{"paper_id":"cdb4cef2-eeac-4a23-9ced-619ccc11fd88","body_text":"/\n  \n1 Estimating   the   impact   of   reopening   schools   on   the   reproduction   number   \n2 of   SARS-CoV-2   in   England,   using   weekly   contact   survey   data   \n3 James   D   Munday* 1a ,   Christopher   I   Jarvis* 1b ,   Amy   Gimma 1c ,   Kerry   LM   Wong 1d ,   Kevin   van   \n4 Zandvoort 1e ,   CMMID   COVID-19   Working   Group,   Sebastian   Funk 1f ,   W.   John   Edmunds 1g     \n5 1   Centre   for   Mathematical   Modelling   of   Infectious   Disease,   London   School   of   Hygiene   and   \n6 Tropical   Medicine.   \n7 a:   James.Munday@lshtm.ac.uk   (Corresponding   Author)   \n8 b:   Christopher.Jarvis@lshtm.ac.uk   \n9 c:   Amy.Gimma@lshtm.ac.uk   \n10 d:   Kerry.Wong@lshtm.ac.uk   \n11 e:   Kevin.Van-Zandvoort@lshtm.ac.uk   \n12 f:   Sebastian.Funk@lshtm.ac.uk   \n13 g:   John.Edmunds@lshtm.ac.uk     \n  \n   \n1   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n\n/\n  \n14 Abstract     \n15 Background   \n16 Schools   have   been   closed   in   England   since   the   4th   of   January   2021   as   part   of   the   national   \n17 restrictions   to   curb   transmission   of   SARS-CoV-2.   The   UK   Government   plans   to   reopen   \n18 schools   on   the   8th   of   March.   Although   there   is   evidence   of   lower   individual-level   \n19 transmission   risk   amongst   children   compared   to   adults,   the   combined   effects   of   this   with   \n20 increased   contact   rates   in   school   settings   are   not   clear.     \n21 Methods   \n22 We   measured   social   contacts   when   schools   were   both   open   or   closed,   amongst   other   \n23 restrictions.   We   combined   these   data   with   estimates   of   the   susceptibility   and   infectiousness   \n24 of   children   compared   with   adults   to   estimate   the   impact   of   reopening   schools   on   the   \n25 reproduction   number.     \n26 Results   \n27 Our   results   suggest   that   reopening   all   schools   could   increase   R   from   an   assumed   baseline   \n28 of   0.8   to   between   1.0   and   1.5,   or   to   between   0.9   and   1.2   reopening   primary   or   secondary   \n29 schools   alone.     \n30 Conclusion   \n31 Our   results   suggest   that   reopening   schools   is   likely   to   halt   the   fall   in   cases   observed   in   \n32 recent   months   and   risks   returning   to   rising   infections,   but   these   estimates   rely   heavily   on   the   \n33 current   estimates   or   reproduction   number   and   the   current   validity   of   the   susceptibility   and   \n34 infectiousness   profiles   we   use.   \n35 Keywords :   School   closure,   SARS-CoV-2,   COVID-19,   Social   Contacts,   Reproduction   \n36 Number,   CoMix     \n2   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n37 Introduction   \n38 School   closures   have   been   implemented   in   many   countries   as   part   of   a   broader   response   to   \n39 the   COVID-19   pandemic    [1] .    It   is   well   established   that   children   are   at   low   risk   of   \n40 hospitalisation   and   death   as   a   direct   result   of   infection    [2,   3] .   Despite   this   lower   risk,   there   is   \n41 concern   that   allowing   transmission   amongst   younger   age-groups   increases   risk   of   infection   \n42 in   adults,   who   are   at   substantially   higher   risk.    The   role   of   schools   in   transmission   is   \n43 therefore   an   important   question.   On   the   4th   of   January   2021,   a   third   national   lockdown   was   \n44 announced   in   England   to   curb   transmission   of   SARS-CoV-2    [4] .   This   included   the   closure   of   \n45 schools,   a   measure   the   UK   government   plans   to   reverse   on   the   8th   of   March.   \n46 The   direct   and   indirect   impact   of   school   closures   and   eventual   reopening   is   still   unclear.   \n47 There   is   mixed   evidence   around   the   role   of   schools   in   community   transmission.   Existing   \n48 studies   of   transmission   within   schools   have   wide   ranging   results    [5–7] .   Other   work   \n49 demonstrates   an   increased   prevalence   amongst   school-aged-children   when   schools   return   \n50 [8,   9]    and   a   higher   risk   of   infections   entering   households   through   children   than   adults.   \n51 However,   the   evidence   that   schools   drive   transmission   in   the   community   remains   scarce    [10,   \n52 11] .   A   particular   challenge   for   many   analyses   is   bias   resulting   from   the   age-dependence   in   \n53 case   ascertainment   due   to   varying   rates   of   asymptomatic   infection    [12] .   This   challenge   is   \n54 then   further   complicated   by   changes   in   epidemiology   due   to   the   emergence   of   new   variants   \n55 [13] .   \n56 The   potential   change   in   transmission   of   SARS-CoV-2   upon   reopening   schools   predominantly   \n57 depends   on   a   combination   of   two   factors.   Firstly,   the   age-specific   risk   of   transmission   upon   \n58 contact.   Secondly,   the   likely   increased   rate   of   contact   between   members   of   the   population   \n59 due   to   school   reopening.   Multiple   studies   aimed   at   understanding   the   relative   transmission   \n60 risk   associated   with   children   indicate   lower   susceptibility    [14–16]    and   some   indicate   lower   \n61 infectiousness    [14] .   However,   evidence   of   lower   transmission   risk   amongst   children   alone   is   \n62 insufficient   to   quantify   the   impact   of   reopening   schools.   There   is   a   need   to   combine   the   \n3   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n63 estimates   of   reduced   susceptibility   and   infectiousness   with   age   specific   contact   patterns   in   \n64 this   age-group   social   contacts   amongst   school-aged-children.     \n65 There   is   abundant   evidence   that   children’s   contacts   increase   when   schools   are   open,   \n66 presenting   opportunities   for   increased   infectious   disease   transmission   which   is   well   \n67 documented   in   other   pathogens   such   as   influenza    [17] .   Nonetheless,   it   is   important   to   \n68 capture   how   these   contacts   vary   under   the   specific   conditions   presented   during   the   current   \n69 pandemic   response,   where   social   distancing   and   other   mitigations   are   in   effect   within   \n70 schools.   \n71 CoMix   is   a   large-scale   comprehensive   social   contact   survey   which   has   collected   data   on   \n72 social   contacts   in   the   UK   on   a   weekly   basis   since   the   24th   of    March   2020    [18] .   In   this   paper,   \n73 we   estimate   the   impact   of   opening   schools   on   the   reproduction   number   in   England,   by   \n74 combining   social-contact   data   collected   during   periods   where   schools   were   open   and   closed   \n75 [18]    with   estimates   of   age-stratified   susceptibility   and   infectiousness    [14–16] .     \n4   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n76 Methods   \n77 CoMix   Data   \n78 CoMix   is   a   longitudinal   behavioural   survey,   launched   on   the   24 th    of   March   2020.   The   sample   \n79 is   broadly   representative   of   the   UK   adult   population   with   data   collected   from   approximately   \n80 2000   individuals   per   week.   Participants   are   invited   to   respond   to   the   survey   once   every   two   \n81 weeks.   We   collected   weekly   data   by   running   two   alternating   panels.   Parents   complete   the   \n82 survey   on   behalf   of   children   (17   years   old   or   younger).   Participants   record   direct,   \n83 face-to-face   contacts   made   on   the   previous   day,   specifying   certain   characteristics   for   each   \n84 contact   including   the   age   and   sex   of   the   contact,   whether   contact   was   physical   (skin-to-skin   \n85 contact),   and   where   the   contact   occurred   (e.g.   at   home,   work,   while   undertaking   leisure   \n86 activities,   etc).   Further   details   have   been   published   elsewhere    [18] .   The   contact   survey   is   \n87 based   on   an   approach   developed   for   the   POLYMOD   contact   survey    [19] .   We   provide   a   brief   \n88 descriptive   analysis   of   the   contacts   recorded   during   the   November   and   January   lockdown   \n89 periods   by   age   group   and   geographical   region.     \n90 Constructing   contact   matrices   and   estimating   reproduction   number   \n91 We   constructed   age-stratified   contact   matrices   for   nine   age-groups   (0-4,   5-11,   12-17,   18-29,   \n92 30-39,   40-49,   50-59,   60-69,   and   70+).   Participants   did   not   report   exact   ages   of   contacts,   we   \n93 therefore   sampled   from   the   reported   age-group   with   a   weighting   consistent   with   contacts   \n94 reported   in   the   POLYMOD   survey.   We   fitted   a   truncated   negative   binomial   model   to   calculate   \n95 the   mean   contacts   between   each   participant   and   contact   age-groups.   To   ensure   reciprocity   \n96 in   contacts,   we   multiplied   the   matrix   by   population   size   vector   for   England,   using   United   \n97 Nations   World   Population   Prospects   data    [20] ,   before   taking   the   cross-diagonal   mean   and   \n98 then   dividing   by   the   same   population   vector   again.     \n99 Profiles   of   Age-dependent   transmission   risk   \n100 We   consider   five   age-dependent   susceptibility   and   infectiousness   profiles   (Table   1):     \n5   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n101 The   first   profile   (i)   assumed   equal   susceptibility   and   infectiousness   in   all   age   groups.   This   is   \n102 unlikely   to   reflect   reality   but   provides   an   upper   limit   as   a   reference   point   to   compare   the   other   \n103 profiles.   \n104 For   the   second   profile   (ii)   we   used   results   from   a   mathematical   modelling   study   by   Davies   et.   \n105 al    [14] .   which   estimated   relative   susceptibility   and   clinical   fraction   in   9   age   groups.   The   work   \n106 also   reports   estimates   of   50%   infectiousness   of   sub-clinical   cases   and   reports   clinical   \n107 fraction   by   age.   We   used   this   to   calculate   infectiousness   per   age   group   further   detailed   in   \n108 Table   1.     \n109 The   third   profile   (iii),   was   based   on   analyses   of   household   transmission   patterns   from   the   \n110 Office   for   National   Statistics   (ONS)   Community   Infection   Study    [15] ;   50%   susceptibility   in   \n111 children   relative   to   adults   but   equal   infectiousness.   \n112 For   the   fourth   profile   (iv),   we   performed   a   meta-analysis   of   prevalence   studies   included   in   a  \n113 systematic   review   by   Viner   et   al    [16] .   We   used   a   random   effects   model   based   on   the   data   \n114 from   Figure   4   of   their   paper.   This   resulted   in   64%   (51%   -   81%,   95%   confidence   interval   [CI])   \n115 susceptibility   in   children   relative   to   adults,   we   assumed   equal   infectiousness   between   \n116 children   and   adults    [16] ;     \n117 For   the   fifth   profile   (v),   we   used   an   independent   estimate   of   relative   susceptibility   in   children   \n118 (31%,   see   results   section),   quantified   by   comparing   reproduction   numbers   estimated   from   \n119 CoMix   data   and   using   a   well-established   time-series   method   developed   by   Abbott   et.   al    [21] ,   \n120 which   uses   a   time-series   of   cases   to   determine   the   instantaneous   reproduction   number   \n121 under   an   assumed   generation   interval   and   infection   to   reporting   delay   distribution.     \n  \n  \n  \n  \n6   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n122 Table   1    Susceptibility   and   infectiousness   profiles   taken   from   Davies   et.al. [14] ,   ONS   reports   \n123 and   Viner   et   al [16]   \n  \n7   \nStudy   Age   groups   Susceptibility   Infectiousness   Clinical   Fraction   \nDavies   et   al 1   0-4   0.4   (0.25,   0.57)   0.61   0.29   (0.18,   0.44)   \n5-10   0.4   (0.25,   0.57)   0.61   0.29   (0.18,   0.44)   \n11-17   0.4   (0.27,   0.53)   0.61   0.21   (0.12,   0.31)   \n18-29   0.79   (0.59,   0.96)   0.64   0.27   (0.18,   0.38)   \n30-39   0.86   (0.69,   0.98)   0.67   0.33   (0.24,   0.43)   \n40-49   0.80   (0.61,   0.96)   0.70   0.40   (0.28,   0.52)   \n50-59   0.82   (0.63,   0.97)   0.75   0.49   (0.37,   0.60)   \n60-69   0.88   (0.70,   0.99)   0.82   0.63   (0.49,   0.76)   \n70+   0.74   (0.56,   0.90)   0.85   0.69   (0.57,   0.82)   \n      Susceptibility   Infectiousness      \nONS 2   \n0-4   0.5   (0.35,   0.75)   1.0   (0.7,   1.5)      \n5-10   0.5   (0.35,   0.75)   1.0   (0.7,   1.5)      \n11-17   0.5   (0.35,   0.75)   1.0   (0.7,   1.5)      \n18-29   1.0   1.0      \n30-39   1.0   1.0      \n40-49   1.0   1.0      \n50-59   1.0   1.0      \n60-69   1.0   1.0      \n70+   1.0   1.0      \n      Susceptibility   Infectiousness      \nViner   et   al 3   \n0-4   0.64   (0.51,   0.81)   1.0   (assumed)      \n5-10   0.64   (0.51,   0.81)   1.0   (assumed)      \n11-17   0.64   (0.51,   0.81)   1.0   (assumed)      \n18-29   1.0   1.0      \n30-39   1.0   1.0      \n40-49   1.0   1.0      \n50-59   1.0   1.0      \n60-69   1.0   1.0      \n   70+   1.0   1.0      \n      Susceptibility   Infectiousness      \nCoMix   fit   0-4   0.31   (0.30,   0.31)   1.0      \n5-10   0.31   (0.30,   0.31)   1.0      \n11-17   0.31   (0.30,   0.31)   1.0      \n18-29   1.0   1.0      \n30-39   1.0   1.0      \n40-49   1.0   1.0      \n50-59   1.0   1.0      \n60-69   1.0   1.0      \n70+   1.0   1.0      \n1    95%   Credible   Intervals   \n2    Approximate   results   inferred   from   plot   in [15]    unknown   quantification   of   \nuncertainty   \n3    95%   Confidence   Interval      \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n124 Inferring   age   dependent   transmission   risk   using   CoMix   data   \n125 We   established   independent   estimates   of   susceptibility   and   infectiousness   in   children   \n126 relative   to   adults.   We   did   this   by   comparing   estimates   of    R    using   CoMix   contact   data   with   \n127 estimates   of   the   time-varying   reproduction   number   in   England   calculated   using   case   data  \n128 [21] .   To   capture   the   change   in   contact   rates   as   schools   returned   in   September   2020   \n129 We   calculated   a   reproduction   number   resulting   from   two-weekly   rolling   contact   matrices    C t   \n130 and   assumed   relative   susceptibility   and   infectiousness   vectors     s    and     i     to   be:   \n  \n131 We   simplified    s    and    i    such   that   adult   age-groups   (18+)   were   1.0   and   child   age   groups   were   \n132 equal,    s    and    i    .   We   inferred    s    and    r,    keeping    i    at   1.0 ,    by   fitting   our   estimates   using   maximum   \n133 likelihood   estimation   to   those   calculated   using   the   EpiNow2   package    [21] .   We   assumed   \n134 gamma   distributed   uncertainty   in   the   time-varying   estimates   which   we   parameterised   using   \n135 the   mean     and   standard   deviation     of   these   estimates   over   each   survey   period   used   to  μrt σrt  \n136 calculate   CoMix   derived   eigenvalues.   \n  \n137 To   show   the   likelihood   surface   of   relative   susceptibility   and   infectiousness,   we   calculated   the   \n138 likelihood   of   a   range   of   combinations   of    i    and    s    while   fitting    r .     \n139 We   fitted   over   2   periods   of   time.   Firstly,   between   27th   July   and   10th   October   to   most   clearly   \n140 capture   the   impact   of   schools   returning   in   the   summer   whilst   minimising   issues   related   to   \n141 gradual   acquisition   of   natural   immunity.   Second,   We    fitted   over   a   longer   period   of   time   \n142 incorporating   data   from   10th   June.     \n143 We   omitted   data   at   the   end   of   August   in   both   fits   due   to   a   short   spike   in   reproduction   number   \n144 estimates,   which   we   believe   resulted   from   large   numbers   of   imported   cases   from   \n145 recreational   travel.   We   further   omitted   two   weeks   in   July   when   contacts   were   not   recorded   \n8   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n146 for   children.   We   assessed   sensitivity   to   the   fitted   period,   by   using   a   range   of   fitting   options   \n147 (Figure   S4).   \n148 Evaluating   the   impact   of   reopening   schools   on   Reproduction   Number   \n149 We   created   contact   matrices   using   CoMix   data   collected   during   the   second   lockdown,   (5th   \n150 November   to   2nd   December   2020)   to   represent   contacts   during   a   lockdown   with   schools   \n151 open.   We   used   data   from   5th   to   18th   of   January   2021   for   contacts   during   a   lockdown   with   \n152 schools   closed   (Supplementary   Figures,   Figure   S1).   We   constructed   further   synthetic   \n153 contact   matrices   representing   opening   primary   or   secondary   schools   by   replacing   the   \n154 contacts   of   5-10   year-olds   (primary)   and   11-17   year-olds   (secondary)   in   the   ‘schools   open’   \n155 contact   matrix   (second   lockdown),   with   those   from   the   ‘schools   closed’   contact   matrix   (third   \n156 lockdown)   (Supplementary   Figures,   Figure   S2).     \n157 Since   the   basic   reproduction   number   scales   linearly   with   the   dominant   eigenvalue   of   a   matrix   \n158 of   effective   contact    [22] ,   the   ratio   of   the   eigenvalues   of   two   effective   contact   matrices   \n159 provides   a   relative   change   in   reproduction   number   between   the   three   scenarios   considered.     \n160 In   the   case   where   infectiousness   and   susceptibility   are   equal   in   all   age   groups,   the   effective   \n161 contact   matrix   is   proportional   to   the   contact   matrix   itself.   Under   the   scenarios   where   we   \n162 assumed   infectiousness   and   susceptibility   vary   with   age,   we   converted   measured   contact   \n163 matrices   to   effective   contact   matrices   by   taking   the   outer   product   of   the   estimated   age   \n164 stratified   infectiousness   profile   and   susceptibility   profile   vectors   and   calculating   the   \n165 eigenvalues   of   the   Hadamard   product   of   the   resulting   matrix   and   the   contact   matrices.     \n166 To   demonstrate   the   potential   impact   of   reopening   schools,   we   estimated   the   relative   increase   \n167 ( k )   in   reproduction   number   ( R )   by   calculating   the   ratio   of   dominant   eigenvalues   of   the   \n168 effective   contact   matrix   associated   with   the   respective   reopening   scenario   and   from   the   \n169 current   lockdown   period.     \n  \n9   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n170 We   also   calculated   how    R    varies   from   baseline   values   between   0.7   and   1.0,   from   official   UK   \n171 estimates   of   the   reproduction   number   from    [23] .     \n   \n10   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n172 Results   \n173 Descriptive   analysis   \n174 Adults’   contacts   were   similar   when   comparing   both   periods   of   national   lockdown,   this   is   \n175 consistent   across   all   settings   and   regions.   Although   children’s   contacts   at   home   were   similar   \n176 between   the   two   periods,   contacts   at   school   and   other   locations   were   consistently   higher   in   \n177 lockdown   2   than   lockdown   3.   Contacts   were   very   similar   between   lockdowns   in   all   age-group   \n178 combinations   other   than   those   between   children   (Figure   1).   For   participants   under   18   \n179 years-old,   the   mean   number   of   contacts   that   were   also   under   18   years-old   was   between   6.3   \n180 (3.9   -   9.0,   90%   CI)   and   16.7   (13.1   -   20.4,   90%   CI)   across   the   regions   of   England   during   the   \n181 November   Lockdown.   Such   contacts   were   highest   in   South   East,   South   West   and   Yorkshire   \n182 and   Humber   and   lowest   in   London.   The   mean   number   of   contacts   between   children   reduced   \n183 to   between   1.8   (1.3   -   2.5,   90%   CI)   and   2.6   (1.9   -   3.3,   90%   CI)   during   the   January   Lockdown.   \n184 Estimating   susceptibility   in   children   relative   to   adults   using   CoMix   data.     \n185 Fitting   the    R    estimates   from   CoMix   data   to   time-varying    R    estimates   over   a   period   from   27th   \n186 July   to   10th   October   we   estimated   susceptibility   of   44%   (43.5%   -   0.45.4%,   95%   CI)   in   \n187 children   relative   to   adults   (Figure   2,   A   &   C),   consistent   with   profiles   ii   and   iii.   When   we   fitted   \n188 from   the   10th   June   to   10th   October,   2020,   we   estimated   31%   (29.8%   -    31.4%,   95%   CI)   \n189 relative   susceptibility   in   children   compared   to   adults   (Figure   2,   B   &   D),   near   the   lower   range   \n190 of   ONS   and   Davies   et   al   estimates.   We   chose   to   apply   the   second   estimate   as   the   fifth   \n191 susceptibility   profile   (v)   to   represent   this   lower   bound   (Table   1)   and   present   fits   to   other   date   \n192 ranges   in   the   supplementary   material   (Supplementary   Figures,   Figure   S4).   \n193 Evaluation   of   the   impact   of   reopening   schools     \n194   Incorporating   estimates   of   differential   susceptibility   and   infectiousness   of   children   compared   \n195 with   adults   (profiles   ii   -   v),   full   school   reopening   increased    R    by   a   factor   of   between   1.3   and   \n196 1.9   times   the   baseline   value   across   the   four   profiles   used   (including   90%   CI   range)   (Figure   \n11   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n197 3,   Table   2).   This   would   result   in   an   increase   of    R    from   0.8   to   above   1.0   for   these   four   profiles.   \n198 Partial   school   reopening   resulted   in   smaller   increases   in    R    from   0.8   to   between   0.9   and   1.2.     \n199 Table   2    Expected   resultant    R    if   schools   were   reopened   for   different   baseline   values   of    R   \n200 reported   as   median   (90%   CI)     \n  \n201 When   we   assumed   equal   infectiousness   and   susceptibility   between   all   age   groups   (profile   i),   \n202 reopening   schools   resulted   in   more   substantial   relative   changes   in    R .   Full   school   reopening   \n203 increased    R    by   a   factor   of   between   2.1   and   2.3   (Figure   3,   Table   2),   resulting   in   an   increase   \n204 of    R    to   roughly   1.7-1.9   from   a   baseline   of   0.8   (Table   2).   Partial   re-opening   increased    R    from   \n205 0.8   to   1.2-1.3   (Figure   3).   We   included   these   estimates   for   completeness   but   stress   that   \n206 assuming   that   children   are   equally   infectious   and   susceptible   as   adults   is   not   compatible   \n207 with   results   from   previous   studies   or   our   own   estimates   (Figure   2).     \n   \n12   \n    Baseline    R   \nSusceptibility/     \nInfectiousness   \nAttendance   0.7   0.8   0.9   1.0    \n(Scale   factor)  \n1.   Equal   \nBoth   1.6   (1.5   -   1.6)   1.8   (1.7   -   1.9)  2.0   (1.9   -   2.1)  2.2   (2.1   -   2.3)  \nPrimary   1.1   (1.0   -   1.1)   1.2   (1.2   -   1.3)  1.4   (1.3   -   1.5)  1.5   (1.4   -   1.6)  \nSecondary   1.1   (1.0   -   1.2)   1.3   (1.2   -   1.3)  1.4   (1.3   -   1.5)  1.6   (1.5   -   1.7)  \n2.   Davies   et   al   \nBoth   1.1   (1.0   -   1.1)   1.2   (1.1   -   1.3)  1.4   (1.3   -   1.4)  1.5   (1.4   -   1.6)  \nPrimary   0.9   (0.8   -   0.9)   1.0   (0.9   -   1.0)  1.1   (1.1   -   1.2)  1.2   (1.2   -   1.3)  \nSecondary   0.9   (0.8   -   0.9)   1.0   (1.0   -   1.1)  1.1   (1.1   -   1.2)  1.3   (1.2   -   1.3)  \n3.   ONS     \nBoth   1.1   (1.1   -   1.2)   1.3   (1.2   -   1.3)  1.4   (1.4   -   1.5)  1.6   (1.5   -   1.7)  \nPrimary   0.9   (0.8   -   0.9)   1.0   (1.0   -   1.1)  1.1   (1.1   -   1.2)  1.3   (1.2   -   1.3)  \nSecondary   0.9   (0.9   -   1.0)   1.0   (1.0   -   1.1)  1.2   (1.1   -   1.2)  1.3   (1.3   -   1.4)  \n4.   Viner   et   al   \nBoth   1.3   (1.2   -   1.3)   1.4   (1.4   -   1.5)  1.6   (1.5   -   1.7)  1.8   (1.7   -   1.9)  \nPrimary   0.9   (0.9   -   1.0)   1.1   (1.0   -   1.1)  1.2   (1.1   -   1.3)  1.3   (1.3   -   1.4)  \nSecondary   1.0   (0.9   -   1.0)   1.1   (1.1   -   1.2)  1.2   (1.2   -   1.3)  1.4   (1.3   -   1.4)  \n5.   CoMix   fit   \nBoth   0.9   (0.9   -   1.0)   1.1   (1.0   -   1.1)  1.2   (1.2   -   1.3)  1.4   (1.3   -   1.4)  \nPrimary   0.8   (0.8   -   0.9)   0.9   (0.9   -   1.0)  1.1   (1.0   -   1.1)  1.2   (1.1   -   1.2)  \nSecondary   0.8   (0.8   -   0.9)   1.0   (0.9   -   1.0)  1.1   (1.0   -   1.1)  1.2   (1.2   -   1.3)  \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n208 Discussion   \n209 The   potential   impact   of   reopening   schools   on   transmission   of   SARS-CoV-2   is   uncertain.   \n210 Although   there   have   been   many   attempts   to   quantify   the   relative   susceptibility   and   \n211 infectiousness   of   children   and   adults,   these   estimates   need   to   be   assessed   alongside   rates   \n212 of   contact   to   give   an   indication   of   the   overall   risk   of   transmission   in   any   given   setting.   We   \n213 combined   social   contact   data   from   a   large-scale   survey   in   England   during   two   periods   of   \n214 national   lockdown,   one   with   schools   open   and   the   other   with   schools   closed,   with   estimates   \n215 of   relative   susceptibility   of   children   and   adults.   We   used   these   data   to   quantify   the   potential   \n216 impact   of   reopening   schools   on   reproduction   number.     \n217 Whereas   adults’   contacts   were   generally   similar   between   the   two   periods   of   lockdown,   there   \n218 was   markedly   higher   contact   between   children   during   the   November   lockdown,   when   \n219 schools   were   open.   We   observed   the   change   in   contacts   at   school   but   also   in   other   contacts   \n220 outside   of   the   home.   Increased   contact   outside   of   school   and   home   settings   includes   \n221 contacts   in   wrap   around   care,   which   would   be   expected   to   rise,   however   it   could   also   \n222 indicate   reduced   overall   adherence   amongst   children   when   attending   schools   physically.   \n223 The   differences   in   contacts   suggest   that   reopening   all   schools   is   highly   likely   to   increase    R   \n224 above   1.0,   from   an   assumed   current   value   0.8.   Reopening   primary   or   secondary   is   likely   to   \n225 increase     R    above   1.0.   This   would   be   expected   to   stop   or   reverse   the   fall   in   cases   that   has   \n226 been   observed   since   January   2021    [24] .   The   risk   of   cases   increasing   following   the   reopening   \n227 of   schools   is   highly   dependent   on   the   current   value   of    R .   Although   cases   of   the   current   \n228 dominant   variant   (B.1.1.7)   appeared   to   be   increasing   whilst   national   lockdown   was   still   in   \n229 place   in   November    [10,   13] ,   the   latest   national   serology   surveys   suggest   that   immunity   levels   \n230 have   substantially   increased   across   the   UK    [24] ,   resultant   from   both   infections   and   the   \n231 national   COVID-19   vaccination   program.   These   changes   in   overall   immunity   should   be   \n232 reflected   in   the   current   estimates   of    R,    but   these   estimates   are   lagged   due   to   delays   in   \n233 reporting    [25] .     \n13   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n234 In   November,   when   schools   were   open,   there   was   substantial   variation   in   contacts   between   \n235 children   by   region.   We   have   not   presented   regional   estimates   of   the   impact   of   reopening   \n236 schools   on    R    due   to   low   numbers   of   observations   between   the   lower-level   age-group   \n237 aggregation   used   in   the   construction   of   contact   matrices,   however   the   variation   in   mean   \n238 contacts   points   to   potential   geographical   variation   in   the   impact   of   reopening   schools,   which   \n239 may   be   lower   in   London   than   other   parts   of   the   country.     \n240 There   are   a   number   of   important   limitations   to   this   work:   Contacts   in   different   settings   likely   \n241 contribute   differently   to   transmission,   but   we   assumed   all   contacts   make   equal   contributions   \n242 to   transmission,   as   these   differences   are   not   well   quantified   in   the   context   of   control   \n243 measures.   If   contacts   at   school   are   lower   risk   than   those   outside   of   school   the   impact   of  \n244 reopening   schools   would   be   lower.   The   age-stratified   susceptibility   profile   is   likely   to   change   \n245 over   time   as   natural   immunity   is   acquired   in   the   population.   The   profiles   we   used   each   reflect   \n246 a   single   point   in   time.   Changes   in   the   relative   immunity   in   children   would   alter   the   relative   \n247 impact   of   school   contacts   on   overall   transmission.   We   assume   adult   contacts   revert   to   those   \n248 observed   when   all   schools   were   open,   which   is   conservative,   in   reality,   particularly   for   partial   \n249 reopening   scenarios,   adult   contacts   may   not   fully   return   to   the   same   levels.   Furthermore,   \n250 there   may   also   be   differences   in   adherence   to   restrictions   between   the   two   lockdowns,   \n251 unrelated   to   school   closure.   However,   the   change   in   adults’   contacts   between   the   two   \n252 periods   was   relatively   small.   The   proportion   of   children   in   school   varied   over   time   due   to   \n253 exclusion-based   control   measures   during   the   autumn,   though   the   proportion   attending   \n254 school   remained   high   during   the   November   lockdown   (Supplementary   Figures,   Figure   S3).   \n255 Contacts   of   children   are   reported   by   parents,   which   may   impact   their   reliability,   particularly   in   \n256 school,   where   parents   are   unlikely   to   witness   students’   behaviour,   it   is   unclear   whether   this   \n257 would   lead   to   systematic   bias   in   reporting   either   more   or   fewer   contacts.    \n258 Our   work   evaluates   the   impact   of   reopening   schools   on   the   reproduction   number   in   England,   \n259 which   gives   an   indication   of   how   transmission   may   be   affected.   However,   there   are   other   \n260 factors   that   reopening   schools   may   introduce,   such   as   the   potential   for   children’s   contact   at   \n14   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n261 school   to   provide   routes   of   transmission   between   households,   facilitating   long   chains   of   \n262 transmission   that   would   be   otherwise   impossible [26] .   We   are   not   able   to   capture   these   \n263 network   effects   in   this   analysis,   however   they   may   play   an   important   role   in   the   change   in   \n264 epidemiology   between   school   closure   and   reopening.    Second,   there   is   evidence   for   lower   \n265 prevalence   in   primary   school   than   secondary   schools    [8] .   Our   framework   has   not   captured   \n266 these   differences   suggesting   there   may   be   additional   factors   that   reduce   the   impact   of   \n267 reopening   primary   schools   relative   to   secondary   schools.   Furthermore,   additional   \n268 management   strategies   such   as   mass   testing   of   school   children,   may   serve   to   reduce   the   \n269 risk   that   a   contact   in   a   school   results   in   infection   beyond   those   implemented   last   year.   \n270 Importantly,   with   the   recent   emergence   of   new   variants,   particularly   B.1.1.7    [27] ,   the   baseline   \n271 R    will   depend   on   proportions   of   these   variants   as   well   as   contact   patterns.   Furthermore,   \n272 these   proportions   are   likely   to   change,   potentially   altering   the   implications   of   reopening   \n273 schools.     \n274 Our   results   suggest   reopening   schools   is   likely   to   increase    R    close   to   or   above   1.0,   which   \n275 would   stop   the   decrease   in   cases   observed   in   recent   months.   However,   precise   estimates   \n276 rely   heavily   on   the   baseline   values   of    R    and   the   profiles   of   susceptibility,   generally   assuming   \n277 lower   susceptibility   and   no   greater   infectiousness   in   children   relative   to   adults.       \n15   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n  \n  \n278 List   of   abbreviations   \n279 CI   Confidence   Interval     \n280 ONS Office   for   National   Statistics   \n281 UK United   Kingdom   \n  \n282 Declarations   \n283 Ethics   approval   and   consent   to   participate   \n284 Participation   in   this   opt-in   study   was   voluntary,   and   all   analyses   were   carried   out   on   \n285 anonymised   data.   The   study   and   method   of   informed   consent   was   approved   by   the   ethics   \n286 committee   of   the   London   School   of   Hygiene   &   Tropical   Medicine   Reference   number   21795.   \n287 Consent   to   publish   \n288 Not   applicable   \n289 Availability   of   data   and   materials   \n290 Although   it   is   not   possible   to   share   the   contact   survey   data   used   to   generate   the   contact   \n291 matrices   used   in   this   analysis.   The   analysis   code   and   contact   matrices   used   are   available   in   \n292 an   online   repository   here:    https://github.com/jdmunday/CoMix_schools_reopening   \n293 Competing   interests   \n294 None   \n295 Funding   \n296 CoMix   is   funded   by   the   EU   Horizon   2020   Research   and   Innovations   Programme   -   project   \n297 EpiPose   (Epidemic   Intelligence   to   Minimize   COVID-19’s   Public   Health,   Societal   and   \n298 Economical   Impact,   No   101003688)   and   by   the   Medical   Research   Council   (Understanding   \n299 the   dynamics   and   drivers   of   the   COVID-2019   epidemic   using   real-time   outbreak   analytics   \n300 MC_PC   19065).     \n16   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n301 The   following   funding   sources   are   acknowledged   as   providing   funding   for   the   named   \n302 authors.   Elrha   R2HC/UK   FCDO/Wellcome   Trust/This   research   was   partly   funded   by   the   \n303 National   Institute   for   Health   Research   (NIHR)   using   UK   aid   from   the   UK   Government   to   \n304 support   global   health   research.   The   views   expressed   in   this   publication   are   those   of   the   \n305 author(s)   and   not   necessarily   those   of   the   NIHR   or   the   UK   Department   of   Health   and   Social   \n306 Care   (KvZ).   This   project   has   received   funding   from   the   European   Union's   Horizon   2020   \n307 research   and   innovation   programme   -   project   EpiPose   (101003688:   AG,   WJE).   \n308 FCDO/Wellcome   Trust   (Epidemic   Preparedness   Coronavirus   research   programme   \n309 221303/Z/20/Z:   KvZ).   This   research   was   partly   funded   by   the   Global   Challenges   Research   \n310 Fund   (GCRF)   project   'RECAP'   managed   through   RCUK   and   ESRC   (ES/P010873/1:   CIJ).   \n311 NIHR   (PR-OD-1017-20002:   WJE).   UK   MRC   (MC_PC_19065   -   Covid   19:   Understanding   the   \n312 dynamics   and   drivers   of   the   COVID-19   epidemic   using   real-time   outbreak   analytics:   WJE).   \n313 Wellcome   Trust   (210758/Z/18/Z:   JDM,   SFunk).   Department   of   Health   and   Social   Care   \n314 School   Infection   Study   (PHSEZU7510)   (JDM,   WJE).   No   funding   (KW).   \n315 The   following   funding   sources   are   acknowledged   as   providing   funding   for   the   working   group   \n316 authors.   BBSRC   LIDP   (BB/M009513/1:   DS).   This   research   was   partly   funded   by   the   Bill   &   \n317 Melinda   Gates   Foundation   (INV-001754:   MQ;   INV-003174:   KP,   MJ,   YL;   INV-016832:   SRP;   \n318 NTD   Modelling   Consortium   OPP1184344:   CABP,   GFM;   OPP1139859:   BJQ;   OPP1183986:   \n319 ESN;   OPP1191821:   MA).   BMGF   (INV-016832;   OPP1157270:   KA).   EDCTP2   \n320 (RIA2020EF-2983-CSIGN:   HPG).   ERC   Starting   Grant   (#757699:   MQ).   This   project   has   \n321 received   funding   from   the   European   Union's   Horizon   2020   research   and   innovation   \n322 programme   -   project   EpiPose   (101003688:   KP,   MJ,   PK,   RCB,   YL).   FCDO/Wellcome   Trust   \n323 (Epidemic   Preparedness   Coronavirus   research   programme   221303/Z/20/Z:   CABP).   This   \n324 research   was   partly   funded   by   the   Global   Challenges   Research   Fund   (GCRF)   project   \n325 'RECAP'   managed   through   RCUK   and   ESRC   (ES/P010873/1:   TJ).   HDR   UK   \n326 (MR/S003975/1:   RME).   HPRU   (This   research   was   partly   funded   by   the   National   Institute   for   \n327 Health   Research   (NIHR)   using   UK   aid   from   the   UK   Government   to   support   global   health   \n328 research.   The   views   expressed   in   this   publication   are   those   of   the   author(s)   and   not   \n17   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n329 necessarily   those   of   the   NIHR   or   the   UK   Department   of   Health   and   Social   Care200908:   \n330 NIB).   MRC   (MR/N013638/1:   NRW).   Nakajima   Foundation   (AE).   NIHR   (16/136/46:   BJQ;   \n331 16/137/109:   BJQ,   FYS,   MJ,   YL;   Health   Protection   Research   Unit   for   Modelling   Methodology   \n332 HPRU-2012-10096:   TJ;   NIHR200908:   AJK,   RME;   NIHR200929:   FGS,   MJ,   NGD;   \n333 PR-OD-1017-20002:   AR).   Royal   Society   (Dorothy   Hodgkin   Fellowship:   RL;   RP\\EA\\180004:   \n334 PK).   UK   DHSC/UK   Aid/NIHR   (PR-OD-1017-20001:   HPG).   UK   MRC   (MC_PC_19065   -   Covid   \n335 19:   Understanding   the   dynamics   and   drivers   of   the   COVID-19   epidemic   using   real-time   \n336 outbreak   analytics:   NGD,   RME,   SC,   TJ,   YL;   MR/P014658/1:   GMK).   Authors   of   this   research  \n337 receive   funding   from   UK   Public   Health   Rapid   Support   Team   funded   by   the   United   Kingdom   \n338 Department   of   Health   and   Social   Care   (TJ).   UKRI   Research   England   (NGD).   Wellcome   Trust   \n339 (206250/Z/17/Z:   AJK,   TWR;   206471/Z/17/Z:   OJB;   208812/Z/17/Z:   SC,   SFlasche;   \n340 210758/Z/18/Z:   JH,   KS,   SA,   SRM).   No   funding   (AMF,   AS,   CJVA,   DCT,   JW,   KEA,   YWDC).   \n341 Authors   contributions   \n342 JDM,   CIJ,   WJE   conceived   of   and   planned   the   analysis;   JDM   and   CIJ   performed   the   main   \n343 analysis   with   input   from   WEJ   and   SF;   SF   provided   estimates   of   time-varying   reproduction   \n344 number;   CIJ,   KvZ,   and   WEJ   designed   the   CoMix   contact   survey,   CIJ,   AG,   KW,   and   KvZ   \n345 cleaned   and   managed   the   contact   survey   data;   All   authors   wrote   and   reviewed   the   \n346 manuscript.   The   CMMID   COVID-19   Working   Group   provided   discussion   and   comments.   \n347 Acknowledgements   \n348 The   authors   wish   to   thank   Dr   Thomas   House   for   his   support   with   interpretation   of   the   ONS   \n349 susceptibility   estimates.   We   also   thank   members   of   SPI-M   for   their   useful   discussion   which   \n350 helped   shape   the   final   version   of   this   work.   We   would   like   to   thank   the   team   at   Ipsos,   who   \n351 have   been   excellent   in   running   the   survey,   collecting   the   data   and   allowing   for   the   CoMix   \n352 study   to   be   implemented   rapidly.   Finally,   we   thank   Katie   Collis   for   proof   reading   and   \n353 excellent   discussions.   \n18   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n354 The   following   authors   were   part   of   the   Centre   for   Mathematical   Modelling   of   Infectious   Disease   \n355 COVID-19   Working   Group.   Each   contributed   in   processing,   cleaning   and   interpretation   of   data,   \n356 interpreted   findings,   contributed   to   the   manuscript,   and   approved   the   work   for   publication:   Yang   Liu,   \n357 Joel   Hellewell,   Nicholas   G.   Davies,   C   Julian   Villabona-Arenas,   Rosalind   M   Eggo,   Akira   Endo,   Nikos   I   \n358 Bosse,   Hamish   P   Gibbs,   Carl   A   B   Pearson,   Fiona   Yueqian   Sun,   Mark   Jit,   Kathleen   O'Reilly,   Yalda   \n359 Jafari,   Katherine   E.   Atkins,   Naomi   R   Waterlow,   Alicia   Rosello,   Yung-Wai   Desmond   Chan,   Anna   M   \n360 Foss,   Billy   J   Quilty,   Timothy   W   Russell,   Stefan   Flasche,   Simon   R   Procter,   William   Waites,   Rosanna   C   \n361 Barnard,   Adam   J   Kucharski,   Thibaut   Jombart,   Graham   Medley,   Rachel   Lowe,   Fabienne   Krauer,   \n362 Damien   C   Tully,   Kiesha   Prem,   Jiayao   Lei,   Oliver   Brady,   Frank   G   Sandmann,   Sophie   R   Meakin,   Kaja   \n363 Abbas,   Gwenan   M   Knight,   Matthew   Quaife,   Mihaly   Koltai,   Sam   Abbott,   Samuel   Clifford.   \n364 Additional   Files   \n365 Supplementary   Figures   \n   \n19   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n366 Figure   Captions   \n367 Figure   1.   Contacts   in   the   national   lockdown   periods   in   November   (Lockdown   2)   and   \n368 January   (Lockdown   3) .    A)    the   distribution   of   the   number   of   reported   contacts   in   Home,   \n369 Work,   School   and   Other   locations   for   Adult   (>   17   years   old)   and   Child   (<=   17   years   old)   \n370 participants.    B)    Mean   contacts   reported   between   Children   and   Adults   in   each   region   of   \n371 England.   Error   bars   show   the   90%   CI   (bootstrapped,   1000   samples).   \n  \n372 Figure   2:   R   estimates   using   CoMix   data   fit   to   time-varying   reproduction   number   \n373 estimates   based   on   the   time   series   of   cases    [21] .    Transformed   likelihood   for   different   \n374 combinations   of   relative   susceptibility   and   infectiousness   based   on   data   from    A)    August   to   \n375 October   and    B)    June   to   October   and   the   corresponding   R   estimates   in    C)    and    D)   \n376 respectively.   90%   CI   of   the   estimates   are   shown   by   Grey   rectangles   for   CoMix   and   the   red  \n377 ribbon   for   the   time-varying   reproduction   number   estimates   from   case   data,   red   bars   show   \n378 their   mean   for   the   CoMix   survey   periods.   Grey   shaded   areas   indicate   fitted   periods.   \n  \n379 Figure   3:   The   impact   of   reopening   schools   on   the   reproduction   number.   A)    the   relative   \n380 increase   in   R   (the   ratio   of   dominant   eigenvalues   between   contact   matrices   for   each   \n381 reopening   scenario   and   that   for   current   contact   patterns)   under   different   estimates   of   the   age   \n382 profile   of   susceptibility   and   infectiousness.    B)    The   estimated   R   after   reopening   schools   \n383 (points,   90%   CI   bars)   from   baseline   R   of   0.7,   0.8,   0.9   and   1.0   (vertical   line).   Dashed   vertical   \n384 lines   show   R   =   1.0.     \n20   \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n/\n  \n385 References   \n386 1.   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Using   data   on   social   contacts   to   estimate   \n450 age-specific   transmission   parameters   for   respiratory-spread   infectious   agents.   Am   J   \n451 Epidemiol.   2006;164:936–44.   \n452 23.   The   R   value   and   growth   rate   in   the   UK.   \n453 https://www.gov.uk/guidance/the-r-number-in-the-uk.    Accessed   10   Feb   2021.   \n454 24.   Office   for   National   Statistics.   Coronavirus   (COVID-19)   Infection   Survey,   UK.   Office   for   \n455 National   Statistics;   2021.   \n456 https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddi \n457 seases/bulletins/coronaviruscovid19infectionsurveypilot/12february2021.    Accessed   4   Mar   \n458 2021.   \n459 25.   Gostic   KM,   McGough   L,   Baskerville   EB,   Abbott   S,   Joshi   K,   Tedijanto   C,   et   al.   Practical  \n460 considerations   for   measuring   the   effective   reproductive   number,   Rt.   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(which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n●\n●\n●\n●\n●\n●\n●\n● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 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● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●\n● ●\n●\n●\n●\n●●●\n●\n●\n● ●\n● ● ● ● ●\n● ●\n●\n●\n●\n●\n●\n● ● ● ● ● ● ● ● ● ● ● ● ● ●\n●\n● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●\nHome Work School Other\nAdult ParticipantChild Participant\n1\n10\n100\n1000\n1\n10\n100\n1000\n1\n10\n100\n1000\n1\n10\n100\n1000\n1\n10\n100\n1000\n1\n10\n100\n1000\nNo. Contacts\nParticipants\nA\n●● ●● ●● ●●● ●●●\n●● ● ●●●\n● ●●\n●● ●\n●\n●●\n● ● ●●● ●\n●\n● ●\n●\n●\n● ●\n●\n●\n●\n●\n●\n● ●\n●\n●\n●\n●\n●\n●●\n●\n●●\n●\n●\n● ●\n●\n●\n●\n● ●●\n●\n●● ●●\nAdult Contact Child Contact\nAdult ParticipantChild Participant\nEast Midlands\nEast of England\nGreater London\nNorth East\nNorth West\nSouth East\nSouth West\nWest Midlands\nY orkshire and The Humber\nEast Midlands\nEast of England\nGreater London\nNorth East\nNorth West\nSouth East\nSouth West\nWest Midlands\nY orkshire and The Humber\n5\n10\n15\n20\n5\n10\n15\n20\nRegion\nMean Contacts\nPeriod ● ●Lockdown 2 Lockdown 3\nB\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\n●\n0.25\n0.50\n0.75\n1.00\n1.25\n0.25 0.50 0.75 1.00 1.25\nRelative Susceptibility\nRelative Infectiousness\nStudy: ●\n1. Equal 2. Davies et al 3. ONS 4. Viner et al\n0.5 1.0 1.5 2.0\nexp(−ll/1000)\nA\n●\n0.25\n0.50\n0.75\n1.00\n1.25\n0.25 0.50 0.75 1.00 1.25\nRelative Susceptibility\nRelative Infectiousness\nStudy: ●\n1. Equal 2. Davies et al 3. ONS 4. Viner et al\n0.25 0.50 0.75 1.00\nexp(−ll/1000)\nB\n0.4\n0.8\n1.2\n1.6\n2.0\nAug Sep Oct Nov Dec Jan\ndate\nR estimate\nC\n0.4\n0.8\n1.2\n1.6\n2.0\nJun Jul Aug Sep Oct Nov Dec Jan\ndate\nR estimate\nD\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint \n\nSecondary\nPrimary\nBoth\n1.0 1.5 2.0 2.5\n1.\n2.\n3.\n4.\n5.\n1.\n2.\n3.\n4.\n5.\n1.\n2.\n3.\n4.\n5.\nRelative increase in R\nStudy:\n1. Equal 2. Davies et al 3. ONS 4. Viner et al 5. CoMix fit\nA\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\n●\nBaseline R = 1\nBaseline R = 0.9\nBaseline R = 0.8\nBaseline R = 0.7\n0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4\nPrimary\nSecondary\nBoth\nPrimary\nSecondary\nBoth\nPrimary\nSecondary\nBoth\nPrimary\nSecondary\nBoth\nR\nB\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}