Fig. 1c</xref>).</p><p id="Par8">Numerous reports of superspreading events provide further evidence for variation in <italic>ν</italic>. We reviewed 37 published accounts of SSEs for 11 directly transmitted infections (<xref rid="Fig1" ref-type="fig">Fig. 1d</xref>; see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>). Unrecognized or misdiagnosed illness is the most common cause of these SSEs, followed by alternative modes of spread (especially airborne), high contact rates, and co-infections that aid transmission. High pathogen load or shedding rates are occasionally implicated, but are rarely measured. A consistent and general definition of SSEs is currently lacking—for SARS, an SSE has been arbitrarily defined as <italic>Z</italic> ≥ 8 (ref. <xref ref-type="bibr" rid="CR6">6</xref>), <italic>Z</italic> ≥ 10 (ref. <xref ref-type="bibr" rid="CR5">5</xref>), <italic>Z</italic> > 10 (ref. <xref ref-type="bibr" rid="CR26">26</xref>) or ‘many more than the average number’<sup><xref ref-type="bibr" rid="CR9">9</xref></sup>, and different thresholds are surely needed for measles (<italic>R</italic><sub>0</sub>∼11–18; ref. <xref ref-type="bibr" rid="CR3">3</xref>) or monkeypox (<italic>R</italic><sub>0</sub> < 1).</p><p id="Par9">We propose this general protocol for defining a superspreading event: (1) estimate the effective reproductive number, <italic>R</italic>, for the disease and population in question; (2) construct a Poisson distribution with mean <italic>R</italic>, representing the expected range of <italic>Z</italic> due to stochasticity without individual variation; (3) define an SSE as any infected individual who infects more than <italic>Z</italic><sup>(<italic>n</italic>)</sup> others, where <italic>Z</italic><sup>(<italic>n</italic>)</sup> is the <italic>n</italic>th percentile of the Poisson(<italic>R</italic>) distribution. A 99th-percentile SSE is then any case causing more infections than would occur in 99% of infectious histories in a homogeneous population (<xref rid="Fig1" ref-type="fig">Fig. 1d</xref>). This approach complements <italic>a priori</italic> identification of potential superspreaders when that is feasible, as for sexually transmitted diseases (where promiscuity drives risk)<sup><xref ref-type="bibr" rid="CR3">3</xref>,<xref ref-type="bibr" rid="CR12">12</xref></sup>. In addition, the definition enables prediction of the frequency of SSEs once <italic>R</italic><sub>0</sub> and <italic>k</italic> have been estimated (<xref rid="MOESM1" ref-type="media">Supplementary Fig. 1</xref>)—an outstanding challenge in emerging disease epidemiology<sup><xref ref-type="bibr" rid="CR8">8</xref>,<xref ref-type="bibr" rid="CR9">9</xref></sup>.</p><p id="Par10">To assess the effect of individual variation on disease outbreaks, we analyse a branching process model with negative binomial offspring distribution, corresponding to gamma-distributed <italic>ν</italic> (<xref rid="Fig2" ref-type="fig">Fig. 2a</xref>; see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>). Of primary interest is the probability of stochastic extinction, <italic>q</italic>, after the introduction of a single infected individual (<xref rid="Fig2" ref-type="fig">Fig. 2b</xref>). For <italic>R</italic><sub>0</sub> < 1, all invasions die out, as in standard models. For <italic>R</italic><sub>0</sub> > 1, increased variation strongly favours extinction<sup><xref ref-type="bibr" rid="CR8">8</xref></sup>. For example, if <italic>R</italic><sub>0</sub> = 3 then <italic>q</italic> = 0.06 under the assumption of homogeneous <italic>ν</italic> (<italic>k</italic> → ∞), or <italic>q</italic> = 0.33 if <italic>k</italic> = 1, but if <italic>k</italic> = 0.16 (as estimated for SARS) then <italic>q</italic> = 0.76. Extinction risk rises owing to a higher proportion of non-transmitting cases when <italic>ν</italic> is overdispersed (<xref rid="Fig1" ref-type="fig">Figs 1a</xref>, <xref rid="Fig2" ref-type="fig">2a</xref> and <xref rid="MOESM1" ref-type="media">Supplementary Fig. 2a</xref>). This effect thwarts invasion by diseases that are very potent spreaders on average: for arbitrarily high <italic>R</italic><sub>0</sub>, <italic>q</italic> → 1 as <italic>k</italic> → 0 (<xref rid="MOESM1" ref-type="media">Supplementary Fig. 2b</xref>). The expected number of cases before extinction is hardly affected by <italic>k</italic> (<xref rid="MOESM1" ref-type="media">Supplementary Fig. 2c</xref>), because low-<italic>k</italic> outbreaks that fail probably lacked SSEs and thus resemble homogeneous outbreaks with lower <italic>R</italic><sub>0</sub>. Accordingly, when individual variation is large, extinction occurs rapidly or not at all (<xref rid="MOESM1" ref-type="media">Supplementary Fig. 2d</xref>).<fig id="Fig2"><label>Figure 2</label><caption><title><bold>Outbreak dynamics with different degrees of individual variation in infectiousness.</bold></title><p><bold>a</bold>, The individual reproductive number <italic>ν</italic> is drawn from a gamma distribution with mean <italic>R</italic><sub>0</sub> and dispersion parameter <italic>k</italic>. Probability density functions are shown for six gamma distributions with <italic>R</italic><sub>0</sub> = 1.5 (‘<italic>k</italic> = Inf’ indicates <italic>k</italic> → ∞). <bold>b</bold>, Probability of stochastic extinction of an outbreak, <italic>q</italic>, versus population-average reproductive number, <italic>R</italic><sub>0</sub>, following introduction of a single infected individual. The value of <italic>k</italic> increases from top to bottom (values and colours as in <bold>a</bold>). <bold>c</bold>, Growth of simulated outbreaks with <italic>R</italic><sub>0</sub> = 1.5 and one initial case, conditional on non-extinction. Boxes show median and interquartile range (IQR) of the first disease generation with 100 cases; whiskers show most extreme values within 1.5 × IQR of the boxes, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold (roughly 1 - <italic>q</italic>).</p></caption><graphic xlink:href="41586_2005_Article_BFnature04153_Fig2_HTML" id="d29e976"></graphic></fig></p><p id="Par11">For outbreaks avoiding stochastic extinction, epidemic growth rates strongly depend on variation in <italic>ν</italic> (<xref rid="Fig2" ref-type="fig">Fig. 2c</xref> and <xref rid="MOESM1" ref-type="media">Supplementary Fig. 2e, f</xref>). Diseases with high individual variation show infrequent but explosive epidemics after introduction of a single case. This pattern recalls SARS in 2003, for which many settings experienced no epidemic despite unprotected exposure to SARS cases<sup><xref ref-type="bibr" rid="CR27">27</xref>,<xref ref-type="bibr" rid="CR28">28</xref></sup>, whereas a few cities suffered explosive outbreaks<sup><xref ref-type="bibr" rid="CR8">8</xref>,<xref ref-type="bibr" rid="CR9">9</xref>,<xref ref-type="bibr" rid="CR10">10</xref>,<xref ref-type="bibr" rid="CR15">15</xref>,<xref ref-type="bibr" rid="CR26">26</xref></sup>. Our results, using <italic>k̂</italic> = 0.16 for SARS, explain this simply by the presence or absence of high-<italic>ν</italic> individuals in the early generations of each outbreak<sup><xref ref-type="bibr" rid="CR6">6</xref></sup>. In contrast, conventional models (with <italic>k</italic> = 1 or <italic>k</italic> → ∞) cannot simultaneously generate frequent failed invasions and rapid growth rates without additional, subjective model structure.</p><p id="Par12">Disease control interventions could increase or decrease individual variation in infectiousness. Infected individuals might reduce their number of non-essential contacts, or governments might impose quarantine or isolation on particular individuals. Here we explore several idealized cases theoretically, for an outbreak with offspring distribution <italic>Z</italic>∼negative binomial(<italic>R</italic><sub>0</sub>,<italic>k</italic>) before control (see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>). Consider the effect of control effort <italic>c</italic>, where <italic>c</italic> = 0 reflects no control and <italic>c</italic> = 1 reflects complete blockage of transmission. Under population-wide control, the infectiousness of every individual in the population is reduced by a factor <italic>c</italic> (that is, <inline-formula id="IEq1"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq1_HTML.gif"></inline-graphic></inline-formula> for all individuals). Under random, individual-specific control, a proportion <italic>c</italic> of infected individuals (chosen at random) is traced and isolated completely such that they cause zero infections (that is <inline-formula id="IEq2"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq2_HTML.gif"></inline-graphic></inline-formula> for a proportion <italic>c</italic> of infected individuals, and <inline-formula id="IEq3"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq3_HTML.gif"></inline-graphic></inline-formula> for the rest). Individual-specific control raises the degree of heterogeneity in the outbreak as measured by the variance-to-mean ratio of <italic>Z</italic>, whereas population-wide control reduces heterogeneity. Both approaches yield effective reproductive number <italic>R</italic> = (1 - <italic>c</italic>)<italic>R</italic><sub>0</sub>, so the threshold control effort for guaranteed disease extinction is <italic>c</italic> ≥ 1 - 1/<italic>R</italic><sub>0</sub> as in conventional models. For intermediate values of <italic>c</italic>, however, the individual-specific approach always works better (<xref rid="Fig3" ref-type="fig">Fig. 3a</xref> and <xref rid="MOESM1" ref-type="media">Supplementary Fig. 3a, b</xref>), consistent with our finding that higher variation favours disease extinction (<xref rid="Fig2" ref-type="fig">Fig. 2b</xref>). Branching process theory confirms that <italic>q</italic><sup>ind</sup> > <italic>q</italic><sup>pop</sup> whenever <italic>c</italic>∈(0,1 - 1/<italic>R</italic><sub>0</sub>) (see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>).<fig id="Fig3"><label>Figure 3</label><caption><title><bold>Implications for control measures.</bold></title><p><bold>a</bold>, Increase in extinction probability (<italic>q</italic><sup>ind</sup> - <italic>q</italic><sup>pop</sup>) under individual-specific control compared to population-wide control, for diseases with <italic>R</italic><sub>0</sub> = 3 and different degrees of individual variation, <italic>k</italic>, subject to control effort <italic>c</italic>. With population-wide control, the infectiousness of all individuals is reduced by a factor <italic>c</italic>. With individual-specific control, a proportion <italic>c</italic> of infectious individuals (selected at random) have their infectiousness reduced to zero. The outbreak is assumed to begin with one case, with control present from the outset. <bold>b</bold>, Estimates of <italic>R̂</italic> and <italic>k̂</italic> from outbreak data sets before and after control measures were initiated (joined by solid lines; Supplementary Table 2), and post-control values of <italic>k</italic><sub><italic>c</italic></sub> estimated from theoretical models of control as described in the Supplementary Notes. <bold>c</bold>, Effect of random versus targeted control measures. The probability of outbreak containment (defined as never reaching the 100-case threshold) for four diseases with <italic>R</italic><sub>0</sub> = 3 and <italic>k</italic> = 0.1 (blue), <italic>k</italic> = 0.5 (green), <italic>k</italic> = 1 (black) or <italic>k</italic> → ∞ (purple). Control policies are population-wide (solid lines), random individual-specific (dotted lines), or targeted individual-specific (dashed lines, where half of all control effort is focused on the most infectious 20% of cases). For <italic>k</italic> → ∞, all individuals are identical, so targeting has no effect and dotted and dashed lines overlay one another. <bold>d</bold>, The factor by which targeting increases the effect of control on preventing a major outbreak, relative to random individual-specific control (see Supplementary Notes), when 20%, 40% or 60% of the total population is controlled. Results in <bold>c</bold> and <bold>d</bold> are the mean of 10,000 simulations, with control beginning in the second generation of cases.</p></caption><graphic xlink:href="41586_2005_Article_BFnature04153_Fig3_HTML" id="d29e1225"></graphic></fig></p><p id="Par13">To assess the realism of these idealized control scenarios, we analysed contact tracing data from four outbreaks before and after imposition of control measures. Control always lowered the estimated dispersion parameter (that is <italic>k̂</italic><sub>c</sub> < <italic>k̂</italic>) as predicted by the individual-specific model (<xref rid="Fig3" ref-type="fig">Fig. 3b</xref>), although small sample sizes often led to overlapping confidence intervals (<xref rid="MOESM1" ref-type="media">Supplementary Table 2</xref>). This increased skew in transmission arose chiefly from undiagnosed or misdiagnosed individuals, who continued to infect others (and even cause SSEs), whereas controlled individuals infected very few. To further examine our control theories, we calculated <inline-formula id="IEq4"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq4_HTML.gif"></inline-graphic></inline-formula> and <inline-formula id="IEq5"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq5_HTML.gif"></inline-graphic></inline-formula> for each data set; <italic>k̂</italic><sub><italic>c</italic></sub> was always closer to <inline-formula id="IEq6"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq6_HTML.gif"></inline-graphic></inline-formula>, although twice it fell between the two predictions, indicating a possible combination of control mechanisms (<xref rid="Fig3" ref-type="fig">Fig. 3b</xref>). Real-world control thus seems to increase individual variation, favouring extinction but risking ongoing SSEs. Larger data sets are needed to establish this pattern definitively.</p><p id="Par14">If highly infectious individuals can be identified predictively (see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>) then the efficiency of control could be greatly increased (<xref rid="Fig3" ref-type="fig">Fig. 3c</xref>, <xref rid="Fig3" ref-type="fig">d</xref>). Focusing half of all control effort on the most infectious 20% of cases is up to threefold more effective than random control (<xref rid="Fig3" ref-type="fig">Fig. 3d</xref>). When <italic>k</italic> = 0.1 or 0.5, outbreak containment is assured for targeted control levels at roughly half the threshold level of <italic>c</italic> = 1 - 1/<italic>R</italic><sub>0</sub> for random control. Gains in efficiency increase with more intense targeting of high-<italic>ν</italic> cases, but saturate as overall coverage <italic>c</italic> increases (<xref rid="MOESM1" ref-type="media">Supplementary Fig. 3c, d</xref>). Again, branching process theory generalizes these findings: for a given proportion <italic>c</italic> of individuals controlled, greater targeting of higher-<italic>ν</italic> individuals leads to lower effective reproductive number <italic>R</italic> and higher extinction probability <italic>q</italic> (see <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>).</p><p id="Par15">The data sets analysed here were collected from published literature, and may be subject to selection bias for successful invasions and SSEs rather than typical disease behaviour. Surveillance data sets are less vulnerable to this bias, but may under-report isolated cases. We urge that detailed transmission tracing data be collected and made public whenever possible, even if unexceptional. At a minimum, we propose a new measure for inclusion in outbreak reports: the proportion of cases not transmitting (<italic>p</italic><sub>0</sub>), which, together with <italic>R</italic><sub>0</sub> is sufficient to estimate the degree of variation in <italic>ν</italic> (<xref rid="MOESM1" ref-type="media">Supplementary Fig. 4</xref>). As more data become available, trends may emerge in the degree of variation present, for example, for different modes of spread or levels of virulence. Richer data sets may also enable testing of the branching process assumption that case outcomes are independent and identically distributed, by detecting possible correlations in <italic>ν</italic> values within transmission lineages or systematic changes as outbreaks progress.</p><p id="Par16">Our results have broad implications for emerging disease epidemiology, and open challenges for further work. Explosive epidemics demand rapid action by authorities and can strain health infrastructures. High extinction probabilities indicate that disease introductions or host species jumps may be more frequent than currently suspected. Cluster-size surveillance for pathogen adaptation<sup><xref ref-type="bibr" rid="CR29">29</xref></sup> or dwindling population immunity<sup><xref ref-type="bibr" rid="CR30">30</xref></sup> should be tuned to observed levels of variation. Realization of targeted control measures requires a better understanding of factors determining individual infectiousness. This work must be integrated with established theory of sexually transmitted diseases and social networks, where high-risk groups exert nonlinear influence on <italic>R</italic><sub>0</sub> because contact rates affect infectiousness and susceptibility equally<sup><xref ref-type="bibr" rid="CR3">3</xref>,<xref ref-type="bibr" rid="CR4">4</xref>,<xref ref-type="bibr" rid="CR12">12</xref>,<xref ref-type="bibr" rid="CR13">13</xref>,<xref ref-type="bibr" rid="CR22">22</xref></sup>. All diseases probably show intermediate degrees of covariation between infectiousness and susceptibility, a topic demanding empirical and theoretical study<sup><xref ref-type="bibr" rid="CR17">17</xref></sup>. The central role of <italic>R</italic><sub>0</sub> in epidemic analysis is unassailable, but our findings show that emerging disease outbreaks cannot be fully understood if individual variation in infectiousness is neglected. Examination of other population processes dependent on small numbers of individuals may yield similar insights.</p></sec><sec id="Sec2"><title>Methods</title><sec id="Sec3"><title>Analysis of disease data</title><p id="Par17">For data sets including the full distribution of <italic>Z</italic>, we estimated <italic>R̂</italic><sub>0</sub> and <italic>k̂</italic> using maximum-likelihood methods. The candidate models were compared using Akaike's information criterion (AIC<sub>c</sub>) modified for small sample size. Confidence intervals for <italic>k̂</italic> were estimated by bias-corrected non-parametric bootstrapping and corroborated by four other methods. For data sets including only estimates of <italic>R̂</italic><sub>0</sub> and the proportion of cases not transmitting (<italic>p̂</italic><sub>0</sub>), we estimated <italic>k̂</italic> by solving <italic>p̂</italic><sub>0</sub> = (1 + <italic>R̂</italic><sub>0</sub>/<italic>k</italic>)<sup>-<italic>k</italic></sup> numerically, and evaluated the candidate models using confidence intervals calculated by two methods. Expected proportions of transmission due to particular groups of infectious individuals (<xref rid="Fig1" ref-type="fig">Fig. 1b</xref>, <xref rid="Fig1" ref-type="fig">c</xref>) were calculated using the gamma distribution of <italic>ν</italic> with estimated values of <italic>R̂</italic><sub>0</sub> and <italic>k̂</italic>. See <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref> for details, and for descriptions of data sets.</p></sec><sec id="Sec4"><title>Branching process analysis</title><p id="Par18">Analysis of branching process models centres on the probability generating function (pgf) of the offspring distribution, <inline-formula id="IEq7"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq7_HTML.gif"></inline-graphic></inline-formula>, defined for |<italic>s</italic>| ≤ 1. When <italic>R</italic><sub>0</sub> > 1, the long-term probability of disease extinction after introduction of a single infected individual is the unique solution of <italic>q</italic> = <italic>g</italic>(<italic>q</italic>) on the interval (0,1). For a negative binomial offspring distribution <italic>Z</italic> ≈ NegB(<italic>R</italic><sub>0</sub>,<italic>k</italic>), the pgf is <inline-formula id="IEq8"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq8_HTML.gif"></inline-graphic></inline-formula>. Under population-wide control, <inline-formula id="IEq9"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq9_HTML.gif"></inline-graphic></inline-formula> and therefore <inline-formula id="IEq10"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq10_HTML.gif"></inline-graphic></inline-formula>, and the variance-to-mean ratio is 1 + (1 - <italic>c</italic>)<italic>R</italic><sub>0</sub>/<italic>k.</italic> Under random individual-specific control, the exact pgf is <inline-formula id="IEq11"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq11_HTML.gif"></inline-graphic></inline-formula> with variance-to-mean ratio 1 + <italic>R</italic><sub>0</sub>/<italic>k</italic> + <italic>cR</italic><sub>0</sub>. This scenario can be approximated by <inline-formula id="IEq12"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq12_HTML.gif"></inline-graphic></inline-formula> , where <inline-formula id="IEq13"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq13_HTML.gif"></inline-graphic></inline-formula> is the solution to <inline-formula id="IEq14"><inline-graphic xlink:href="41586_2005_Article_BFnature04153_IEq14_HTML.gif"></inline-graphic></inline-formula> and decreases monotonically as <italic>c</italic> increases. Further details, descriptions of outbreak simulations and formal analysis of control measures are found in the <xref rid="MOESM1" ref-type="media">Supplementary Notes</xref>.</p></sec></sec><sec sec-type="supplementary-material"><title>Supplementary information</title><sec id="Sec5"><p><supplementary-material content-type="local-data" id="MOESM1"><media xlink:href="41586_2005_BFnature04153_MOESM1_ESM.pdf"><caption><title>Supplementary Notes</title><p>This file contains additional discussion of factors contributing to individual variation in infectiousness, methodological details on statistical and modelling analyses, and details of outbreak datasets and superspreading events. (PDF 435 kb)</p></caption></media></supplementary-material></p><p><supplementary-material content-type="local-data" id="MOESM2"><media xlink:href="41586_2005_BFnature04153_MOESM2_ESM.pdf"><caption><title>Supplementary Figures</title><p>The file includes Supplementary Figures 1 to 4, with captions. The figures address the prediction of superspreading event frequency, further results on outbreak dynamics and control, and estimation of the dispersion parameter <italic>k</italic> with limited data. (PDF 322 kb)</p></caption></media></supplementary-material></p><p><supplementary-material content-type="local-data" id="MOESM3"><media xlink:href="41586_2005_BFnature04153_MOESM3_ESM.pdf"><caption><title>Supplementary Table 1</title><p>A summary of results from our statistical analysis of uncontrolled outbreaks (corresponds to Figure 1a–c). (PDF 71 kb)</p></caption></media></supplementary-material></p><p><supplementary-material content-type="local-data" id="MOESM4"><media xlink:href="41586_2005_BFnature04153_MOESM4_ESM.pdf"><caption><title>Supplementary Table 2</title><p>Detailed results from our statistical analysis of uncontrolled outbreaks (elaborating on Supplementary Table 1), and the analysis of data before and after control measures were applied in four outbreaks. (PDF 94 kb)</p></caption></media></supplementary-material></p></sec></sec></body><back><ack><title>Acknowledgements</title><p>We are grateful for comments and data suggestions from B. Bolker, J. Edmunds, N. Ferguson, A. Galvani, R. Gani, N. Gay, J. Gog, B. Grenfell, H. Hethcote, D. Heymann, A. Hubbard, N. Jewell, J. Lauer, R. May, T. Porco, C. Roth, D. Smith and B. Williams. We thank R. Gani for providing unpublished data from a previous publication, and L. Matthews for sharing work ahead of print. Our research was supported by the NSF, NIH-NIDA, the James S. McDonnell Foundation, the NSF/NIH Ecology of Infectious Disease Program, and the South African Centre for Epidemiological Modelling and Analysis (SACEMA). Author Contributions J.O.L.-S. and W.M.G. conceived the study. J.O.L.-S. collected and analysed outbreak data, conducted dynamic modelling, and drafted and revised the text. S.J.S. conducted formal analysis of branching processes and control measures. W.M.G. provided technical input on superspreading and control analyses. All authors contributed conceptually, and edited or commented on the text.</p></ack><notes notes-type="COI-statement"><title>Competing interests</title><p id="Par19">Reprints and permissions information is available at <ext-link ext-link-type="uri" xlink:href="http://npg.nature.com/reprintsandpermissions">npg.nature.com/reprintsandpermissions</ext-link>. The authors declare no competing financial interests.</p></notes><ref-list id="Bib1"><title>References</title><ref id="CR1"><label>1</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Levin</surname><given-names>SA</given-names></name><name><surname>Grenfell</surname><given-names>B</given-names></name><name><surname>Hastings</surname><given-names>A</given-names></name><name><surname>Perelson</surname><given-names>AS</given-names></name></person-group><article-title>Mathematical and computational challenges in population biology and ecosystems science</article-title><source>Science</source><year>1997</year><volume>275</volume><fpage>334</fpage><lpage>343</lpage><pub-id pub-id-type="doi">10.1126/science.275.5298.334</pub-id><pub-id pub-id-type="pmid">8994023</pub-id></element-citation></ref><ref id="CR2"><label>2</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Becker</surname><given-names>NG</given-names></name><name><surname>Britton</surname><given-names>T</given-names></name></person-group><article-title>Statistical studies of infectious disease incidence</article-title><source>J. R. Stat. Soc. B</source><year>1999</year><volume>61</volume><fpage>287</fpage><lpage>307</lpage><pub-id pub-id-type="doi">10.1111/1467-9868.00177</pub-id></element-citation></ref><ref id="CR3"><label>3</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Anderson</surname><given-names>RM</given-names></name><name><surname>May</surname><given-names>RM</given-names></name></person-group><source>Infectious Diseases of Humans: Dynamics and Control</source><year>1991</year></element-citation></ref><ref id="CR4"><label>4</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Diekmann</surname><given-names>O</given-names></name><name><surname>Heesterbeek</surname><given-names>JAP</given-names></name></person-group><source>Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis, and Interpretation</source><year>2000</year></element-citation></ref><ref id="CR5"><label>5</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Leo</surname><given-names>YS</given-names></name><etal></etal></person-group><article-title>Severe acute respiratory syndrome—Singapore, 2003</article-title><source>Morbid. Mortal. Wkly Rep.</source><year>2003</year><volume>52</volume><fpage>405</fpage><lpage>411</lpage></element-citation></ref><ref id="CR6"><label>6</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Shen</surname><given-names>Z</given-names></name><etal></etal></person-group><article-title>Superspreading SARS events, Beijing, 2003</article-title><source>Emerg. Infect. Dis.</source><year>2004</year><volume>10</volume><fpage>256</fpage><lpage>260</lpage><pub-id pub-id-type="doi">10.3201/eid1002.030732</pub-id><pub-id pub-id-type="pmid">15030693</pub-id></element-citation></ref><ref id="CR7"><label>7</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dye</surname><given-names>C</given-names></name><name><surname>Gay</surname><given-names>N</given-names></name></person-group><article-title>Modeling the SARS epidemic</article-title><source>Science</source><year>2003</year><volume>300</volume><fpage>1884</fpage><lpage>1885</lpage><pub-id pub-id-type="doi">10.1126/science.1086925</pub-id><pub-id pub-id-type="pmid">12766208</pub-id></element-citation></ref><ref id="CR8"><label>8</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lipsitch</surname><given-names>M</given-names></name><etal></etal></person-group><article-title>Transmission dynamics and control of severe acute respiratory syndrome</article-title><source>Science</source><year>2003</year><volume>300</volume><fpage>1966</fpage><lpage>1970</lpage><pub-id pub-id-type="doi">10.1126/science.1086616</pub-id><pub-id pub-id-type="pmid">12766207</pub-id></element-citation></ref><ref id="CR9"><label>9</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Riley</surname><given-names>S</given-names></name><etal></etal></person-group><article-title>Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions</article-title><source>Science</source><year>2003</year><volume>300</volume><fpage>1961</fpage><lpage>1966</lpage><pub-id pub-id-type="doi">10.1126/science.1086478</pub-id><pub-id pub-id-type="pmid">12766206</pub-id></element-citation></ref><ref id="CR10"><label>10</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bauch</surname><given-names>CT</given-names></name><name><surname>Lloyd-Smith</surname><given-names>JO</given-names></name><name><surname>Coffee</surname><given-names>M</given-names></name><name><surname>Galvani</surname><given-names>AP</given-names></name></person-group><article-title>Dynamically modeling SARS and other newly-emerging respiratory illnesses: past, present, future</article-title><source>Epidemiology</source><year>2005</year><volume>16</volume><fpage>791</fpage><lpage>801</lpage><pub-id pub-id-type="doi">10.1097/01.ede.0000181633.80269.4c</pub-id><pub-id pub-id-type="pmid">16222170</pub-id></element-citation></ref><ref id="CR11"><label>11</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Koopman</surname><given-names>J</given-names></name></person-group><article-title>Modeling infection transmission</article-title><source>Annu. Rev. Public Health</source><year>2004</year><volume>25</volume><fpage>303</fpage><lpage>326</lpage><pub-id pub-id-type="doi">10.1146/annurev.publhealth.25.102802.124353</pub-id><pub-id pub-id-type="pmid">15015922</pub-id></element-citation></ref><ref id="CR12"><label>12</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>May</surname><given-names>RM</given-names></name><name><surname>Anderson</surname><given-names>RM</given-names></name></person-group><article-title>Transmission dynamics of HIV infection</article-title><source>Nature</source><year>1987</year><volume>326</volume><fpage>137</fpage><lpage>142</lpage><pub-id pub-id-type="doi">10.1038/326137a0</pub-id><pub-id pub-id-type="pmid">3821890</pub-id></element-citation></ref><ref id="CR13"><label>13</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Woolhouse</surname><given-names>MEJ</given-names></name><etal></etal></person-group><article-title>Heterogeneities in the transmission of infectious agents: Implications for the design of control programs</article-title><source>Proc. Natl Acad. Sci. USA</source><year>1997</year><volume>94</volume><fpage>338</fpage><lpage>342</lpage><pub-id pub-id-type="doi">10.1073/pnas.94.1.338</pub-id><pub-id pub-id-type="pmid">8990210</pub-id></element-citation></ref><ref id="CR14"><label>14</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lloyd-Smith</surname><given-names>JO</given-names></name><name><surname>Getz</surname><given-names>WM</given-names></name><name><surname>Westerhoff</surname><given-names>HV</given-names></name></person-group><article-title>Frequency-dependent incidence in models of sexually transmitted diseases: portrayal of pair-based transmission and effects of illness on contact behaviour</article-title><source>Proc. R. Soc. Lond. B</source><year>2004</year><volume>271</volume><fpage>625</fpage><lpage>634</lpage><pub-id pub-id-type="doi">10.1098/rspb.2003.2632</pub-id></element-citation></ref><ref id="CR15"><label>15</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Anderson</surname><given-names>RM</given-names></name><etal></etal></person-group><article-title>Epidemiology, transmission dynamics and control of SARS: the 2002–2003 epidemic</article-title><source>Phil. Trans. R. Soc. Lond. B</source><year>2004</year><volume>359</volume><fpage>1091</fpage><lpage>1105</lpage><pub-id pub-id-type="doi">10.1098/rstb.2004.1490</pub-id><pub-id pub-id-type="pmid">15306395</pub-id></element-citation></ref><ref id="CR16"><label>16</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gani</surname><given-names>R</given-names></name><name><surname>Leach</surname><given-names>S</given-names></name></person-group><article-title>Epidemiologic determinants for modeling pneumonic plague outbreaks</article-title><source>Emerg. Infect. Dis.</source><year>2004</year><volume>10</volume><fpage>608</fpage><lpage>614</lpage><pub-id pub-id-type="doi">10.3201/eid1004.030509</pub-id><pub-id pub-id-type="pmid">15200849</pub-id></element-citation></ref><ref id="CR17"><label>17</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Becker</surname><given-names>N</given-names></name><name><surname>Marschner</surname><given-names>I</given-names></name></person-group><source>Stochastic Processes in Epidemic Theory</source><year>1990</year><fpage>90</fpage><lpage>103</lpage></element-citation></ref><ref id="CR18"><label>18</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Becker</surname><given-names>N</given-names></name></person-group><source>Analysis of Infectious Disease Data</source><year>1989</year><fpage>48</fpage><lpage>59</lpage></element-citation></ref><ref id="CR19"><label>19</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Bailey</surname><given-names>NTJ</given-names></name></person-group><source>The Mathematical Theory of Infectious Diseases</source><year>1975</year><fpage>263</fpage><lpage>265</lpage></element-citation></ref><ref id="CR20"><label>20</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Keeling</surname><given-names>MJ</given-names></name><name><surname>Grenfell</surname><given-names>BT</given-names></name></person-group><article-title>Disease extinction and community size: Modeling the persistence of measles</article-title><source>Science</source><year>1997</year><volume>275</volume><fpage>65</fpage><lpage>67</lpage><pub-id pub-id-type="doi">10.1126/science.275.5296.65</pub-id><pub-id pub-id-type="pmid">8974392</pub-id></element-citation></ref><ref id="CR21"><label>21</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lloyd</surname><given-names>AL</given-names></name></person-group><article-title>Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods</article-title><source>Proc. R. Soc. Lond. B</source><year>2001</year><volume>268</volume><fpage>985</fpage><lpage>993</lpage><pub-id pub-id-type="doi">10.1098/rspb.2001.1599</pub-id></element-citation></ref><ref id="CR22"><label>22</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Meyers</surname><given-names>LA</given-names></name><name><surname>Pourbohloul</surname><given-names>B</given-names></name><name><surname>Newman</surname><given-names>MEJ</given-names></name><name><surname>Skowronski</surname><given-names>DM</given-names></name><name><surname>Brunham</surname><given-names>RC</given-names></name></person-group><article-title>Network theory and SARS: predicting outbreak diversity</article-title><source>J. Theor. Biol.</source><year>2005</year><volume>232</volume><fpage>71</fpage><lpage>81</lpage><pub-id pub-id-type="doi">10.1016/j.jtbi.2004.07.026</pub-id><pub-id pub-id-type="pmid">15498594</pub-id></element-citation></ref><ref id="CR23"><label>23</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Boswell</surname><given-names>MT</given-names></name><name><surname>Patil</surname><given-names>GP</given-names></name></person-group><source>Random Counts in Models and Structures</source><year>1970</year><fpage>7</fpage><lpage>8</lpage></element-citation></ref><ref id="CR24"><label>24</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Burnham</surname><given-names>KP</given-names></name><name><surname>Anderson</surname><given-names>DR</given-names></name></person-group><source>Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach</source><year>2002</year></element-citation></ref><ref id="CR25"><label>25</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lloyd-Smith</surname><given-names>JO</given-names></name><name><surname>Galvani</surname><given-names>AP</given-names></name><name><surname>Getz</surname><given-names>WM</given-names></name></person-group><article-title>Curtailing transmission of severe acute respiratory syndrome within a community and its hospital</article-title><source>Proc. R. Soc. Lond. B</source><year>2003</year><volume>270</volume><fpage>1979</fpage><lpage>1989</lpage><pub-id pub-id-type="doi">10.1098/rspb.2003.2481</pub-id></element-citation></ref><ref id="CR26"><label>26</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wallinga</surname><given-names>J</given-names></name><name><surname>Teunis</surname><given-names>P</given-names></name></person-group><article-title>Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures</article-title><source>Am. J. Epidemiol.</source><year>2004</year><volume>160</volume><fpage>509</fpage><lpage>516</lpage><pub-id pub-id-type="doi">10.1093/aje/kwh255</pub-id><pub-id pub-id-type="pmid">15353409</pub-id></element-citation></ref><ref id="CR27"><label>27</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ha</surname><given-names>LD</given-names></name><etal></etal></person-group><article-title>Lack of SARS transmission among public hospital workers, Vietnam</article-title><source>Emerg. Infect. Dis.</source><year>2004</year><volume>10</volume><fpage>265</fpage><lpage>268</lpage><pub-id pub-id-type="doi">10.3201/eid1002.030707</pub-id><pub-id pub-id-type="pmid">15030695</pub-id></element-citation></ref><ref id="CR28"><label>28</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Park</surname><given-names>BJ</given-names></name><etal></etal></person-group><article-title>Lack of SARS transmission among healthcare workers, United States</article-title><source>Emerg. Infect. Dis.</source><year>2004</year><volume>10</volume><fpage>244</fpage><lpage>248</lpage><pub-id pub-id-type="pmid">15030690</pub-id></element-citation></ref><ref id="CR29"><label>29</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ferguson</surname><given-names>NM</given-names></name><name><surname>Fraser</surname><given-names>C</given-names></name><name><surname>Donnelly</surname><given-names>CA</given-names></name><name><surname>Ghani</surname><given-names>AC</given-names></name><name><surname>Anderson</surname><given-names>RM</given-names></name></person-group><article-title>Public health risk from the avian H5N1 influenza epidemic</article-title><source>Science</source><year>2004</year><volume>304</volume><fpage>968</fpage><lpage>969</lpage><pub-id pub-id-type="doi">10.1126/science.1096898</pub-id><pub-id pub-id-type="pmid">15143265</pub-id></element-citation></ref><ref id="CR30"><label>30</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Farrington</surname><given-names>CP</given-names></name><name><surname>Kanaan</surname><given-names>MN</given-names></name><name><surname>Gay</surname><given-names>NJ</given-names></name></person-group><article-title>Branching process models for surveillance of infectious diseases controlled by mass vaccination</article-title><source>Biostatistics</source><year>2003</year><volume>4</volume><fpage>279</fpage><lpage>295</lpage><pub-id pub-id-type="doi">10.1093/biostatistics/4.2.279</pub-id><pub-id pub-id-type="pmid">12925522</pub-id></element-citation></ref></ref-list></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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