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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">School dismissal as a pandemic influenza response: When, where and
for how long?</title><author><name sortKey="Germann, Timothy C" sort="Germann, Timothy C" uniqKey="Germann T" first="Timothy C." last="Germann">Timothy C. Germann</name><affiliation><nlm:aff id="A1">Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA</nlm:aff></affiliation></author><author><name sortKey="Gao, Hongjiang" sort="Gao, Hongjiang" uniqKey="Gao H" first="Hongjiang" last="Gao">Hongjiang Gao</name><affiliation><nlm:aff id="A2">Community Interventions for Infection Control Unit, Centers for Disease Control and Prevention, Atlanta, GA 30329 USA</nlm:aff></affiliation></author><author><name sortKey="Gambhir, Manoj" sort="Gambhir, Manoj" uniqKey="Gambhir M" first="Manoj" last="Gambhir">Manoj Gambhir</name><affiliation><nlm:aff id="A3">National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333 USA</nlm:aff></affiliation><affiliation><nlm:aff id="A4">School of Public Health and Preventive Medicine, Monash University, Victoria 3800 Australia</nlm:aff></affiliation></author><author><name sortKey="Plummer, Andrew" sort="Plummer, Andrew" uniqKey="Plummer A" first="Andrew" last="Plummer">Andrew Plummer</name><affiliation><nlm:aff id="A2">Community Interventions for Infection Control Unit, Centers for Disease Control and Prevention, Atlanta, GA 30329 USA</nlm:aff></affiliation></author><author><name sortKey="Biggerstaff, Matthew" sort="Biggerstaff, Matthew" uniqKey="Biggerstaff M" first="Matthew" last="Biggerstaff">Matthew Biggerstaff</name><affiliation><nlm:aff id="A3">National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333 USA</nlm:aff></affiliation></author><author><name sortKey="Reed, Carrie" sort="Reed, Carrie" uniqKey="Reed C" first="Carrie" last="Reed">Carrie Reed</name><affiliation><nlm:aff id="A3">National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333 USA</nlm:aff></affiliation></author><author><name sortKey="Uzicanin, Amra" sort="Uzicanin, Amra" uniqKey="Uzicanin A" first="Amra" last="Uzicanin">Amra Uzicanin</name><affiliation><nlm:aff id="A2">Community Interventions for Infection Control Unit, Centers for Disease Control and Prevention, Atlanta, GA 30329 USA</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">31235334</idno><idno type="pmc">6956848</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6956848</idno><idno type="RBID">PMC:6956848</idno><idno type="doi">10.1016/j.epidem.2019.100348</idno><date when="2019">2019</date><idno type="wicri:Area/Pmc/Corpus">000E58</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000E58</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">School dismissal as a pandemic influenza response: When, where and
for how long?</title><author><name sortKey="Germann, Timothy C" sort="Germann, Timothy C" uniqKey="Germann T" first="Timothy C." last="Germann">Timothy C. Germann</name><affiliation><nlm:aff id="A1">Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA</nlm:aff></affiliation></author><author><name sortKey="Gao, Hongjiang" sort="Gao, Hongjiang" uniqKey="Gao H" first="Hongjiang" last="Gao">Hongjiang Gao</name><affiliation><nlm:aff id="A2">Community Interventions for Infection Control Unit, Centers for Disease Control and Prevention, Atlanta, GA 30329 USA</nlm:aff></affiliation></author><author><name sortKey="Gambhir, Manoj" sort="Gambhir, Manoj" uniqKey="Gambhir M" first="Manoj" last="Gambhir">Manoj Gambhir</name><affiliation><nlm:aff id="A3">National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333 USA</nlm:aff></affiliation><affiliation><nlm:aff id="A4">School of Public Health and Preventive Medicine, Monash University, Victoria 3800 Australia</nlm:aff></affiliation></author><author><name sortKey="Plummer, Andrew" sort="Plummer, Andrew" uniqKey="Plummer A" first="Andrew" last="Plummer">Andrew Plummer</name><affiliation><nlm:aff id="A2">Community Interventions for Infection Control Unit, Centers for Disease Control and Prevention, Atlanta, GA 30329 USA</nlm:aff></affiliation></author><author><name sortKey="Biggerstaff, Matthew" sort="Biggerstaff, Matthew" uniqKey="Biggerstaff M" first="Matthew" last="Biggerstaff">Matthew Biggerstaff</name><affiliation><nlm:aff id="A3">National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333 USA</nlm:aff></affiliation></author><author><name sortKey="Reed, Carrie" sort="Reed, Carrie" uniqKey="Reed C" first="Carrie" last="Reed">Carrie Reed</name><affiliation><nlm:aff id="A3">National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333 USA</nlm:aff></affiliation></author><author><name sortKey="Uzicanin, Amra" sort="Uzicanin, Amra" uniqKey="Uzicanin A" first="Amra" last="Uzicanin">Amra Uzicanin</name><affiliation><nlm:aff id="A2">Community Interventions for Infection Control Unit, Centers for Disease Control and Prevention, Atlanta, GA 30329 USA</nlm:aff></affiliation></author></analytic><series><title level="j">Epidemics</title><idno type="ISSN">1755-4365</idno><idno type="eISSN">1878-0067</idno><imprint><date when="2019">2019</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p id="P3">We used individual-based computer simulation models at community,
regional and national levels to evaluate the likely impact of coordinated
pre-emptive school dismissal policies during an influenza pandemic. Such
policies involve three key decisions: when, over what geographical scale, and
how long to keep schools closed. Our evaluation includes uncertainty and
sensitivity analyses, as well as model output uncertainties arising from
variability in serial intervals and presumed modifications of social contacts
during school dismissal periods. During the period before vaccines become widely
available, school dismissals are particularly effective in delaying the epidemic
peak, typically by 4–6 days for each additional week of dismissal.
Assuming the surveillance is able to correctly and promptly diagnose at least
5–10% of symptomatic individuals within the jurisdiction, dismissals at
the city or county level yield the greatest reduction in disease incidence for a
given dismissal duration for all but the most severe pandemic scenarios
considered here. Broader (multi-county) dismissals should be considered for the
most severe and fast-spreading (1918-like) pandemics, in which multi-month
closures may be necessary to delay the epidemic peak sufficiently to allow for
vaccines to be implemented.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Biggerstaff, M" uniqKey="Biggerstaff M">M Biggerstaff</name></author><author><name sortKey="Jhung, M" uniqKey="Jhung M">M Jhung</name></author><author><name sortKey="Kamimoto, L" uniqKey="Kamimoto L">L Kamimoto</name></author><author><name sortKey="Balluz, L" uniqKey="Balluz L">L Balluz</name></author><author><name sortKey="Finelli, L" uniqKey="Finelli L">L Finelli</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Biggerstaff, M" uniqKey="Biggerstaff M">M Biggerstaff</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Blower, Sm" uniqKey="Blower S">SM Blower</name></author><author><name sortKey="Dowlatabadi, H" uniqKey="Dowlatabadi H">H Dowlatabadi</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Brown, St" uniqKey="Brown S">ST 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sortKey="Ajelli, M" uniqKey="Ajelli M">M Ajelli</name></author><author><name sortKey="Merler, S" uniqKey="Merler S">S Merler</name></author><author><name sortKey="Ferguson, Nm" uniqKey="Ferguson N">NM Ferguson</name></author><author><name sortKey="Cauchemez, S" uniqKey="Cauchemez S">S Cauchemez</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Fung, Ic H" uniqKey="Fung I">IC-H Fung</name></author><author><name sortKey="Gambhir, M" uniqKey="Gambhir M">M Gambhir</name></author><author><name sortKey="Glasser, Jw" uniqKey="Glasser J">JW Glasser</name></author><author><name sortKey="Gao, H" uniqKey="Gao H">H Gao</name></author><author><name sortKey="Washington, Ml" uniqKey="Washington M">ML Washington</name></author><author><name sortKey="Uzicanin, A" uniqKey="Uzicanin A">A Uzicanin</name></author><author><name sortKey="Meltzer, Mi" uniqKey="Meltzer M">MI Meltzer</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Gerdil, C" 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sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<pmc-dir>properties manuscript</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-journal-id">101484711</journal-id><journal-id journal-id-type="pubmed-jr-id">36817</journal-id><journal-id journal-id-type="nlm-ta">Epidemics</journal-id><journal-id journal-id-type="iso-abbrev">Epidemics</journal-id><journal-title-group><journal-title>Epidemics</journal-title></journal-title-group><issn pub-type="ppub">1755-4365</issn><issn pub-type="epub">1878-0067</issn></journal-meta><article-meta><article-id pub-id-type="pmid">31235334</article-id><article-id pub-id-type="pmc">6956848</article-id><article-id pub-id-type="doi">10.1016/j.epidem.2019.100348</article-id><article-id pub-id-type="manuscript">HHSPA1065432</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>School dismissal as a pandemic influenza response: When, where and
for how long?</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Germann</surname><given-names>Timothy C.</given-names></name><xref ref-type="aff" rid="A1">a</xref></contrib><contrib contrib-type="author"><name><surname>Gao</surname><given-names>Hongjiang</given-names></name><xref ref-type="aff" rid="A2">b</xref><xref rid="CR1" ref-type="corresp">*</xref></contrib><contrib contrib-type="author"><name><surname>Gambhir</surname><given-names>Manoj</given-names></name><xref ref-type="aff" rid="A3">c</xref><xref ref-type="aff" rid="A4">d</xref><xref rid="FN1" ref-type="author-notes">1</xref></contrib><contrib contrib-type="author"><name><surname>Plummer</surname><given-names>Andrew</given-names></name><xref ref-type="aff" rid="A2">b</xref><xref rid="FN2" ref-type="author-notes">2</xref></contrib><contrib contrib-type="author"><name><surname>Biggerstaff</surname><given-names>Matthew</given-names></name><xref ref-type="aff" rid="A3">c</xref></contrib><contrib contrib-type="author"><name><surname>Reed</surname><given-names>Carrie</given-names></name><xref ref-type="aff" rid="A3">c</xref></contrib><contrib contrib-type="author"><name><surname>Uzicanin</surname><given-names>Amra</given-names></name><xref ref-type="aff" rid="A2">b</xref></contrib></contrib-group><aff id="A1"><label>a</label>Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA</aff><aff id="A2"><label>b</label>Community Interventions for Infection Control Unit, Centers for Disease Control and Prevention, Atlanta, GA 30329 USA</aff><aff id="A3"><label>c</label>National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333 USA</aff><aff id="A4"><label>d</label>School of Public Health and Preventive Medicine, Monash University, Victoria 3800 Australia</aff><author-notes><fn fn-type="present-address" id="FN1"><label>1</label><p id="P1">Present address: IBM Health Modeling and Analytics Melbourne Research
Laboratory, Melbourne, Victoria 3006 Australia.</p></fn><fn fn-type="present-address" id="FN2"><label>2</label><p id="P2">Present address: TRICARE/Defense Health Agency, Reston, VA 20190
USA.</p></fn><corresp id="CR1"><label>*</label>Corresponding author. <email>hgao@cdc.gov</email>(H. Gao).</corresp></author-notes><pub-date pub-type="nihms-submitted"><day>6</day><month>1</month><year>2020</year></pub-date><pub-date pub-type="epub"><day>12</day><month>6</month><year>2019</year></pub-date><pub-date pub-type="ppub"><month>9</month><year>2019</year></pub-date><pub-date pub-type="pmc-release"><day>13</day><month>1</month><year>2020</year></pub-date><volume>28</volume><fpage>100348</fpage><lpage>100348</lpage><pmc-comment>elocation-id from pubmed: 10.1016/j.epidem.2019.100348</pmc-comment>
<permissions><license license-type="open-access" xlink:href="http://creativecommons.org/licenses/BY-NC-ND/4.0/"><license-p><pmc-comment>CREATIVE COMMONS</pmc-comment>This is an open access article under the CC BY-NC-ND license
(<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/BY-NC-ND/4.0/">http://creativecommons.org/licenses/BY-NC-ND/4.0/</ext-link>).</license-p></license></permissions><abstract id="ABS1"><p id="P3">We used individual-based computer simulation models at community,
regional and national levels to evaluate the likely impact of coordinated
pre-emptive school dismissal policies during an influenza pandemic. Such
policies involve three key decisions: when, over what geographical scale, and
how long to keep schools closed. Our evaluation includes uncertainty and
sensitivity analyses, as well as model output uncertainties arising from
variability in serial intervals and presumed modifications of social contacts
during school dismissal periods. During the period before vaccines become widely
available, school dismissals are particularly effective in delaying the epidemic
peak, typically by 4–6 days for each additional week of dismissal.
Assuming the surveillance is able to correctly and promptly diagnose at least
5–10% of symptomatic individuals within the jurisdiction, dismissals at
the city or county level yield the greatest reduction in disease incidence for a
given dismissal duration for all but the most severe pandemic scenarios
considered here. Broader (multi-county) dismissals should be considered for the
most severe and fast-spreading (1918-like) pandemics, in which multi-month
closures may be necessary to delay the epidemic peak sufficiently to allow for
vaccines to be implemented.</p></abstract><kwd-group><kwd>Pandemic influenza</kwd><kwd>School dismissal</kwd><kwd>Stochastic individual-based model</kwd><kwd>EpiCast</kwd></kwd-group></article-meta></front><body><sec id="S1"><label>1.</label><title>Introduction</title><p id="P4">Influenza pandemics occur when a novel influenza virus gains sustained
human-to-human transmission and spreads globally, resulting in potentially high
levels of morbidity and/or mortality. Following the emergence of a novel pandemic
strain, several months are typically required to develop, produce, and distribute a
well-matched pandemic vaccine (<xref rid="R19" ref-type="bibr">Gerdil, 2003</xref>;
<xref rid="R8" ref-type="bibr">Centers for Disease Control and Prevention,
2010</xref>; <xref rid="R36" ref-type="bibr">President’s Council of
Advisors on Science and Technology, 2010</xref>). Moreover, the use of antiviral
drugs for chemoprophylaxis may be limited due to concerns regarding drug resistance
and limited supply during an evolving pandemic (<xref rid="R28" ref-type="bibr">Lipsitch et al., 2007</xref>; <xref rid="R9" ref-type="bibr">Centers for
Disease Control and Prevention, 2011</xref>). As a result, non-pharmaceutical
interventions (NPIs) are essential, potentially providing time for pandemic vaccines
to be developed and distributed, decreasing the peak demand for healthcare services
prior to pandemic vaccine roll-out, and reducing the overall morbidity and mortality
caused by the novel virus. Among potential NPIs, school closure/dismissal has long
been one of the first to be implemented during previous pandemics (Markel et al.,
2007a; <xref rid="R6" ref-type="bibr">Cauchemez et al., 2009</xref>), given the
major role that school-aged children play in the transmission of influenza in the
household (<xref rid="R29" ref-type="bibr">Longini et al., 1982</xref>; <xref rid="R40" ref-type="bibr">Viboud et al., 2004</xref>) and community (<xref rid="R10" ref-type="bibr">Chao et al., 2010</xref>), likely due to intense
social contacts among children in schools (<xref rid="R34" ref-type="bibr">Mossong
et al., 2008</xref>).</p><p id="P5">In the absence of clear evidence for the effectiveness of school closures on
large geographic scales, it has been very difficult for public officials to make
policy recommendations and develop national guidance. Mathematical and computational
disease spread models offer invaluable platforms for performing
“what-if” studies to assess potential future pandemic scenarios and
intervention strategies, complementing observational or field studies that are
necessarily limited to historical events and decisions (<xref rid="R20" ref-type="bibr">Germann et al., 2006</xref>; <xref rid="R25" ref-type="bibr">Halloran et al., 2008</xref>). In particular, they enable us to model a variety
of school dismissal strategies and assess their effectiveness in slowing the spread
of a hypothetical future influenza pandemic (<xref rid="R22" ref-type="bibr">Haber
et al., 2007</xref>; <xref rid="R32" ref-type="bibr">Milne et al., 2008</xref>;
<xref rid="R23" ref-type="bibr">Halder et al., 2010</xref>; <xref rid="R27" ref-type="bibr">Lee et al., 2010</xref>; <xref rid="R24" ref-type="bibr">Halder
et al., 2011</xref>; <xref rid="R4" ref-type="bibr">Brown et al., 2011</xref>;
<xref rid="R33" ref-type="bibr">Milne et al., 2013</xref>; <xref rid="R35" ref-type="bibr">Nishiura et al., 2014</xref>; <xref rid="R18" ref-type="bibr">Fung et al., 2015</xref>). However, previous pre-pandemic policy
recommendations used a measure of pandemic severity that was based on disease
severity measures, such as case fatality ratio and excess death rate (<xref rid="R7" ref-type="bibr">Centers for Disease Control and Prevention, 2007</xref>), while
modeling studies primarily considered the effectiveness of school dismissal
strategies for various disease transmissibility levels, usually represented by the
basic reproduction number R0 (<xref rid="R20" ref-type="bibr">Germann et al.,
2006</xref>; <xref rid="R25" ref-type="bibr">Halloran et al., 2008</xref>;
Harber et al., 2007; <xref rid="R32" ref-type="bibr">Milne et al., 2008</xref>;
<xref rid="R23" ref-type="bibr">Halder et al., 2010</xref>; <xref rid="R27" ref-type="bibr">Lee et al., 2010</xref>; <xref rid="R24" ref-type="bibr">Halder
et al., 2011</xref>; <xref rid="R4" ref-type="bibr">Brown et al., 2011</xref>;
<xref rid="R33" ref-type="bibr">Milne et al., 2013</xref>; <xref rid="R35" ref-type="bibr">Nishiura et al., 2014</xref>; <xref rid="R18" ref-type="bibr">Fung et al., 2015</xref>). A recently developed two-dimensional pandemic
severity assessment framework considers both transmissibility and clinical severity
as two independent factors (<xref rid="R38" ref-type="bibr">Reed et al.,
2013</xref>). This framework provides the basis for the development of national
pre-pandemic NPI guidance, for which school closure is thought to be one of the most
effective early mitigation measures. The purpose of the present study is to evaluate
whether school dismissal should be recommended and, if so, when such dismissals
should be initiated, how broadly (in geographic terms, e.g., community, county, or
state-wide dismissals), and how long they should last. As described in the <xref rid="S2" ref-type="sec">Methods</xref>, we utilize simulations at three
different scales to answer these questions in a computationally feasible manner. A
single community model (<sup>~</sup>2000 people) is used for sensitivity
studies, and a regional model (<sup>~</sup>8.6 million people in the Chicago
metropolitan area) to address timing (“when” and “how
long”) and local vs. regional dismissal policies. The insights gleaned from
these smaller-scale simulations are then used to design the final simulation suite,
employing a model of the continental United States (<sup>~</sup>300 million
people).</p></sec><sec id="S2"><label>2.</label><title>Methods</title><sec id="S3"><label>2.1.</label><title>Simulation platform</title><p id="P6">In the present work, we extend and apply the stochastic, individual-based
EpiCast (“Epidemiological Forecasting”) model (<xref rid="R20" ref-type="bibr">Germann et al., 2006</xref>; <xref rid="R25" ref-type="bibr">Halloran et al., 2008</xref>) to evaluate a range of school dismissal
policy options for five potential influenza pandemic strains having
characteristics based upon both historical (1918, 1957, 1968, and 2009) and
potential H5N1-like pandemics, spanning the four quadrants (with independent
severity and transmissibility axes) of the pandemic severity assessment
framework (<xref rid="R38" ref-type="bibr">Reed et al., 2013</xref>). Full
details about EpiCast are provided in the <xref rid="SD1" ref-type="supplementary-material">SI</xref>.</p></sec><sec id="S4"><label>2.2.</label><title>Model parameters and assumptions</title><p id="P7">For each of these five pandemic scenarios and three geographical scales,
four other parameters are varied (see <xref rid="T1" ref-type="table">Table
1</xref>) in order to span their likely ranges and ascertain their impact on
mitigation. First, we consider two alternative disease natural histories
(“Short” and “Long”), with serial intervals (average
time between successive cases) of <sup>~</sup>2.8 and 4 days,
respectively. These two choices have been used in several previous modeling
studies (<xref rid="R25" ref-type="bibr">Halloran et al., 2008</xref>), and
almost exactly span the 95% confidence interval of 2.9–4.3 days observed
in a household study during the 2007 interpandemic influenza season in Hong Kong
(<xref rid="R13" ref-type="bibr">Cowling et al., 2009</xref>)</p><p id="P8">Second, we considered different triggers for school dismissal, all
involving the diagnosis of some threshold number of symptomatic school children
within a community. Once that threshold is reached, all schools within that
community are closed, and possibly those in surrounding communities, depending
upon the specific policy. Since it will be impossible to quickly identify and
accurately diagnose all symptomatic children, the surveillance sensitivity is an
important factor. In the present study, no other actions (e.g., therapeutic
antivirals, isolation, or quarantine) other than self-isolation (staying home
when sick, as specified in <xref rid="SD1" ref-type="supplementary-material">SI
section 1 F</xref>) are taken following diagnosis. Consequently, the
diagnosis ratio (the percentage of newly symptomatic individuals correctly and
promptly identified following illness onset) and the trigger threshold (the
number of diagnosed school children required to activate a dismissal) can be
coupled to provide a single independent parameter for the trigger, the number of
symptomatic (but not necessarily diagnosed) school children. For example, if the
diagnosis of a single child is sufficient to trigger intervention, then
diagnosis ratios of 1%, 5%, 10%, and 20% require 100, 20, 10, and five
symptomatic school children, respectively, in a community before the first
symptomatic child is diagnosed, triggering the intervention.</p><p id="P9">Third, the geographic scale of school dismissal can range from the
individual community (which may be considered as a very small
<sup>~</sup>2000-person school district), to single county,
multi-county, or even potentially state- or nation-wide closures in the most
severe situation, as in the 1918-like scenario D. With the regional model, we
consider school dismissal at either the individual community or region-wide
levels, and at the national scale consider four scales of dismissal: community,
county, adjoining county region, or (for the 1918-like scenario D only)
state-wide dismissals.</p><p id="P10">Finally, in the face of a limited amount of survey and field study data
on social contact behaviors in and out of school from the United States (<xref rid="R34" ref-type="bibr">Mossong et al., 2008</xref>; <xref rid="R21" ref-type="bibr">Gog et al., 2014</xref>; <xref rid="R16" ref-type="bibr">Earn et al., 2012</xref>; <xref rid="R12" ref-type="bibr">Copeland et al.,
2013</xref>; <xref rid="R11" ref-type="bibr">Chowell et al., 2011</xref>;
<xref rid="R26" ref-type="bibr">Heymann et al., 2004</xref>; <xref rid="R31" ref-type="bibr">Markel et al., 2007</xref>; <xref rid="R15" ref-type="bibr">Eames et al., 2012</xref>), we utilize a range of assumed social contact
pattern changes during school dismissal that is consistent with the available
studies and span those used in previous modeling work (<xref rid="R20" ref-type="bibr">Germann et al., 2006</xref>; <xref rid="R25" ref-type="bibr">Halloran et al., 2008</xref>; <xref rid="R22" ref-type="bibr">Haber et al.,
2007</xref>; <xref rid="R32" ref-type="bibr">Milne et al., 2008</xref>;
<xref rid="R23" ref-type="bibr">Halder et al., 2010</xref>; <xref rid="R27" ref-type="bibr">Lee et al., 2010</xref>; <xref rid="R24" ref-type="bibr">Halder et al., 2011</xref>; <xref rid="R4" ref-type="bibr">Brown et al.,
2011</xref>; <xref rid="R33" ref-type="bibr">Milne et al., 2013</xref>;
<xref rid="R35" ref-type="bibr">Nishiura et al., 2014</xref>; <xref rid="R18" ref-type="bibr">Fung et al., 2015</xref>). Since these contact
rates contribute to the infection probability for each susceptible person, they
have a strong influence on overall disease transmission, and unrealistic
assumptions (e.g., “no contacts between children during school
dismissal”) can lead to overly optimistic expectations for the benefits
of school dismissal. To provide likely bounds on the effectiveness of school
dismissal policies for each combination of school dismissal policy and pandemic
scenario, we consider two assumptions, representing either a
“worst-case” (with a greater amount of contact during closure, in
which household contacts involving children are doubled, and child-related
contacts outside the home are reduced by only 30%) and a
“best-case” (with no change in household contacts and a 50%
reduction in outside contacts) scenario. In both cases, all schools, preschools,
daycares, and playgroups within the affected community (or communities) are
closed during dismissal, so no transmission occurs within these mixing groups.
Social contact surveys (<xref rid="R15" ref-type="bibr">Eames et al.,
2012</xref>) and mathematical model-based analysis of virological data
(<xref rid="R16" ref-type="bibr">Earn et al., 2012</xref>) during the 2009
summer and fall holiday breaks suggest that there is a reduction of at least
40–50% in contact and transmission among school-age children during such
regularly scheduled dismissals; pre-emptive coordinated school dismissals
undertaken as a countermeasure during an evolving pandemic would likely lead to
additional precautions, reducing contacts even further.</p><p id="P11">We also assume that a well-matched vaccine will be available 6 months
after the first U.S. index case. The assumed vaccine efficacy for susceptibility
VEs = 0.70 (VEs = 0.50 for age 65+) represents the reduced susceptibility to
infection and influenza illness of vaccinated individuals, while the vaccine
efficacy for infectiousness VEi = 0.80 (for all age groups) represents the
reduced infectiousness to others (<xref rid="R30" ref-type="bibr">Longini et
al., 2000</xref>). Full details about vaccine assumption are described in
the <xref rid="SD1" ref-type="supplementary-material">SI</xref>. To separate the
effects of school dismissal alone from that coupled with a vaccination campaign,
we will measure cumulative attack rates both before (on day 180) and after (on
day 240) vaccine introduction.</p></sec><sec id="S5"><label>2.3.</label><title>Sensitivity analysis</title><p id="P12">A model of a single community of 2000 persons is used to identify the
key model parameters and quantify their impact on the mitigation of disease
spread (<xref rid="R3" ref-type="bibr">Blower and Dowlatabadi, 1994</xref>). We
consider six contact settings: households, household clusters, neighborhoods,
communities, schools, and workplaces. Latin hypercube sampling is used to sample
the contact probability in each setting, then partial rank correlation
coefficients are calculated as the outcome measure for sensitivity analysis.
Full details are presented in the <xref rid="SD1" ref-type="supplementary-material">SI</xref>.</p></sec><sec id="S6"><label>2.4.</label><title>Model parameter calibration</title><p id="P13">The model of a small community was also used to develop an initial set
of model parameters for each of the five pandemic scenarios under consideration
(<xref rid="T1" ref-type="table">Table 1</xref>). The specified age-specific
attack-rate patterns, basic reproduction number R0, and case fatality ratios
were fit by adjusting the baseline EpiCast model contact rates (<xref rid="R20" ref-type="bibr">Germann et al., 2006</xref>) to give age-specific and
overall attack rates within 1% of the specified values. For instance, in order
to increase the childhood attack rate, the corresponding school contact rate is
increased. Similarly, to increase the working-age adult attack rate, the
workplace contact rate is raised.</p></sec><sec id="S7"><label>2.5.</label><title>Scoping studies</title><p id="P14">The regional (Chicago-area) model was used for an earlier study
involving EpiCast and two other individual-based, stochastic simulation models
(<xref rid="R25" ref-type="bibr">Halloran et al., 2008</xref>). Here, we use
it for scoping studies to evaluate the impact of the trigger and duration of
school dismissal, which will then be used to down-select to a smaller number of
scenarios to be evaluated using the more computationally expensive
national-scale model. The baseline parameters for each pandemic scenario are
adjusted slightly from their single-community values (reflecting the more
dispersed and heterogeneous population structure of the larger-scale model),
giving the model parameters listed in <xref rid="SD1" ref-type="supplementary-material">Table S1</xref> and baseline epidemic
curves shown in <xref rid="SD1" ref-type="supplementary-material">Fig.
S2</xref>. School dismissal options are then systematically studied by
considering all possible combinations of the model parameters listed in <xref rid="T1" ref-type="table">Table 1</xref>. With regard to the geographic
scale, this model considers either community-by-community or simultaneous
region-wide school dismissals. Furthermore, for the most severe and
transmissible 1918-like scenario D, longer durations of closure (e.g.,
16–24 weeks) are also explored.</p></sec><sec id="S8"><label>2.6.</label><title>National-scale simulation studies</title><p id="P15">For simulations of pandemic spread across the continental United States,
the manner of introduction of a pandemic influenza strain must be considered. In
particular, a human-transmissible strain may emerge either domestically or
overseas, in both cases most likely in a rural area. As discussed in the <xref rid="SD1" ref-type="supplementary-material">SI</xref>, the subsequent
epidemic will slowly spread through the more dispersed rural population before
reaching a dense urban population where it can thrive, and it is during this
early, rural, spread, whether in the U.S. or overseas, that early
characterization and vaccine development can begin. One plausible domestic
emergence scenario is modeled by the introduction of 10 infected individuals
into Sussex County, Delaware, a large poultry-farming region on the
Delaware-Maryland-Virginia (DelMarVa) peninsula. Previous studies (<xref rid="R20" ref-type="bibr">Germann et al., 2006</xref>) have found that
introduction via air travel into major metropolitan areas, or point source
introductions into large cities (either New York or Los Angeles), result in
nearly identical national-level incidence rates, with only a difference in the
details of the spatiotemporal spread. Consequently, we assume an introduction
via arriving international air passengers (2 per 10,000) for this overseas
scenario, a rate comparable with that used for the regional model.</p><p id="P16">Given the greatly increased computational cost of the national-scale
model, the comprehensive set of regional model results is used to identify the
most useful set of larger-scale simulations. As the two scenarios with the
highest clinical severity and the least and most transmissible spread, pandemic
scenarios C and D are both included in the national-scale study. School
dismissal is unlikely to be invoked for the low-transmissibility, low-severity
scenario A, so it is not considered further. While there are subtle differences
in results for scenarios B1 and B2, we focus on B2 due to its higher severity
and transmissibility than B1. We consider three geographic scales of school
dismissal for each of these scenarios: community, county, multi-county region
(including the affected county and all immediately adjacent counties), and
additionally a coordinated (simultaneous) state-wide dismissal for the
worst-case scenario D.</p></sec></sec><sec id="S9"><label>3.</label><title>Results</title><sec id="S10"><label>3.1.</label><title>Single community model</title><p id="P17">By attributing each new infection to a single source based on relative
contributions of contacts to the overall transmission probability, we find that
household transmission dominates (<sup>~</sup>40%), followed by the
age-appropriate daytime mixing group (school or work) (<sup>~</sup>30%)
and non-specific contact settings (also <sup>~</sup>30%), both for the
original contact parameters and for the modified contact parameters calibrated
for the five pandemic scenarios (<xref rid="SD1" ref-type="supplementary-material">Fig. S3</xref> in the Supplementary
information (SI)). This is consistent with the pattern used in other modeling
work, with perhaps a slightly increased household transmission. In accord with
this finding, sensitivity analyses performed on the single-community model
confirm that the assumed household, school, and workplace contacts (in that
order) have the greatest impact on the resulting cumulative attack rate, with
non-specific community transmission (which contributes to roughly a quarter of
all cases) following closely behind. The relationship between these contact
matrix elements and the epidemic timing is even more interesting. The partial
rank correlation coefficient (PRCC) shown in <xref rid="SD1" ref-type="supplementary-material">Fig. S4</xref>, which measures the
sensitivity of output variables to inputs, indicates that school transmission
has, by far, the largest impact on the number of days from initial outbreak to
peak incidence (a PRCC of −0.55), followed by household transmission
(−0.27) (The negative values simply indicate that for
<italic>increasing</italic> contact rates, the time to peak incidence
<italic>decreases</italic>.). Interestingly, the workplace contact rate PRCC
(+0.11) has the opposite (positive) sign, but its small magnitude may indicate
that this is merely a statistical fluke.</p></sec><sec id="S11"><label>3.2.</label><title>Regional model</title><p id="P18">The impacts of school dismissal policies for the regional model are
summarized in <xref rid="T2" ref-type="table">Table 2</xref>, which presents the
cumulative attack rate (averaged over five stochastic realizations) and its
reduction from its baseline value (without any school dismissal) under each
simulation scenario. The results in <xref rid="T2" ref-type="table">Table
2</xref> are for a shorter serial interval and “best-case”
contact rates (i.e., the least plausible amount of person-to-person contact)
during school dismissal (see <xref rid="S2" ref-type="sec">Methods</xref>);
corresponding tables for the longer serial interval and/or worst-case contact
patterns are provided in the <xref rid="SD1" ref-type="supplementary-material">SI</xref>, <xref rid="SD1" ref-type="supplementary-material">Tables
S2</xref>–<xref rid="SD1" ref-type="supplementary-material">S4</xref>. From <xref rid="T2" ref-type="table">Table 2</xref>, if we compare
community-wide and region-wide school dismissals of the same duration, pandemic
scenarios and diagnosis ratio, the reductions of overall clinical attack rate
for community-wide closures are usually higher than for region-wide closures for
pandemic scenarios A, B1, B2, and D (see <xref rid="S2" ref-type="sec">Methods</xref> for a description of pandemic scenarios). In pandemic
scenario C, with longer school dismissals (> 4 weeks), region-wide
dismissals most often have a greater attack rate reduction than the
community-wide closures. Similar trends are observed whether the cumulative
incidence is measured before (at day 180, <xref rid="SD1" ref-type="supplementary-material">Tables S5</xref>–<xref rid="SD1" ref-type="supplementary-material">S8</xref>) or after (at day 240, <xref rid="T2" ref-type="table">Tables 2</xref> and <xref rid="SD1" ref-type="supplementary-material">S2</xref>–<xref rid="SD1" ref-type="supplementary-material">S4</xref>) the onset of an assumed
vaccination campaign, particularly for the more transmissible scenarios B2 and
D. Consequently, we will limit our subsequent discussion to the post-vaccination
results based on the full 240-day simulation.</p><p id="P19">Further insight is provided by the epidemic curves for different
dismissal scenarios, such as those shown in <xref rid="F1" ref-type="fig">Fig.
1</xref> for the region-wide dismissal, shorter serial interval, worst-case
contact patterns, and trigger of 20 symptomatic children (i.e., dismissal upon
the first diagnosed case for a 5% diagnosis ratio). Here we can see that the
primary benefit of dismissals are to delay the epidemic peak, by 5–6 days
per week of dismissal for most pandemic scenarios, until the peak is postponed
long enough for vaccines to be introduced and reduce the spread. These delays
are comparable with the <sup>~</sup>5 days per week of dismissal recently
found with a compartmental model for more severe epidemics (with a 30% baseline
attack rate) (<xref rid="R18" ref-type="bibr">Fung et al., 2015</xref>). For the
mildest pandemic scenario C, the spread is so slow and the peak so late that it
is only delayed by 3–4 days per week of dismissal.</p></sec><sec id="S12"><label>3.3.</label><title>National model</title><p id="P20">For national-scale simulations, different manners of introduction of the
pandemic influenza strain resulted in different disease spread dynamics. For
instance, the emergence of a domestic strain from a rural area in the U.S. would
likely take longer to result in widespread transmission than the importation of
a novel virus from overseas which was already spreading from human to human
before arriving at an urban area (where international airports are located) in
the U.S. (see <xref rid="SD1" ref-type="supplementary-material">Figs. S7</xref>and <xref rid="SD1" ref-type="supplementary-material">S8 in the SI</xref>). In
addition to this, our simulation indicated that emergence of a domestic strain
in a rural area had a finite prob- ability of extinction, and its peak
transmission may lag behind 1–3 months compared to that of a novel virus
introduction into an urban area. For these reasons, we focus hereinafter on the
results from the national-scale models that assume an overseas emergence of the
novel virus with entry into the United States via air travel.</p><p id="P21">National-scale model outcomes, in terms of (symptomatic) cases averted
for two pandemic scenarios (B2 and D) for different dismissal triggers,
durations, and geographic scales, are presented in <xref rid="F2" ref-type="fig">Fig. 2</xref>. A different view of the impacts of varying spatial extent of
school dis- missal is shown in <xref rid="F3" ref-type="fig">Fig. 3</xref> for
pandemic scenarios B2 and D, with a 4-week closure after 20 symptomatic children
appear in a community (i.e., dismissing schools upon the first detected child at
a 5% diagnosis ratio). Epidemic curves are compared in the top panels for the
two considered contact rate changes upon school dismissal. In the bottom panels,
we show the number of schools closed over time. (These results are for the
worst-case contact-rate assumption; those for the best-care contact rates are
shown in <xref rid="SD1" ref-type="supplementary-material">Fig. S6</xref>.) As
shown in <xref rid="SD1" ref-type="supplementary-material">Figs. S9</xref> and
<xref rid="SD1" ref-type="supplementary-material">S10</xref>, the reduced
transmissibility of scenario C, combined with the slower spread across the
dispersed U.S. population, causes it to have not yet reached its epidemic peak
by the assumed availability date of an effective vaccine, six months after the
first introduction. As subsequent vaccination slows and ultimately stamps out
the outbreak, the effect of vaccination dominates the impact of any school
dismissal and precludes any further consideration of this scenario for the
national-scale model.</p><p id="P22">From <xref rid="F3" ref-type="fig">Fig. 3</xref>, we observe that
community-wide school dismissals reduce the peak incidence without significantly
delaying the time-to-peak incidence. On the other hand, multi-county and
state-wide school dismissals have more impact on delaying the time-to-peak than
reducing the peak incidence. Furthermore, county-wide school dismissals have a
similar time-to-epidemic-peak as multi-county and state-wide school dismissals,
but with a lower peak incidence than either. These results (<xref rid="F2" ref-type="fig">Fig. 2</xref>) for the effectiveness of community-wide
school-dis- missal strategies are consistent with the results for the regional
model (see <xref rid="T2" ref-type="table">Table 2</xref>). In particular, for a
low (but plausible) diagnosis ratio of 1%, waiting to close individual schools
until even the first detected case may never occur. Efficacy increases with both
the diagnosis ratio and duration, although a diminishing return is observed for
longer dismissal durations, in particular the extended 16- and 20-week durations
for scenario D. However, the chief advantage of the national-scale model is that
it allows us to explore varying geographic scales of school dismissal. We find
that the optimal geographic scale of school dismissal depends on the duration
and trigger/diagnosis ratio (see <xref rid="F2" ref-type="fig">Fig. 2</xref>).
More proactive dismissals (i.e., those over broader geographic regions) are only
advantageous if the closure is sufficiently long to enable vaccination, which
often means a month or longer dismissal. Additionally, more proactive school
dismissals over a larger geographic area (multi-county, or state level) will be
more appropriate (and effective, see <xref rid="F2" ref-type="fig">Fig.
2</xref>) for settings where influenza surveillance is less sensitive (i.e.,
where the diagnosis ratio is likely to be low).</p></sec><sec id="S13"><label>3.4.</label><title>Observations</title><p id="P23">From these regional and national model results, several observations can
be made. First, the main effect of school dismissals across wider geographic
scales is to slow the spread of the virus, as reflected by delayed time-to-peak,
which confers multiple benefits. One is to delay and reduce peak demand for
healthcare, which is particularly important at the start of a pandemic when
systems are not yet prepared to deal with an ever-increasing patient load. An
even greater benefit is achieved if this delay extends sufficiently long for an
effective vaccine to be developed, produced, and distributed to the population
(see <xref rid="F3" ref-type="fig">Fig. 3</xref>). Second, the effects of school
closure are very sensitive to the ability of the local surveillance system to
detect influenza circulation and, in turn, provide a “trigger” for
closing schools. For a diagnosis ratio as low as 1%, which might occur if
laboratory confirmation is required (<xref rid="R37" ref-type="bibr">Reed et
al., 2009</xref>), dismissals may not be triggered in time and, thus, will
have no effect on morbidity (see <xref rid="T2" ref-type="table">Table
2</xref>). In contrast, when surveillance systems are able to detect 5% or more
influenza cases in the community, school closures of any duration and on any
scale start reducing cumulative incidence, with the effect being particularly
prominent for closures lasting 8 weeks or longer (see <xref rid="F2" ref-type="fig">Fig. 2</xref>).</p><p id="P24">Finally, school closures for shorter duration of closure (1–4
weeks) generally result in a greater number of cases averted at the local
community level, compared to simultaneous school closures of the same duration
implemented over a larger geographic area (county, multi-county, or state [see
<xref rid="F2" ref-type="fig">Fig. 2</xref>]). However, such simultaneous
(coordinated) school closures proactively implemented over a wider region are
usually superior in terms of number of cases averted if the closure is sustained
over a longer period of time (8 weeks or more [see <xref rid="F2" ref-type="fig">Fig. 2</xref>]). In addition, simultaneous (proactive) school dismissal
policies more effectively delay the spread of the disease compared to the
community-wide school closures of the same duration, albeit at the greater cost
to society due to the larger number of schools that must remain closed than if
the closures were implemented on an individual community-by-community basis (see
bottom panels of <xref rid="F3" ref-type="fig">Fig. 3</xref>). By primarily
slowing, rather than reducing, the disease spread, such closures are capable of
reducing the peak burden significantly if the delay extends into the time window
when vaccines become available. In contrast, individual school dismissals do not
have a substantial impact on when the peak burden is reached, but if implemented
promptly after the occurrence of a few initial cases within a school or school
district, they may help reduce its magnitude and, thus, the transitory surge on
the healthcare system (see top panels of <xref rid="F3" ref-type="fig">Fig.
3</xref>).</p></sec></sec><sec id="S14"><label>4.</label><title>Discussion</title><p id="P25">The primary benefit of pre-emptive school dismissals in mitigating the
spread of a novel influenza virus is the delayed time-to-peak that is seen in
dismissals of any duration considered in our study, typically by 4–6 days for
each week of dismissal. Delaying local outbreak peaks helps to decompress the demand
on the healthcare system during the initial pandemic wave and, under certain
circumstances, it may help “buy time” to prepare and roll out a
pandemic vaccine. That the main effect of school dismissals is delaying the
time-to-peak is fully consistent with the nature of an intervention that does not
provide specific protection. Overall, longer pre-emptive school dismissals
(≥4 weeks) implemented simultaneously on a wider geographic scale (e.g.,
county level or wider) are most impactful in mitigating an influenza pandemic in its
early stages, while awaiting the production and distribution of a pandemic vaccine.
However, as <xref rid="F1" ref-type="fig">Fig. 1</xref> indicates, for highly
transmissible strains, it may be difficult to close schools long enough to delay the
epidemic peak until vaccines become available. Thus, efforts to increase the speed
of vaccine production and distribution are essential to ensure that the time bought
by school dismissal yields the optimal benefit (<xref rid="R2" ref-type="bibr">Biggerstaff et al., 2015</xref>).</p><p id="P26">In addition to delaying the time-to-peak, school dismissals of sufficient
duration implemented pre-emptively on a wide-enough geographic scale may also reduce
the cumulative attack rate. Our results suggest that shorter precisely targeted
dismissals (1–4 weeks) implemented on an individual community-by-community
basis following detection of initial cases among students at these schools appear to
be superior to dismissals of the same duration implemented in a coordinated
county-wide, multi-county, or state-wide manner. However, such dismissals may not be
feasible in practice, as precise targeting requires prompt laboratory confirmation
of initial cases in each and every community, coupled with quick dismissal of an
affected school before virus spread occurs within the school and between the school
and the surrounding community. For longer (multi-month) dismissals, we find that a
greater reduction in cases is achieved by coordinated larger-scale dismissals
(county-level or wider), being proactive rather than waiting until cases are
detected in each individual community. Therefore, for the most severe pandemic
scenarios, we believe that the optimal geographic unit for implementation of
pre-emptive school closures as a pandemic countermeasure will be county-wide or
beyond.</p><p id="P27">For less transmissible strains causing severe disease (e.g., a potential
H5N1-like scenario) represented by the scenario C in our study, the effect of school
dismissal on cumulative disease incidence is quite pronounced, even for shorter
dismissals implemented on a narrower geographic scale. The already-low
transmissibility (low R<sub>0</sub>) in such a scenario provides an opportunity to
achieve local extinction by strategically targeted and timed school closure
following the initial local introduction even without vaccination. In contrast, for
the most transmissible strains associated with a high clinical disease severity
considered in our study (i.e., scenario D comparable to 1918), a significant
reduction in cumulative disease incidence by school closure alone may only be
possible when schools are out of session for 16 weeks or longer, at a county-wide or
wider geographic scale. It should be noted, how- ever, that depending on the timing
of the initial pandemic waves, the effect of a long continuous school dismissal (16+
weeks) may be realized through a combination of planned school holidays and an
additional dismissal (or delayed start of a semester) in response to the
pandemic.</p><p id="P28">These results highlight an important practical issue, namely that the
effectiveness of school dismissals is highly dependent on the local surveillance
systems’ ability to quickly detect virus transmission in communities and,
thus, implement (or “trigger”) the intervention in a timely fashion.
Delayed detection, associated with a less-sensitive surveillance method (e.g., by
waiting for laboratory confirmation) results in a delayed implementation of the
intervention and, thus, a diminished effect with regard to slowing down the
transmission. For a low diagnosis ratio of 1%, delaying the closure of individual
schools (or communities) until a child there is confirmed is a threshold that may
never be reached. (For a 2000-person community in which 22% of the population is
school-aged, there are only 440 school children; it is unlikely that 100 of them
will be ill at the same time.) In these cases, more sensitive triggers or
surveillance approaches may be needed to ensure school outbreaks are identified
promptly. Interestingly, the opposite behavior is observed for simultaneous school
dismissal. In that case, the greater risk is closing (and then reopening) schools
too quickly before the epidemic reaches its peak. For a low diagnosis ratio, this is
the only choice, and may be the most realistic in practice: if a school has so many
affected students that it is forced to close, neighboring schools will benefit by
proactively dismissing. In a way, the original school (which is unlikely to benefit
from closing, since it may be too late) will serve as a sentinel event, signaling
the impending risk of severity to surrounding communities. Given the extreme
sensitivity of the effects of school dismissals to early detection of initial cases,
an aggressive surveillance system, coupled with intense pre-pandemic planning for
rapid implementation of community-based interventions such as school dis- missals,
is needed in all settings. This may be particularly important in dense urban
settings around major international hubs, where introductions of novel influenza
virus strains are most probable and where an extremely high population density may
facilitate transmission of strains that may be less capable of circulating in more
sparsely populated areas.</p><p id="P29">To our knowledge, this is the first study that systematically explored
potential effects of school closures implemented on different geographic scales
relevant for the U.S. (corresponding to local, county, regional/ state, and national
governmental authorities) and in different pandemic severity scenarios.</p><p id="P30">Our findings are consistent with previously published studies considering
school closures as the only intervention in response to an evolving pandemic. In
particular, prior observational and modeling studies suggested that schools are the
key community setting for pandemic influenza transmission (<xref rid="R10" ref-type="bibr">Chao et al., 2010</xref>; <xref rid="R21" ref-type="bibr">Gog et
al., 2014</xref>). School closures have been found to be effective in slowing
down influenza transmission, whether implemented as a mitigation strategy or due to
other reasons (e.g., regular school breaks, teacher’s strike, etc.) (<xref rid="R16" ref-type="bibr">Earn et al., 2012</xref>; <xref rid="R12" ref-type="bibr">Copeland et al., 2013</xref>; <xref rid="R11" ref-type="bibr">Chowell et al., 2011</xref>; <xref rid="R26" ref-type="bibr">Heymann et al.,
2004</xref>; <xref rid="R31" ref-type="bibr">Markel et al., 2007</xref>). In
addition, other modeling studies have explored school closure as a mitigation
strategy (<xref rid="R25" ref-type="bibr">Halloran et al., 2008</xref>; <xref rid="R22" ref-type="bibr">Haber et al., 2007</xref>; <xref rid="R32" ref-type="bibr">Milne et al., 2008</xref>; <xref rid="R23" ref-type="bibr">Halder et al., 2010</xref>; <xref rid="R27" ref-type="bibr">Lee et al.,
2010</xref>; <xref rid="R24" ref-type="bibr">Halder et al., 2011</xref>; <xref rid="R4" ref-type="bibr">Brown et al., 2011</xref>; <xref rid="R33" ref-type="bibr">Milne et al., 2013</xref>; <xref rid="R17" ref-type="bibr">Fumanelli et al., 2016</xref>; <xref rid="R14" ref-type="bibr">De LuCa et al.,
2018</xref>). However, to our knowledge, ours is the most comprehensive modeling
study to evaluate the effectiveness of different school-closure strategies –
including the tradeoffs between local, regional, and national dismissals – in
mitigating influenza in the United States during an evolving pandemic. Model
adjustments and validation were undertaken to address the research question at hand
using the best currently available empirical and observational data for model
parameterization, and sensitivity analyses were used to test the robustness of key
findings.</p><p id="P31">As has been comprehensively reviewed by (<xref rid="R39" ref-type="bibr">Riley 2007</xref>) and Carrasco et al (<xref rid="R5" ref-type="bibr">Carrasco
et al., 2013</xref>), the great flexibility of such models is also their
Achilles heel, as model developers, users, and consumers often construct models and
parameters in data-poor (or data-free) environments. Intentionally (as is most
always the case) or not, these decisions can lead to greater confidence in model
predictions than may be warranted, given their typically tenuous tie to observed
truth. However, although quantitative model predictions should generally be viewed
with a healthy appreciation for their limitations, in many cases, qualitative trends
have been proven to be reliable and useful in pre-pandemic planning efforts (<xref rid="R7" ref-type="bibr">Centers for Disease Control and Prevention,
2007</xref>). We have endeavored to consider and address the key limitations that
are always present in mathematical modeling studies. In the present case, the
greatest uncertainty concerns how contact rates (within different mixing groups and
ages) might change during the disruption accompanying an unplanned school dismissal.
These will presumably vary with time (as a so-called “fear-based social
distancing” gradually decays towards normal contact rate patterns), and
severity (e.g., the greater case fatality ratio of pandemic scenarios C and D are
more likely to lead to a greater acceptance of, and compliance with, recommended
social distancing measures. Currently, to our knowledge, there are no empirical data
to inform how contact patterns may change during a prolonged closure; without such
data, this limitation cannot be confidently addressed. On the disease side, there
remains a great deal of variability and uncertainty about the natural history of
influenza, most notably its serial interval (we considered two possibilities which
bracket the likely range) and the role of asymptomatic individuals in transmission
(we have assumed 50% of all cases are asymptomatic; previous studies assume either
30% or 50%). As mentioned previously, the triggering of any mitigation measures is
dependent upon a timely detection, while realistic diagnosis ratios for pandemic
planning purposes remain uncertain (<xref rid="R1" ref-type="bibr">Biggerstaff et
al., 2012</xref>).</p><p id="P32">In addition to testing the effects of school closures with regard to timing,
duration, and geographic scale of their implementation during an evolving pandemic
prior to vaccine rollout, we have performed several analyses to test the robustness
of our key findings. A sensitivity and uncertainty analysis demonstrates that
schools are the key community setting for influenza transmission, apart from
households. Hence, reducing school transmission provides the greatest lever for
slowing the disease spread before vaccination. While such analyses have rarely been
performed for large, complex simulation models, many further questions remain for
future research. For example, it would be important to explore to what extent the
networking of multiple communities, as in our regional and national models, affects
these parameter sensitivities and variability of outcomes through nonlinear effects.
Since it is impossible to predict the precise characteristics of the next pandemic
influenza strain, and the efficacy of potential pharmaceutical and
non-pharmaceutical countermeasures, the results presented here are somewhat
qualitative in nature. However, during the next pandemic, the real-time estimation
of these key unknowns (a challenging task in itself) will constrain models such as
those presented here, thus yielding quantitative, testable predictions.</p><p id="P33">Finally, we note that the present study also identifies several areas in
which further research should be carried out. As is often the case with modeling
studies, new empirical data are essential to further constrain and corroborate the
models, particularly with regard to contact rates during times of social disruption,
including school closures. We recognize that school dismissal incurs substantial
economic and societal costs (in addition to removing a convenient location for
implementing a childhood vaccination campaign), and a more complete economic
analysis should be performed before recommending any specific policies. Several
economic analyses of different policy options have been reported (<xref rid="R6" ref-type="bibr">Cauchemez et al., 2009</xref>; <xref rid="R24" ref-type="bibr">Halder et al., 2011</xref>; <xref rid="R4" ref-type="bibr">Brown et al.,
2011</xref>; <xref rid="R33" ref-type="bibr">Milne et al., 2013</xref>; <xref rid="R35" ref-type="bibr">Nishiura et al., 2014</xref>), but a more
comprehensive economic analysis of school closures as a pandemic mitigation
strategy, both on its own and in conjunction with pandemic vaccination, would be
helpful, as well as further consideration of societal options that may mitigate the
secondary impact of school closures.</p></sec><sec sec-type="supplementary-material" id="SM1"><title>Supplementary Material</title><supplementary-material content-type="local-data" id="SD1"><label>SI</label><media xlink:href="NIHMS1065432-supplement-SI.docx" orientation="portrait" xlink:type="simple" id="d36e779" position="anchor"></media></supplementary-material></sec></body><back><ack id="S15"><title>Acknowledgements</title><p id="P34">We gratefully acknowledge Martin Meltzer, Noreen Qualls, Jeanette Rainey,
Stephen Redd, and David Swerdlow for their support and advice during this study.</p><p id="P35">This work was sponsored by the United States Centers for Disease Control and
Prevention. Los Alamos National Laboratory, an affirmative action/equal opportunity
employer, is operated by Los Alamos National Security, LLC, for the National Nuclear
Security Administration of the United States Department of Energy under contract
DE-AC52-06NA25396. Because this research did not involve human subjects, it was not
subject to IRB review requirements.</p></ack><fn-group><fn id="FN3"><p id="P36">Disclaimer</p><p id="P37">The findings and conclusions in this report are those of the authors and
do not necessarily represent the official position of the Centers for Disease
Control and Prevention.</p></fn><fn id="FN4"><p id="P38">Appendix A. Supplementary data</p><p id="P39">Supplementary material related to this article can be found, in the
online version, at doi: <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/j.epidem.2019.100348">https://doi.org/10.1016/j.epidem.2019.100348</ext-link>.</p></fn></fn-group><ref-list><title>References</title><ref id="R1"><mixed-citation publication-type="journal"><name><surname>Biggerstaff</surname><given-names>M</given-names></name>, <name><surname>Jhung</surname><given-names>M</given-names></name>, <name><surname>Kamimoto</surname><given-names>L</given-names></name>, <name><surname>Balluz</surname><given-names>L</given-names></name>, <name><surname>Finelli</surname><given-names>L</given-names></name>, <year>2012</year><article-title>Self-reported influenza-like illness
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<fpage>684</fpage>–<lpage>689</lpage>.<pub-id pub-id-type="pmid">15353055</pub-id></mixed-citation></ref></ref-list></back><floats-group><fig id="F1" orientation="portrait" position="float"><label>Fig. 1.</label><caption><p id="P40">Effect of school dismissal duration upon epidemic curves for
simultaneous (region-wide) school dismissal for the regional model (the Chicago
metropolitan area, with 8.6 M people). Results are shown for the shorter serial
interval and nominal (worst-case) contact rate changes upon dismissal, activated
when 20 children are symptomatic in a community (i.e., closure upon the first
diagnosed case if the diagnosis ratio is 5%). Results are shown for five
pandemic scenarios: four historically referenced 20th century influenza
pandemics (A: 2009, B1:1968, B2: 1957, D: 1918) and a fifth scenario (C) that
corresponds to a clinically severe but less transmissible pandemic.</p></caption><graphic xlink:href="nihms-1065432-f0001"></graphic></fig><fig id="F2" orientation="portrait" position="float"><label>Fig. 2.</label><caption><p id="P41">U.S. model predictions of the number of (symptomatic) influenza cases
averted by a combination of self-isolation, school dismissals, and vaccination,
for the shorter serial interval. School dismissal is activated when one
symptomatic child is diagnosed at an assumed diagnosis ratio of 5%, 10%, or 20%.
Two alternative assumptions for contact rates (CR) during school dismissal are
considered: “worst-case” (filled bars: CR involving children in
households are doubled and child-related contacts outside the home are reduced
by 30%) and “best-case” (extensions: CR involving children in
households are unchanged, and child-related contacts outside the home are
reduced by 50%). Beginning on day 180, 1 million people per day are vaccinated
(see text and <xref rid="SD1" ref-type="supplementary-material">SI</xref> for
details).</p></caption><graphic xlink:href="nihms-1065432-f0002"></graphic></fig><fig id="F3" orientation="portrait" position="float"><label>Fig. 3.</label><caption><p id="P42">U.S. model results for pandemic scenarios B2 (left panels) and D (right
panels). School dismissal activated when 20 children are symptomatic (closure
upon first diagnosed at a 5% diagnosis ratio) and a 4-week duration, for the
shorter serial interval. (Top) Epidemic curves. (Bottom) Number of schools
closed at any time during the outbreak. The “worst- case”
assumption for contact rates during school dismissal is used (contact rates
involving children in households are doubled, and child-related contacts outside
the home are reduced by 30%). Analogous results for the
“best-case” contact rates are shown in <xref rid="SD1" ref-type="supplementary-material">Fig. S6</xref>. Beginning on day 180, 1
million people per day are vaccinated (see text and <xref rid="SD1" ref-type="supplementary-material">SI</xref> for details). Note that for
scenario D, the multi-county and state-wide dismissals are virtually
indistinguishable, particularly for the epidemic curves.</p></caption><graphic xlink:href="nihms-1065432-f0003"></graphic></fig><table-wrap id="T1" position="float" orientation="landscape"><label>Table 1</label><caption><p id="P43">Summary of key EpiCast model parameters for this study (see <xref rid="SD1" ref-type="supplementary-material">Supporting Online
Material</xref> and Germann et al (<xref rid="R20" ref-type="bibr">Germann
et al., 2006</xref>) for further details).</p></caption><table frame="hsides" rules="none"><colgroup span="1"><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col></colgroup><thead><tr><th align="left" valign="middle" rowspan="1" colspan="1">Parameter</th><th align="left" valign="middle" rowspan="1" colspan="1">Options</th><th align="left" valign="middle" rowspan="1" colspan="1">Key attributes</th><th align="left" valign="middle" rowspan="1" colspan="1"></th><th align="left" valign="middle" rowspan="1" colspan="1"></th><th align="left" valign="middle" rowspan="1" colspan="1"></th><th align="left" valign="middle" rowspan="1" colspan="1"></th></tr><tr><th colspan="7" align="left" valign="middle" rowspan="1"><hr></hr></th></tr></thead><tbody><tr><td align="left" valign="top" rowspan="1" colspan="1">Pandemic scenario<sup><xref rid="TFN1" ref-type="table-fn">a</xref></sup></td><td align="left" valign="top" rowspan="1" colspan="1">A(2009 like)</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">18% (32%, 15%, 7%), 1.3</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td rowspan="2" align="left" valign="top" colspan="1"> Overall and age-specific (child, adult,
elderly<sup><xref rid="TFN2" ref-type="table-fn">b</xref></sup>)
attack rates and R<sub>0</sub></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">B1(1968 like)</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">22% (39%, 18%, 8%), 1.5</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">B2(1957 like)</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">28% (50%, 23%, 11%), 1.8</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">C(H5N1 like)</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">10% (18%, 8%, 4%), 1.2</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">D(1918 like)</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">30% (54%, 25%, 12%), 2.0</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">Serial interval<sup><xref rid="TFN3" ref-type="table-fn">c</xref></sup></td><td align="left" valign="top" rowspan="1" colspan="1">Short</td><td align="left" valign="top" rowspan="1" colspan="1">1.98, 1.98, 1.61 days</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td rowspan="2" colspan="2" align="left" valign="top"> Mean
latent, incubation, and infectious period durations</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">Long</td><td align="left" valign="top" rowspan="1" colspan="1">1.2, 1.9, 4.1 days</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">School dismissal trigger<sup><xref rid="TFN4" ref-type="table-fn">d</xref></sup></td><td align="left" valign="top" rowspan="1" colspan="1">1%</td><td align="left" valign="top" rowspan="1" colspan="1">100</td><td rowspan="3" colspan="4" align="left" valign="top"> Diagnosis ratio<sup><xref rid="TFN3" ref-type="table-fn">c</xref></sup> (percentage of symptomatic
individuals correctly identified) and corresponding number of
symptomatic schoolchildren in a community required to trigger
dismissal</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">5%</td><td align="left" valign="top" rowspan="1" colspan="1">20</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">10%</td><td align="left" valign="top" rowspan="1" colspan="1">10</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">20%</td><td align="left" valign="top" rowspan="1" colspan="1">5</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">School dismissal duration</td><td colspan="2" align="left" valign="top" rowspan="1">1, 2, 4, 8, and 12 weeks</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td colspan="3" align="left" valign="top" rowspan="1">and 16, 20, 24 weeks for scenario
D</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">School dismissal geographic scale</td><td align="left" valign="top" rowspan="1" colspan="1">Community</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td colspan="3" align="left" valign="top" rowspan="1">For regional model: Community or
Regional</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">County</td><td colspan="5" align="left" valign="top" rowspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">Multi-county</td><td colspan="5" align="left" valign="top" rowspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">State</td><td colspan="5" align="left" valign="top" rowspan="1"></td></tr><tr><td rowspan="2" align="left" valign="top" colspan="1">Child-related contact changes
during dismissal</td><td align="left" valign="top" rowspan="1" colspan="1">Worst-case</td><td colspan="3" align="left" valign="top" rowspan="1"> 100% increase in
child-related household contacts</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td colspan="3" align="left" valign="top" rowspan="1"> 30% reduction in
child-related non-household contacts</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">Best-case</td><td colspan="3" align="left" valign="top" rowspan="1"> No change in
child-related household contacts</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td colspan="3" align="left" valign="top" rowspan="1"> 50% reduction in
child-related non-household contacts</td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td></tr></tbody></table><table-wrap-foot><fn id="TFN1"><label>a</label><p id="P44">Pandemic scenarios are based on a two-dimensional framework recently
developed by (<xref rid="R38" ref-type="bibr">Reed et al.
(2013)</xref>).</p></fn><fn id="TFN2"><label>b</label><p id="P45">Ages 0–18 years are considered children, 19–64 adult,
and 65+ years elderly.</p></fn><fn id="TFN3"><label>c</label><p id="P46">The serial interval, or generation time, is the interval between
successive cases in a chain of transmission.</p></fn><fn id="TFN4"><label>d</label><p id="P47">School dismissal is triggered when the first confirmed symptomatic
school-age child is detected in a community. The diagnosis ratio is the
percentage of symptomatic individuals that are positively identified; for
instance, with a 5% diagnosis ratio, the first confirmed case may not be
identified until 20 children are symptomatic.</p></fn></table-wrap-foot></table-wrap><table-wrap id="T2" position="float" orientation="landscape"><label>Table 2:</label><caption><p id="P48">Cumulative attack rates (AR) with the reduction from the baseline
scenario in parentheses (δ) using the regional model, with the shorter
(mean <sup>~</sup>2.8 day) serial interval and best-case contact pattern
change (a 50% reduction in non-household contacts) during school dismissal.
Analogous tables for the longer serial interval and/or worst-case contact
patterns are provided in the <xref rid="SD1" ref-type="supplementary-material">SI</xref>.</p></caption><table frame="hsides" rules="none"><colgroup span="1"><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col><col align="left" valign="middle" span="1"></col></colgroup><thead><tr><th align="left" valign="top" rowspan="1" colspan="1">Pandemic scenario</th><th align="left" valign="top" rowspan="1" colspan="1">Baseline Clinical Attack Rate<sup><xref rid="TFN5" ref-type="table-fn">a</xref></sup></th><th align="left" valign="top" rowspan="1" colspan="1">Trigger</th><th colspan="5" align="left" valign="top" rowspan="1">Community School
Dismissal<sup><xref rid="TFN7" ref-type="table-fn">c</xref></sup></th><th colspan="5" align="left" valign="top" rowspan="1">Regional School
Dismissal<sup><xref rid="TFN7" ref-type="table-fn">c</xref></sup></th></tr><tr><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1"></th><th colspan="5" align="left" valign="top" rowspan="1"><hr></hr></th><th colspan="5" align="left" valign="top" rowspan="1"><hr></hr></th></tr><tr><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1">Diag. ratio<sup><xref rid="TFN6" ref-type="table-fn">b</xref></sup></th><th colspan="5" align="left" valign="top" rowspan="1">Duration</th><th colspan="5" align="left" valign="top" rowspan="1">Duration</th></tr><tr><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1"></th><th colspan="5" align="left" valign="top" rowspan="1"><hr></hr></th><th colspan="5" align="left" valign="top" rowspan="1"><hr></hr></th></tr><tr><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1"></th><th align="left" valign="top" rowspan="1" colspan="1">1 wk<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">2 wks<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">4 wks<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">8 wks<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">12 wks<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">1 wk<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">2 wks<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">4 wks<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">8 wks<break></break>AR(δ)</th><th align="left" valign="top" rowspan="1" colspan="1">12 wks<break></break>AR(δ)</th></tr><tr><th colspan="13" align="left" valign="top" rowspan="1"><hr></hr></th></tr></thead><tbody><tr><td align="left" valign="top" rowspan="1" colspan="1">A (2009-like)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4%</td><td align="left" valign="top" rowspan="1" colspan="1">1%</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">18.4 (0.0)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">5%</td><td align="left" valign="top" rowspan="1" colspan="1">17.1 (1.3)</td><td align="left" valign="top" rowspan="1" colspan="1">16.6 (1.8)</td><td align="left" valign="top" rowspan="1" colspan="1">16.4 (2.1)</td><td align="left" valign="top" rowspan="1" colspan="1">16.2 (2.2)</td><td align="left" valign="top" rowspan="1" colspan="1">16.1 (2.3)</td><td align="left" valign="top" rowspan="1" colspan="1">17.9 (0.5)</td><td align="left" valign="top" rowspan="1" colspan="1">17.3 (1.1)</td><td align="left" valign="top" rowspan="1" colspan="1">14.9 (3.5)</td><td align="left" valign="top" rowspan="1" colspan="1">8.2 (10.2)</td><td align="left" valign="top" rowspan="1" colspan="1">3.0 (15.4)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">10%</td><td align="left" valign="top" rowspan="1" colspan="1">14.6 (3.8)</td><td align="left" valign="top" rowspan="1" colspan="1">12.8 (5.6)</td><td align="left" valign="top" rowspan="1" colspan="1">11.8 (6.6)</td><td align="left" valign="top" rowspan="1" colspan="1">10.9 (7.5)</td><td align="left" valign="top" rowspan="1" colspan="1">10.5 (7.9)</td><td align="left" valign="top" rowspan="1" colspan="1">18.1 (0.4)</td><td align="left" valign="top" rowspan="1" colspan="1">17.4 (1.0)</td><td align="left" valign="top" rowspan="1" colspan="1">15.0 (3.4)</td><td align="left" valign="top" rowspan="1" colspan="1">9.7 (8.7)</td><td align="left" valign="top" rowspan="1" colspan="1">4.5 (13.9)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">20%</td><td align="left" valign="top" rowspan="1" colspan="1">12.5 (5.9)</td><td align="left" valign="top" rowspan="1" colspan="1">8.4 (10.0)</td><td align="left" valign="top" rowspan="1" colspan="1">6.0 (12.4)</td><td align="left" valign="top" rowspan="1" colspan="1">5.0 (13.4)</td><td align="left" valign="top" rowspan="1" colspan="1">4.5 (13.9)</td><td align="left" valign="top" rowspan="1" colspan="1">17.9 (0.5)</td><td align="left" valign="top" rowspan="1" colspan="1">17.1 (1.3)</td><td align="left" valign="top" rowspan="1" colspan="1">15.9 (2.5)</td><td align="left" valign="top" rowspan="1" colspan="1">10.7 (7.7)</td><td align="left" valign="top" rowspan="1" colspan="1">5.0 (13.4)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">B1 (1968-like)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6%</td><td align="left" valign="top" rowspan="1" colspan="1">1%</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.6 (0.0)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">5%</td><td align="left" valign="top" rowspan="1" colspan="1">21.1 (1.5)</td><td align="left" valign="top" rowspan="1" colspan="1">20.6 (2.0)</td><td align="left" valign="top" rowspan="1" colspan="1">20.2 (2.4)</td><td align="left" valign="top" rowspan="1" colspan="1">19.7 (2.9)</td><td align="left" valign="top" rowspan="1" colspan="1">19.5 (3.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.5 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">22.3 (0.3)</td><td align="left" valign="top" rowspan="1" colspan="1">21.6 (1.0)</td><td align="left" valign="top" rowspan="1" colspan="1">15.6 (7.0)</td><td align="left" valign="top" rowspan="1" colspan="1">7.9 (14.7)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">10%</td><td align="left" valign="top" rowspan="1" colspan="1">19.4 (3.2)</td><td align="left" valign="top" rowspan="1" colspan="1">17.9 (4.6)</td><td align="left" valign="top" rowspan="1" colspan="1">16.3 (6.3)</td><td align="left" valign="top" rowspan="1" colspan="1">14.2 (8.4)</td><td align="left" valign="top" rowspan="1" colspan="1">13.3 (9.3)</td><td align="left" valign="top" rowspan="1" colspan="1">22.5 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">22.4 (0.2)</td><td align="left" valign="top" rowspan="1" colspan="1">21.7 (0.9)</td><td align="left" valign="top" rowspan="1" colspan="1">17.2 (5.3)</td><td align="left" valign="top" rowspan="1" colspan="1">9.6 (13.0)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">20%</td><td align="left" valign="top" rowspan="1" colspan="1">18.9 (3.7)</td><td align="left" valign="top" rowspan="1" colspan="1">16.0 (6.6)</td><td align="left" valign="top" rowspan="1" colspan="1">12.6 (10.0)</td><td align="left" valign="top" rowspan="1" colspan="1">9.2 (13.4)</td><td align="left" valign="top" rowspan="1" colspan="1">7.5 (15.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.5 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">22.4 (0.2)</td><td align="left" valign="top" rowspan="1" colspan="1">22.0 (0.6)</td><td align="left" valign="top" rowspan="1" colspan="1">18.3 (4.3)</td><td align="left" valign="top" rowspan="1" colspan="1">10.5 (12.0)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">B2 (1957-like)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3%</td><td align="left" valign="top" rowspan="1" colspan="1">1%</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">5%</td><td align="left" valign="top" rowspan="1" colspan="1">25.6 (2.7)</td><td align="left" valign="top" rowspan="1" colspan="1">24.5 (3.8)</td><td align="left" valign="top" rowspan="1" colspan="1">23.3 (5.0)</td><td align="left" valign="top" rowspan="1" colspan="1">22.0 (6.4)</td><td align="left" valign="top" rowspan="1" colspan="1">21.4 (6.9)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.2 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">27.0 (1.3)</td><td align="left" valign="top" rowspan="1" colspan="1">19.7 (8.7)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">10%</td><td align="left" valign="top" rowspan="1" colspan="1">25.2 (3.1)</td><td align="left" valign="top" rowspan="1" colspan="1">23.8 (4.5)</td><td align="left" valign="top" rowspan="1" colspan="1">21.5 (6.9)</td><td align="left" valign="top" rowspan="1" colspan="1">16.7 (11.6)</td><td align="left" valign="top" rowspan="1" colspan="1">14.0 (14.4)</td><td align="left" valign="top" rowspan="1" colspan="1">28.2 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.2 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">27.2 (1.1)</td><td align="left" valign="top" rowspan="1" colspan="1">20.7 (7.6)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">20%</td><td align="left" valign="top" rowspan="1" colspan="1">26.2 (2.1)</td><td align="left" valign="top" rowspan="1" colspan="1">24.8 (3.5)</td><td align="left" valign="top" rowspan="1" colspan="1">21.5 (6.8)</td><td align="left" valign="top" rowspan="1" colspan="1">14.6 (13.7)</td><td align="left" valign="top" rowspan="1" colspan="1">9.4 (18.9)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">28.3 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">28.2 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">27.5 (0.8)</td><td align="left" valign="top" rowspan="1" colspan="1">22.4 (5.9)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">C (H5Nl-like)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1%</td><td align="left" valign="top" rowspan="1" colspan="1">1%</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">12.1 (0.0)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">5%</td><td align="left" valign="top" rowspan="1" colspan="1">11.5 (0.6)</td><td align="left" valign="top" rowspan="1" colspan="1">11.1 (1.0)</td><td align="left" valign="top" rowspan="1" colspan="1">11.0 (1.1)</td><td align="left" valign="top" rowspan="1" colspan="1">11.1 (1.0)</td><td align="left" valign="top" rowspan="1" colspan="1">11.1 (1.0)</td><td align="left" valign="top" rowspan="1" colspan="1">11.0 (1.1)</td><td align="left" valign="top" rowspan="1" colspan="1">9.5 (2.6)</td><td align="left" valign="top" rowspan="1" colspan="1">6.2 (5.9)</td><td align="left" valign="top" rowspan="1" colspan="1">2.8 (9.3)</td><td align="left" valign="top" rowspan="1" colspan="1">0.9 (11.2)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">10%</td><td align="left" valign="top" rowspan="1" colspan="1">9.1 (3.0)</td><td align="left" valign="top" rowspan="1" colspan="1">7.7 (4.4)</td><td align="left" valign="top" rowspan="1" colspan="1">7.0 (5.1)</td><td align="left" valign="top" rowspan="1" colspan="1">6.9 (5.2)</td><td align="left" valign="top" rowspan="1" colspan="1">6.9 (5.2)</td><td align="left" valign="top" rowspan="1" colspan="1">11.2 (0.9)</td><td align="left" valign="top" rowspan="1" colspan="1">10.0 (2.1)</td><td align="left" valign="top" rowspan="1" colspan="1">7.2 (4.9)</td><td align="left" valign="top" rowspan="1" colspan="1">3.8 (8.3)</td><td align="left" valign="top" rowspan="1" colspan="1">1.4 (10.7)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">20%</td><td align="left" valign="top" rowspan="1" colspan="1">6.4 (5.7)</td><td align="left" valign="top" rowspan="1" colspan="1">3.7 (8.4)</td><td align="left" valign="top" rowspan="1" colspan="1">3.0 (9.1)</td><td align="left" valign="top" rowspan="1" colspan="1">2.7 (9.4)</td><td align="left" valign="top" rowspan="1" colspan="1">2.4 (9.7)</td><td align="left" valign="top" rowspan="1" colspan="1">11.5 (0.6)</td><td align="left" valign="top" rowspan="1" colspan="1">9.9 (2.2)</td><td align="left" valign="top" rowspan="1" colspan="1">8.2 (3.9)</td><td align="left" valign="top" rowspan="1" colspan="1">4.4 (7.7)</td><td align="left" valign="top" rowspan="1" colspan="1">1.8 (10.3)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1">D (1918-like)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1%</td><td align="left" valign="top" rowspan="1" colspan="1">1%</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">29.7 (0.4)</td><td align="left" valign="top" rowspan="1" colspan="1">29.5 (0.6)</td><td align="left" valign="top" rowspan="1" colspan="1">29.1 (1.0)</td><td align="left" valign="top" rowspan="1" colspan="1">27.3 (2.8)</td><td align="left" valign="top" rowspan="1" colspan="1">24.7 (5.4)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">5%</td><td align="left" valign="top" rowspan="1" colspan="1">26.8 (3.3)</td><td align="left" valign="top" rowspan="1" colspan="1">25.5 (4.6)</td><td align="left" valign="top" rowspan="1" colspan="1">24.0 (6.1)</td><td align="left" valign="top" rowspan="1" colspan="1">21.5 (8.6)</td><td align="left" valign="top" rowspan="1" colspan="1">20.6 (9.5)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.0 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">27.0 (3.1)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">10%</td><td align="left" valign="top" rowspan="1" colspan="1">27.3 (2.8)</td><td align="left" valign="top" rowspan="1" colspan="1">26.3 (3.8)</td><td align="left" valign="top" rowspan="1" colspan="1">25.0 (5.1)</td><td align="left" valign="top" rowspan="1" colspan="1">19.3 (10.8)</td><td align="left" valign="top" rowspan="1" colspan="1">14.1 (16.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.0 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">27.8 (2.3)</td></tr><tr><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1"></td><td align="left" valign="top" rowspan="1" colspan="1">20%</td><td align="left" valign="top" rowspan="1" colspan="1">28.5 (1.6)</td><td align="left" valign="top" rowspan="1" colspan="1">27.9 (2.2)</td><td align="left" valign="top" rowspan="1" colspan="1">26.9 (3.2)</td><td align="left" valign="top" rowspan="1" colspan="1">21.5 (8.6)</td><td align="left" valign="top" rowspan="1" colspan="1">12.4 (17.7)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.1 (0.0)</td><td align="left" valign="top" rowspan="1" colspan="1">30.0 (0.1)</td><td align="left" valign="top" rowspan="1" colspan="1">28.4 (1.7)</td></tr></tbody></table><table-wrap-foot><fn id="TFN5"><label>a</label><p id="P49">Cumulative clinical attack rates (i.e., the percentage of the total
population who develop clinical symptoms within 240 days of the index case,
i.e. including 60 days after the vaccination campaign has started) are given
for the baseline (no dismissal) scenario and various school dismissal policy
options.</p></fn><fn id="TFN6"><label>b</label><p id="P50">School dismissal is triggered when the first confirmed symptomatic
school-age child is detected in a community. The diagnosis ratio is the
percentage of symptomatic individuals that are positively identified; for
instance, with a 5% diagnosis ratio, the first confirmed case may not be
identified until 20 children are symptomatic.</p></fn><fn id="TFN7"><label>c</label><p id="P51">Upon triggering a dismissal, either only the affected
community’s schools are closed (community dismissal) or a
simultaneous dismissal of all Chicago-area schools (regional dismissal).</p></fn></table-wrap-foot></table-wrap></floats-group></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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