{"paper_id":"ed543365-d3e6-493f-91f5-75110c3713c6","body_text":"The impact of school reopening on the spread of\nCOVID-19 in England.\nMatt J. Keeling 1*, Michael J. Tildesley 1‡, Benjamin D. Atkins 1, Bridget Penman 1, Emma\nSouthall1,2, Glen Guyver-Fletcher1,3, Alex Holmes 1,2, Hector McKimm 1,4, Erin E. Gorsich 1, Edward\nM. Hill1‡, Louise Dyson 1‡.\n1 The Zeeman Institute for Systems Biology & Infectious Disease Epidemiology Research, School of\nLife Sciences and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United\nKingdom.\n2 Mathematics for Real World Systems Centre for Doctoral Training, Mathematics Institute,\nUniversity of Warwick, Coventry, CV4 7AL, United Kingdom.\n3 Midlands Integrative Biosciences Training Partnership, School of Life Sciences, University of\nWarwick, Coventry, CV4 7AL, United Kingdom.\n4 Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom.\n‡These authors contributed equally to this work.\n* Corresponding Author. Email: M.J.Keeling@warwick.ac.uk\nAbstract\nBy mid-May, cases of COVID-19 in the UK had been declining for over a month; a multi-phase\nemergence from lockdown was planned, including a scheduled partial reopening of schools on 1st June.\nAlthough evidence suggests that children generally display mild symptoms, the size of the school-age\npopulation means the total impact of reopening schools is unclear. Here, we present work from mid-\nMay that focused on the imminent opening of schools and consider what these results imply for future\npolicy.\nWe compared eight strategies for reopening primary and secondary schools in England. Modifying a\ntransmission model fitted to UK SARS-CoV-2 data, we assessed how reopening schools affects contact\npatterns, anticipated secondary infections and the relative change in the reproduction number, R.\nWe determined the associated public health impact and its sensitivity to changes in social-distancing\nwithin the wider community.\nWe predicted reopening schools with half-sized classes or focused on younger children was unlikely\nto push R above one. Older children generally have more social contacts, so reopening secondary\nschools results in more cases than reopening primary schools, while reopening both could have pushed\nR above one in some regions. Reductions in community social-distancing were found to outweigh and\nexacerbate any impacts of reopening. In particular, opening schools when the reproduction number\nR is already above one generates the largest increase in cases.\nOur work indicates that while any school reopening will result in increased mixing and infection\namongst children and the wider population, reopening schools alone in June was unlikely to push\nR above one. Ultimately, reopening decisions are a difficult trade-off between epidemiological conse-\nquences and the emotional, educational and developmental needs of children. Into the future, there\nare difficult questions about what controls can be instigated such that schools can remain open if cases\nincrease.\n1\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: 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\nIntroduction 1\nThe emergence of a novel strain of coronavirus, now named SARS-CoV-2, in Wuhan city, China, in 2\nlate 2019, has resulted in a global pandemic that spread to every region in the world. When the SARS- 3\nCoV-2 virus infects humans it can result in COVID-19 disease, with symptoms including a fever, a 4\ncontinuous dry cough, a shortness of breath and a loss of sense of taste and smell [1]. In severe cases, 5\nthe symptoms can require hospitalisation and admission to intensive care, with ventilation required in 6\nthe most severe cases in order to assist with breathing. 7\nAs the number of confirmed cases increased both nationally and globally, there was a concern that 8\nhospital and intensive care capacities would be rapidly overwhelmed without the introduction of in- 9\nterventions to curb the spread of infection. With this in mind, many countries introduced a range of 10\nsocial distancing measures, such as the closing of workplaces, pubs and restaurants, the restriction of 11\nleisure activities and the closing of schools. In the UK, the introduction of many of these measures 12\nwas announced during the week of 16th March, with schools, along with the hospitality sector, closing 13\non Friday 20th March. Full lockdown measures were subsequently introduced three days later, on the 14\nevening of Monday 23rd March. When we completed this work in late May, over 270 , 000 people in 15\nthe UK had been confirmed to have been infected with COVID-19, with over 37, 500 confirmed deaths 16\nof individuals who had tested positive for infection. 17\nThe decision to close schools is a balance between the risk associated with transmission in the school 18\nenvironment and the educational and welfare impact upon children of shutting down education es- 19\ntablishments. Evidence from a range of sources suggests that children are, in general, only mildly 20\naffected by the disease and have low mortality rates [2, 3]. This is reflected in the fact that by 27th 21\nMay 2020 there had been 26 , 235 COVID-19 associated deaths in hospitals in England, but only 16 22\nof those were in the 0-19 year age group [4]. In a retrospective study of 2 , 135 paediatric COVID-19 23\ncases in China [5], 89.7% of children had mild or moderate disease while 5 .8% were severe or critical; 24\nsimilarly low levels of severe disease are reported in other regions [3, 6]. The health risks of school 25\nattendance for any individual child is therefore thought to be low. 26\nHowever, there is less certainty regarding children’s role in the transmission of SARS-CoV-2 [7, 8]. 27\nThis can be broken down into two key questions: (i) how likely are children to become infected, and 28\n(ii) once infected, are children likely to transmit infection? 29\nA meta-analysis concluded that children and young people under the age of 20 may be less likely to 30\nbecome infected: the odds ratio for becoming infected upon contact with an index case compared to 31\nadults (> 20 years old) is 0 .44 (CI 0.29, 0.69) [7]. This conclusion is based on pooling the results of 32\ncontact tracing and population-screening studies, most of which find evidence that the attack rate in 33\nchildren may be lower than in adults [9, 10], but one does not (Bi et al. [11]). All contact tracing 34\nstudies are hampered by the problem that symptom-based surveillance is likely to systematically under 35\ndetect cases in children [11]. Seroprevalence surveys so far do not find any significant effect of age on 36\nthe probability of possessing antibodies against COVID-19, although those under the age of five are 37\nnot always included in surveys [12–14]. Two cross sectional PCR studies hint at lower susceptibility 38\nin children, since they found no SARS-CoV-2 PCR positive children under the age of 10 [15, 16], but 39\na PCR-based survey by the UK Office for National Statistics found no difference in the probability of 40\ninfection between age classes [17]. Further, large-scale seroprevalence studies which fully sample all 41\nage groups will be necessary to fully resolve these questions. Overall the balance of evidence cautiously 42\nsuggests that children may have a lower inherent susceptibility. If it exists, such lower susceptibility 43\ncould be physiological [18] or could be due to cross reactive immune responses from other childhood 44\ninfections, with cross-protection between other human coronaviruses and SARS-CoV-2 hinted at by 45\nrecent studies [19, 20]. 46\n2\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nThere is little evidence from contact tracing and clinical investigations about the relative infectiousness 47\nof children. Children hospitalised with COVID-19 readily shed the virus above the likely transmission 48\nthreshold [21–23], with detection of virus in nasopharyngeal (nasal) swabs, oropharyngeal (throat) 49\nswabs, sputum, or faeces [24, 25]. However, in their review of contact tracing and population-screening 50\nstudies, Viner et al. [7] found just one relevant study comparing infectiousness by age: Zhu et al. [26], 51\nwhich shows that children make up a low proportion of index cases in households. As pointed out by 52\nViner et al. , this particular result could be explained by children being less likely to get infected in 53\nthe first place rather than children being less infectious once they have actually contracted the virus. 54\nThere is also evidence suggesting that mild cases in adults could be less infectious than severe or 55\ncritical cases [10], but it remains unknown whether this result extends to asymptomatic or mild cases 56\nin children. Thus, children with severe symptoms are likely infectious, but it is harder to determine 57\nhow transmissible the virus may be from children with few or no symptoms. 58\nAs of May 2020, we were aware of three reported studies of SARS-CoV-2 infection within the school 59\nenvironment. A retrospective serology study of 661 individuals with links to a school-based outbreak in 60\nOise, France, showed that the infection spread readily within and outside the school to reach students, 61\nteachers, staff, and families [27]. In contrast, an Australian government study of cases in schools in 62\nWestern Australia [28] identified nine children and nine adults who tested positive for SARS-CoV-2 63\n(located across different schools), but found only two secondary cases when testing a third of the 64\nclose contacts of these cases (288 samples). In Ireland, six SARS-CoV-2 cases were identified who 65\nhad attended or taught in schools. None of 924 school related child contacts or 101 school related 66\nadult contacts showed any symptoms, but asymptomatic cases could have been missed [29]. The 67\nAustralian school cases were identified between 5th March and 3rd April, and the first Irish school 68\ncase was identified at the beginning of March. The first Oise school cases, by contrast, were identified 69\non the 2nd February 2020. The greater awareness of COVID-19 by March, during which the WHO 70\ndeclared COVID-19 as a global pandemic, likely helped to control the Australian and Irish school-based 71\noutbreaks sooner than in Oise. 72\nIn the UK, during late May 2020, cases of COVID-19 were declining and there was strong evidence to 73\nsuggest that the effective reproduction number (R ) had dropped below 1 across the country. A multi- 74\nphase relaxation plan for the country to emerge from lockdown began on 13th May, with a greater 75\nemphasis on returning to work if practical. We present here research formulated to address policy 76\nquestions in May, to help inform the expected impact of various groups returning to the classroom. 77\nIn particular, we investigate the epidemiological impacts of reopening schools in England, focusing 78\non different combinations of year groups. We extend a previously developed dynamic transmission 79\nmodel for SARS-CoV-2, which is fit (on a regional basis for the UK) to real-time data on confirmed 80\ncases requiring hospital care and mortality. We compare and contrast multiple possible strategies for 81\nreopening both primary and secondary schools, focusing upon determining the effect of given year 82\ngroups returning to school upon future epidemic behaviour. By elucidating the risks associated with 83\nparticular age groups returning to school, we seek to contribute to the evidence base on the likely 84\nrole of schools in the containment and control of this outbreak. Unlike other modelling studies [30], 85\nwe decouple school reopening from other measures (such as a greater return to work); we feel this 86\ngenerates a clearer picture of the roles of school children and adults [31]. 87\nIn England, primary schools partially reopened on 1st June: reception, year 1 and year 6 children 88\ninitially returned, with an emphasis on maintaining social distancing measures where possible. In 89\nSeptember (August in Scotland), the majority of schools reopened with generally high levels of atten- 90\ndance. We therefore discuss the implications for this work both in terms of the likely effects of schools 91\non the unfolding epidemic and their role in any future imposition of additional control measures. 92\n3\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nMethods 93\nTransmission model 94\nIn order to perform the analysis of school reopening, we extended a previously-developed determinis- 95\ntic, age-structured compartmental SARS-CoV-2 transmission model [32]. The model was matched to 96\na variety of data sources including hospitalisations, ICU occupancy and deaths, while age-dependent 97\nparameters were scaled to achieve agreement with the early age-distributions [33]. We stratified the 98\npopulation according to current disease status, following a susceptible-exposed-infectious-recovered 99\n(SEIR) paradigm (Fig. 1). We assumed the latent period to be Erlang distributed, modelled within 100\nthe compartmental framework via division of the latent state into three stages. Infectious cases were 101\npartitioned by presence of symptoms, meaning we tracked symptomatic and asymptomatic individuals 102\nseparately. Additional layers of complexity included differentiating by isolation and household status. 103\nWe provide a listing of model parameters in Table 1, with a description of the model equations given 104\nin Supporting Text S1. We use the predicted number of symptomatic individuals to estimate the 105\nnumber of hospital admissions, ICU admissions and deaths, by estimating the proportion of symp- 106\ntomatic individuals requiring hospitalisation, ICU admission and the proportion that eventually die, 107\nand the distribution of times through each of these states. For hospital admissions and cases requiring 108\ntreatment in ICU, the proportions going through each state and the distribution of times taken were 109\ndrawn from the COVID-19 Hospitalisation in England Surveillance System (CHESS) data set that 110\ncollects detailed data on patients infected with COVID-19 [34]. The risk of death was also captured 111\nwith an age-dependent probability, while the distribution of delays between hospital admission and 112\ndeath was assumed to be age-independent, with both these two quantities determined from the Public 113\nHealth England (PHE) death records. 114\nWith the inclusion of age-structure, transmission was governed through age-dependent mixing ma- 115\ntrices, based on UK social mixing patterns [35, 36], scaled by an age-dependent susceptibility that 116\nwas determined to produce the early age-distribution of symptomatic cases. To capture the effects of 117\nsocial distancing measures that were introduced in the UK to reduce transmission, we scaled down 118\nthe mixing matrices associated with schools, work and other activities while increasing the within 119\nhousehold transmission matrix (see Supporting Text S2). 120\nIn a refinement to the base model, we imposed an amended age-stratification of the population. Whilst 121\nin previous work the population was stratified into five year age brackets, for this study we separated 122\nthose aged between 0 and 19 years old into single year cohorts, with the remainder of the population 123\nstratified into five year age brackets as before (20-24yrs, 25-29yrs and so on). The final age category 124\ncorresponded to those aged 100 years or above. This fine-scale structure for those younger than 20 is 125\nimportant to be able to capture different policy questions; however resolution at a single year of age is 126\nnot captured within the mixing matrices [35, 36]. We therefore generally retain the mixing structure 127\nbased on five year age groups (Fig. 2), but assume that 70% of mixing within the same five year age 128\ngroup comes from interactions within the same school year. 129\nModelling school reopening scenarios 130\nWe used this model framework to evaluate eight strategies for reopening schools from 1st June. The 131\neight school reopening options we considered assumed that, from the 1st June, the following school 132\nyear groups would return to school: 133\n(i) reception (year 0), year 1 and year 6 (full class sizes); 134\n(ii) reception, year 1 and year 6 (half class sizes); 135\n(iii) all primary schools; 136\n(iv) reception, years 1, 6, 10 and 12 (full class sizes); 137\n4\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nFig. 1: Disease states and transitions. We stratified the population into susceptible, exposed, detectable\ninfectious, undetectable infectious, and removed states. Solid lines correspond to disease state transitions, with\ndashed lines representing mapping from detectable cases to severe clinical cases that require hospital treatment,\ncritical care (ICU), or result in death. We separated those aged between 0 and 19 years old into single years,\nwith the remainder of the population stratified into five year age brackets. See Table 1 for a listing of model\nparameters. Note, we have not included quarantining or household status on this depiction of the system.\n(v) reception, years 1, 6, 10 and 12 (half class sizes); 138\n(vi) primary schools plus year groups 10 and 12; 139\n(vii) all secondary schools; 140\n(viii) all schools. 141\nFor clarity, in all the strategies considered here we assumed that children of key workers continued to 142\nattend school at the currently observed level. 143\nWe assessed the school reopening scenarios at a regional scale, modelling the population of England 144\naggregated to seven regions (East of England, London, Midlands, North East and Yorkshire, North 145\nWest England, South East England, South West England). This involved the use of region-specific 146\nposterior parameters obtained in our prior work, where we fit our base transmission model on a region- 147\nby-region basis, using a Monte Carlo Markov Chain (MCMC) fitting scheme, to four timeseries: (i) new 148\nhospitalisations; (ii) hospital bed occupancy; (iii) ICU bed occupancy; (iv) daily deaths (using data on 149\nthe recorded date of death, wherever possible) [32]. The inference was performed from epidemiological 150\ndata until 12th May 2020. 151\nOur assessment of school reopening strategies comprised of three strands. Firstly, we quantified how 152\nthe process of opening schools and year groups affected contact patterns and anticipated secondary 153\ninfections. Secondly, we related the scale of school opening to the relative change in R, assuming 154\nthe same transmission patterns in the rest of the population as during the strict lockdown phase. 155\nFinally, we gauged the estimated change in clinical case and its sensitivity to changes in community 156\ntransmission following the easing of lockdown measures on 13th May. We outline each item in further 157\ndetail below. 158\n5\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nTable 1: Key model parameters\nParameter Description Value Source\nβ Age-dependent transmission, split into\nhousehold, school, work and other\nDerived from POLYMOD\nmatrices [36]\nϵ Rate of progression to infectious disease\n(1/ϵ is the duration in the exposed class)\n∼ 0.2 Fitted as part of MCMC\nprocess\nγ Recovery rate, changes with τ, the rel-\native level of transmission from unde-\ntected asymptomatics compared to de-\ntected symptomatics\n∼ 0.5 Fitted from early age-\nstratified UK case data\nα Scales the degree to which age-structured\nheterogeneity is due to age-dependent\nprobability of symptoms ( α = 0) or age-\ndependent susceptibility (α = 1)\n0.137(0.1150.146) Fitted as part of MCMC\nprocess\nτ Relative level of transmission from asymp-\ntomatic compared to symptomatic infec-\ntion\n0.138(0.135 − 0.145) Fitted as part of MCMC\nprocess\nda Age-dependent probability of displaying\nsymptoms (and hence being detected),\nchanges with α and τ\n0-1 Fitted from early age-\nstratified UK case data\n(see of MCMC process or\nvaried according to sce-\nnario (see Supporting Fig-\nure S1)\nσa Age-dependent susceptibility, changes\nwith α and τ\n0.4-1 Fitted from early age-\nstratified UK case data\n(see of MCMC process or\nvaried according to sce-\nnario (see Supporting Fig-\nure S1)\nφR Adherence to the lockdown restrictions 0.3 − 0.8 Fitted as part of MCMC\nprocess or varied according\nto scenario (see Supporting\nFigure S1)\nH R Household quarantine proportion 0 − 1 Can be varied according to\nscenario\nN R\na Population size of a given age By region ONS\nContacts and secondary infections 159\nAny school reopening plan will inherently alter age-group contact patterns compared to contact struc- 160\ntures observed during the lockdown. We attempted to resolve how these alterations in social in- 161\nteractions propagated into the transmission dynamics by tracking secondary infections arising from 162\nsymptomatic index cases and infected index cases (either symptomatic or asymptomatic), respec- 163\ntively. 164\nSpecific to this aspect of the analysis we focused on a single region, namely the Midlands and the 165\nposterior parameter set with the maximum likelihood. We first assess the contact structure and 166\ntransmission under two distinct lockdown assumptions (‘strict closure’ and our default assumption of 167\n‘weaker closure’). The ‘strict closure’ scenario assumed that there was no additional mixing between 168\n6\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nschool-age groups during the lockdown period. ‘Weaker closure’ assumed there was more limited 169\nadherence, leading to higher mixing between school-age groups compared to the ‘strict closure’ setting. 170\nWe also consider six of the eight reopening strategies (omitting those with half class sizes as these are 171\nbounded above by the full-class strategy). For each we show the age-mixing matrix between age-groups; 172\nthe transmission matrix from a symptomatic infectious individual; the transmission matrix from an 173\naverage infectious individual (recognising the many will be asymptomatic or in household quarantine); 174\nand the expected number of secondary cases an average infectious individual of a particular age-group 175\nwill generate. 176\nReproduction number analysis 177\nThe reproduction ratio or number (R) has become a universally recognised quantity in the description 178\nof COVID-19 dynamics; it is defined as the average number of secondary cases from an average index 179\ncase — where the second average is important as it samples across all infectious states including 180\nasymptomatics and those currently under household isolation. To prevent the occurrence of a second 181\nphase of exponential growth in infection, it is crucial that relaxation of social distancing measures 182\ndo not result in the value of R rising above 1. On these grounds, there is interest in predicting the 183\nmagnitude of a rise in R that could result from the reopening of schools, and our confidence in this 184\nresult. 185\nWe considered all eight school reopening scenarios and examined the increase in R per region under 186\neach of the eight strategies. To compute R, we used the contact matrices associated with the given 187\nchoice of school reopening and accounting for the regional population structure, whilst assuming the 188\nsame level of mixing in the rest of the population as during the strict lockdown; therefore any changes in 189\nR are driven by changes in school-age mixing. We calculated means and intervals from 1000 simulation 190\nreplicates with parameter sets sampled from the posterior parameter distributions. 191\nClinical case impact 192\nThe prior methods focused on the reproduction numberR, which is both an instantaneous measure (R 193\ncan be calculated at any or every time point) and a long-term calculation (as it utilises an eigenvalue 194\napproach to generate the asymptotic R). Calculation of quantities of public health interest requires 195\nthe simulation of the full temporal dynamics from the start of the outbreak to the closing of schools 196\nfor the summer holidays on 22nd July. In addition, we considered the sensitivity of reopening schools 197\nto other potential changes in population mixing patterns (and hence different values of R) driven by 198\nother changes to the lockdown since 13th May. These changes to population mixing were generated 199\nby reducing the adherence with lockdown measures, bringing the mixing matrices closer to the pre- 200\npandemic norm. 201\nWe performed these simulations, using the full dynamic model to generate estimates of the symp- 202\ntomatic cases, deaths and ICU admissions between 1st June and 22nd July, for each of the eight 203\nschool-opening strategies. We compared these measures, aggregated over this 52-day period, to a 204\nscenario where school closures remain in place beyond the 1st June. 205\nFor each reopening strategy and each region, we performed a total of 1000 replicates. In each replicate 206\nwe sampled parameter values randomly from all posterior parameter distributions, with the exception 207\nof the adherence level. The potential reduction in adherence values, from 13th May, inevitably gen- 208\nerates different R values at the point of school reopening (measured by the observed growth rate of 209\nthe outbreak in the model simulation). As a consequence, for comparative purposes we segregated 210\nthe estimated increases in epidemiological quantities (comparing different school opening strategies for 211\nfixed underlying parameters) into three categories according to the R value before school reopening: 212\nbelow 0.8, between 0.8 and 1, or between 1 and 1.2. 213\n7\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nResults 214\nChoice of reopening strategy influences contact structure and secondary infection risk 215\nWe first investigated the impact of alternate strategies for reopening schools upon contact patterns be- 216\ntween individuals and the effect of this upon transmission of SARS-CoV-2 and occurrences of COVID- 217\n19 infection. Our results for the Midlands, and the posterior parameter-set derived in May that 218\nmaximises the likelihood (giving R ≈ 0.78), are summarised in Fig. 2. For all scenarios investigated 219\nwe observe several common trends. Contacts are most common between individuals of the same, 220\nor similar ages (Fig. 2, first row [36]). There was also greater contact between children and adults 221\nbetween the ages of 25 and 55, reflecting interactions between children and their parents, as well as 222\nbetween elderly people [36]. This increased likelihood of contact within and between those age groups 223\nis reflected in the risk of secondary infections occurring (Fig. 2, second and third rows). The second 224\nrow accounts for age-dependent susceptiblity, and shows the expected number of secondary infections 225\nin each age (y-axis) from a symptomatic index case of a particular age (x-axis). The third row incor- 226\nporates the likely state of an index infection (symptomatic, asymptomatic or in household quarantine 227\n- as predicted by the underlying ODEs) thereby reducing the potential transmission from particular 228\nage-groups (Supporting Figure S2). 229\nIf schools remain closed, with a high level of adherence to the lockdown within this younger age-group 230\n(Fig. 2, first column) we observe that contact between children, and therefore the risk of secondary 231\ninfection occurring, is extremely low. Should adherence to lockdown be weaker (Fig. 2, second column), 232\nwe observe a higher rate of mixing between children and a slight increase in risk of secondary infections 233\noccurring. For both of these scenarios the average number of secondary infections per index infection 234\nis below 1 for all age groups and the value of R remains significantly below 1. 235\nWe now investigate the impact of various strategies for school reopenings. We first investigate the 236\nscenario of reception, year 1 and year 6 children returning to school – the policy that is scheduled to 237\nbe implemented on 1st June in England (Fig. 2, third column). In this scenario, we observe a slight 238\nincrease in contacts compared to the “weaker closure” scenario, with increased transmission between 239\nindividuals in these age groups. However, crucially, even within these age groups, the total number 240\nof secondary infections per index case remains below one (third column, final row, red bars) and the 241\noverall reproduction number value ofR was only observed to have slightly increased from the scenarios 242\nin which schools remain closed. A slight increase in mixing, and hence R, was again observed when 243\nall primary schools are opened (Fig. 2, fourth column), but we predict that R remains below 1. 244\nTo conclude this segment of the analysis, we investigated the impact of school reopening strategies 245\nthat involved some, or all, secondary school children returning to the classroom. If children from key 246\nyears of 10 and 12 return to school (in addition to some or all primary school children), a significant 247\nincrease in mixing was observed within those age groups; the number of secondary infections as a 248\nresult of index infections in secondary schools was predicted to be above one (Fig. 2, fifth and sixth 249\ncolumns). However, this expected number of cases is distributed across multiple age-groups thereby 250\ndissipating the worst effects. In general, we found secondary schools to represent a higher risk of 251\nincreased transmission potential than primary schools. This could lead to higher values of R when all 252\nsecondary schools are opened; but for all scenarios investigated, even the scenario in which all schools 253\nare opened, we found strong support for R remaining below 1 in the Midlands (Fig. 2, final column) 254\nassuming that all other transmission patterns remain unchanged. 255\n8\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nFig.\n2: Mixing matrices and their implications for onwards transmission. We consider the effect on contact structures between different age\ngroups under (first column) strict school closure, (second column) weak closure, (third column) years 0 (reception), 1 and 6 returning to school,\n(fourth column) all primary school children at school , (fifth column) years 0, 1, 6, 10 and 12 at school, (sixth column) all primary school children and\nyears 10 and 12 at school, (seventh column) all secondary school children at school and (eighth column) all children in school. For each school closure\nwe show: (first row) the average number of contacts by age for each index age group [36]; (second row) the average number of secondary infections\nfor a symptomatic infected individual by age (combining the mixing matrix with age-susceptibility); and (third row) the average number of secondary\ninfections for each infected individual by age combining the mixing matrix, age-susceptibility and the impact of asymptomatic transmission). (Fourth\nrow) The total number of secondary infections for each infected index age group. Green bars indicate school year groups who remain at home, whilst red\nbars indicate year groups who return to school.\n9\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nEffect of school reopening on reproduction number 256\nNext, we sought to estimate changes in R that may result from school reopenings alone - assuming 257\nthe transmission patterns in the rest of the population are maintained at strict lockdown phase levels. 258\nIn contrast to the the first part of the analysis, which focused on a single set of parameters and a 259\nsingle region (Fig. 2), here we explore the full parameter uncertainty and compare different parts of 260\nthe country. 261\nFor all school opening scenarios, within the seven regions of England, we observe an increase in R 262\ncompared to what we predict for keeping schools closed until the end of the academic year (Fig. 3 and 263\nSupporting Figure S3). This is to be expected, given the increase in contact between children that 264\nsuch reopening scenarios would allow. However, the magnitude of increase is predicted to be relatively 265\nlow, depending on the age-groups that return to school. In general, the more year groups allowed to 266\nreturn to school at one time, the greater the effect on R, with the return of secondary school children 267\nhaving the greatest impact. 268\nThe impact of allowing multiple year groups to return to school can still be small: opening a fraction 269\nof the age-cohorts in each school generally leads to a moderate (less than 0.05) increase inR, especially 270\nif children can be taught in smaller class sizes which is assumed to lead to a proportionate reduction 271\nin within school transmission. 272\nThere is however considerable variation between the regions and here we focus on four exemplars. 273\nFor London and North East England & Yorkshire, the increase in R was considerably less than that 274\nfor East of England and the Midlands across all reopening scenarios. For the former, even allowing 275\nall age groups to return to school (while maintaining tight control in other age-groups) was highly 276\nunlikely to increase R above 1, with both means and 95% prediction intervals falling well below this 277\nthreshold (Figs. 3(a) and 3(b), the 95% prediction intervals, as the name suggests, contain 95% of 278\nall predicted values across the entire posterior distribution of parameters). This low R value was 279\nespecially true for London, which saw the most abrupt rise and subsequent decline in cases. However, 280\nthis was not the case for the East of England (Fig. 3(c)) and the Midlands (Fig. 3(d)). In these regions, 281\nallowing schools to fully reopen could increaseR above 1, with such an occurrence lying within the 95% 282\nprediction intervals. We attribute these regional differences to both heterogeneity in the observed rate 283\nof epidemic decline and the differential proportion of school age children in each region; the Midlands 284\nhas the highest proportion of older teenagers in the country. 285\nQuantifying clinical case impact stemming from the re-opening of schools 286\nOur final piece of analysis examined the extent to which each of the eight school reopening strategies 287\nmay contribute to clinical case outcomes, using the full dynamic model. We also considered the 288\nsensitivity of reopening schools to other potential changes in population mixing patterns (and hence 289\ndifferent values of R) driven by other changes to the lockdown since 13th May. 290\nIn each scenario, reopening schools increased the absolute number of cases, ICU admissions and deaths 291\nas a result of increased transmission (Fig. 4). Note that these increases will not be restricted to the 292\nchildren that return to school, since the greater transmission will lead to increased cases in other age 293\ngroups. Echoing our earlier findings, strategies in which a larger number of children return to school 294\ngenerally resulted in larger increases. In addition, older children had a greater effect, so that reopening 295\nsecondary schools results in larger increases than only reopening primary schools. 296\nThe opening of schools on 1st June was just one of a collection of changes in a short space of time, 297\nwhich began from 13th May. In the previous sections we focused on school reopening, assuming 298\nthat mixing (and hence transmission) within the wider population remained unchanged. Here we 299\nallowed the relaxation of lockdown measures to precipitate an increase of R within the community 300\n10\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nand calculate the additional change from the opening of schools. We consistently found that school 301\nreopening had a larger impact when R in the community was high, leading to a greater increase in 302\ncases, ICU admissions and deaths. However, by far the largest increase in any of these key quantities 303\nwas driven by the underlying change in R due to relaxations other than the reopening of schools 304\n(Figs. 4(b), 4(d) and 4(f)). 305\n(a)\n (b)\n(c)\n (d)\nFig. 3: Increase in reproduction number, R, under eight school reopening scenarios for four\nregions in England. Estimates are depicted for the following four regions: (a) London (R ≈ 0.69), (b) North\nEast and Yorkshire (R ≈ 0.71, (c) East of England (R ≈ 0.74), (d) the Midlands (R ≈ 0.78). For each scenario,\nbars represent the mean absolute increase in R, compared to what we would observe if schools remained closed.\nWe also give the 95% prediction intervals. Solid red lines identify the absolute increase required to raiseR above\n1, within each region, alongside 50% and 95% intervals (shaded red areas). Means and intervals are calculated\nfrom 1000 replicates sampled from the posterior parameter distributions. All scenarios are implemented on 1st\nJune and continued until 22nd July.\n11\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\n(a)\n (b)\n(c)\n (d)\n(e)\n (f)\nFig. 4: Increase in disease burden and clinical case outcomes from 1st June to 22nd July under\nthe eight different scenarios representing various combinations of school years return to school.\n(a,b) Cases; (c,d) ICU admissions and (e,f) deaths. For each scenario, the three coloured bars give the increase\nrelative to if no schools returned for low (red), intermediate (yellow) and high (purple) reproduction numbers,\nwhile the clear bar (in panels a, c and e) is the mean across all reproduction numbers. Prediction intervals are\ngiven for each scenario representing the uncertainty in the predicted values. In panels b, d and f, we also display\n(in lighter colours) the increase in each quantity that is associated with the change in R from the current low\nsituation.\n12\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nDiscussion 306\nIn this paper, we have described a mathematical model used in May 2020 to consider the implications 307\nof various potential strategies for reopening schools in England. We have compared the different 308\nstrategies by presenting mixing matrices and discussing their implication for onward transmission, and 309\nby analysing the increase in the reproduction number and absolute number of cases, ICU admissions 310\nand deaths compared to those predicted if schools remain closed. Given that in May all regions were 311\nestimated to have reproduction numbers ( R) below 0.8, we predicted that, in the absence of other 312\nchanges, the complete opening of all schools was unlikely to raise the reproduction number above one. 313\nIt must be noted that even though R remains below one, the slight increase in transmission resulting 314\nfrom school reopening subsequently leads to a small increase in the absolute number of cases, ICU 315\nadmissions and deaths. If the reopening of schools is part of a wider policy of relaxing controls, then 316\nthe impact of these additional changes must also be factored into the analysis [30, 31]. 317\nReopening schools, in any form, inevitably leads to more mixing between children, an increase in R 318\nand thus more transmission of the disease. However, we can constrain and potentially minimise the 319\nextent of this increase by selecting a subset of year-groups to return to school. In doing so, we restrict 320\nthe increase in R to very low levels and, crucially, avoid any possibility of increasingR above 1. These 321\nfindings are in agreement with studies applied to other nations suggesting that school settings are 322\nnot a major driver of SARS-CoV-2 transmission. A statistical study in US counties looking at the 323\nrelationship between the reduction in growth rate and the timing of different state and local government 324\nsocial distancing interventions found school closures to not be statistically significant [37]. Further, in 325\nterms of suppressing spread of SARS-CoV-2, a mechanistic transmission model evaluating the impact 326\nof non-pharmaceutical interventions in Switzerland, by their potential to reduceR below 1 at a national 327\nlevel, predicted school closures alone would typically be insufficient to induce control [38]. 328\nIn choosing a specific reopening policy, decision-makers must weigh-up the benefits to both children and 329\nparents that are gained from allowing more year groups to return to school, with the risks associated 330\nwith increased transmission. In light of the variation in effects onR between regions, reopening policies 331\nmay benefit from heterogeneity across the country, in order to allow the most children possible to 332\nreturn to school without threatening a resurgence of disease prevalence. Our results also highlighted 333\nthe benefit to be gained from small class sizes and hence maintaining such measures of social distancing, 334\nwith the impact of this form of non-pharmaceutical intervention within the school environment difficult 335\nto infer without explicit data. 336\nOur results also predicted a higher risk of increased transmission associated with reopening secondary 337\nschools compared to the reopening of primary schools. Such a relationship may be partly attributed 338\nto the observed larger number of contacts of secondary school children compared to primary school 339\nchildren [36]. Additionally, other contributory factors include differences between age groups in terms 340\nof susceptibility and, if infected, displaying symptoms [7, 8]. These may consequently lead to secondary 341\nschool children having a larger contribution to overall transmission throughout the population. This 342\ncould potentially be offset by the greater ability of older pupils to understand and abide by social 343\ndistancing advice. 344\nIncreasing levels of contacts between school children inevitably leads to greater absolute numbers of 345\ninfections, detected cases, ICU admissions and, regrettably, deaths, even if the reproduction number 346\nis not raised above one. For this reason, we also estimate the increase in these outcomes as a result 347\nof reopening schools using the different strategies. The ranking of the different strategies for these 348\noutcomes mirrors the ranking in terms of increases in R. The epidemiological impact of reopening 349\nschools also depends on the behaviour of the wider population. If there is more mixing within the adult 350\n(and elderly) population, the effect of reopening schools will be exacerbated by the generally higher 351\ninfection levels and contacts in the community. Reopening schools will then lead to greater increases in 352\n13\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\ncase numbers over and above the increases due to greater mixing. In general, we found that even small 353\nchanges inR due to the behaviour of the general population swamp the impacts of reopening schools. 354\nWe would stress that, such increases must be viewed in the context of the restrictions currently placed 355\non pupils and parents. Ultimately, it is a societal decision to balance the benefits to pupils’ welfare 356\nand education against the epidemiological consequences. 357\nTo consider the effects of specific school years returning, this work made some simplifying assumptions, 358\nand our results therefore have limitations. In particular, in this paper we consider only an England- 359\nspecific context. The devolved administrations employ a different school system from England, includ- 360\ning different school term dates, which may affect the outcome of reopening schools. Future work could 361\nincorporate such differences, some of the epidemic variability between nations will be captured by the 362\nmodel parameter fits that are already performed for all the devolved nations. In our analysis of schools 363\nwe have made the pessimistic assumption that there will be limited non-pharmaceutical intervention 364\nwithin the school setting, however, we have ignored the potentially greater mixing of parents or other 365\nadults when taking younger children to school. Also, the model is deterministic, and captures the 366\nreturn to school in terms of increased mixing between school ages; it cannot capture the inevitable 367\nheterogeneity between schools, with some schools experiencing many cases while others have none. 368\nSimilarly, we make no attempt to replicate the reactive closure of classes to prevent further spread 369\nonce cases are identified. 370\nAs we have shown, the context in which school reopening happens will also have an impact on its 371\neffect. While we consider different population level mixing patterns, this exploration is necessarily 372\nconstrained; for example it may also be the case that the opening of schools allows more parents to 373\nreturn to work, increasing their risk of infection [30]. Indeed, a surge in cases in Seoul, South Korea 374\nlinked to a distribution centre, has identified at least one SARS-CoV-2 positive high-school student, 375\nwhose family member worked at the centre; this was followed by the re-implementation of localised 376\nlockdown and social distancing measures, including the closure of 251 schools, days after their phased 377\nreopening [39]. It is also be important to consider the impact of school re-openings in combination 378\nwith other concurrent measures, such as the NHS test and trace system in England (that began on 379\n28th May) [40], which aims to trace close recent contacts of anyone who tests positive for SARS-CoV-2 380\nand, if necessary, notify them to self-isolate at home to prevent onward transmission. Effective contact 381\ntracing breaks transmission chains, but may also subject school classes to tracing and isolation. Even 382\nwithout national-scale relaxation in the lockdown measures, the behaviour of the general population 383\nis likely to change over time, in ways that are difficult to predict. Beyond these considerations, we 384\nhave also neglected the many possible side effects of reopening schools, such as parents interacting at 385\nthe school gates, teachers’ exposure while travelling to school (or in the staff room), or the effects of 386\nschool reopening on children mixing outside of school. 387\nThese analyses, performed in May, indicated that it should have been feasible to reopen all schools 388\nin June. Reopening schools (for June and July) while other measures remained constant would have 389\nallowed accurate information regarding the impact of children returning to the classroom for a rela- 390\ntively short period, and would have provided invaluable evidence on the role of younger age-groups 391\nin transmission. In practice, there was only a partial reopening on 1st June, with reception (year 0), 392\nyear 1 and year 6 returning to primary schools, and the sporadic return of some years 10 and 12 to 393\nsenior schools from 15th June. We predicted that the general return of just three primary school years 394\nwould have a minimal impact on R, and very few school-based outbreaks were reported before the 395\nmain summer holidays [41]. Unfortunately, before the return of all children to school in September, 396\nmultiple regions (notably Leicester, Manchester and the North West) of England experienced high 397\ncase numbers, while R continued to rise - such that it was likely to be above 1 before the reopening of 398\nschools. However, our modelling still generates some useful predictions. School reopening is predicted 399\nto have a larger impact in September than it would have done in June, although the impact is still 400\n14\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nrelatively small compared to other relaxations of lockdown. Our work also suggests that measures to 401\nmitigate the rise in cases as we approach winter would be best focused on other routes of transmission, 402\nas even when R is significantly above 1, the effect of opening or closing schools is minimal. 403\nAcknowledgements 404\nThe authors would like to thank Massimiliano Tamborrino for contributing to data curation, and the 405\nRAMP Rapid Review Group for their useful comments on this manuscript. 406\nAuthor contributions 407\nConceptualisation: Matt J. Keeling. 408\nData curation: Matt J. Keeling; Glen Guyver-Fletcher; Alexander Holmes. 409\nFormal analysis: Matt J. Keeling. 410\nInvestigation: Matt J. Keeling. 411\nMethodology: Matt J. Keeling. 412\nSoftware: Matt J. Keeling; Edward M. Hill; Louise Dyson; Michael J. Tildesley. 413\nValidation: Matt J. Keeling; Edward M. Hill; Benjamin D. Atkins; Louise Dyson; Michael J. Tildes- 414\nley. 415\nVisualisation: Matt J. Keeling. 416\nWriting - original draft: Michael J. Tildesley; Edward M. Hill; Louise Dyson; Benjamin D. Atkins; 417\nMatt J. Keeling; Bridget Penman; Erin Gorsich; Emma Southall. 418\nWriting - review & editing: Matt J. Keeling; Edward M. Hill; Louise Dyson; Benjamin D. Atkins; 419\nErin E. Gorsich; Bridget Penman; Glen Guyver-Fletcher; Alexander Holmes; Hector McKimm; Emma 420\nSouthall; Michael J. Tildesley. 421\nFinancial disclosure 422\nThis work has been funded by the Engineering and Physical Sciences Research Council through the 423\nMathSys CDT [grant number EP/S022244/1] and by the Medical Research Council through the 424\nCOVID-19 Rapid Response Rolling Call [grant number MR/V009761/1]. The funders had no role in 425\nstudy design, data collection and analysis, decision to publish, or preparation of the manuscript. 426\nEthical considerations 427\nThe data were supplied from the CHESS database after anonymisation under strict data protection 428\nprotocols agreed between the University of Warwick and Public Health England. The ethics of the 429\nuse of these data for these purposes was agreed by Public Health England with the Government’s 430\nSPI-M(O) / SAGE committees. 431\n15\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nData availability 432\nData on cases were obtained from the COVID-19 Hospitalisation in England Surveillance System 433\n(CHESS) data set that collects detailed data on patients infected with COVID-19. Data on COVID- 434\n19 deaths were obtained from Public Health England. These data contain confidential information, 435\nwith public data deposition non-permissible for socioeconomic reasons. The CHESS data resides with 436\nthe National Health Service (www.nhs.gov.uk) whilst the death data are available from Public Health 437\nEngland (www.phe.gov.uk). 438\nCompeting interests 439\nAll authors declare that they have no competing interests. 440\nReferences\n[1] Li Lq, Huang T, Wang Yq, Wang Zp, Liang Y, et al. COVID-19 patients’ clinical characteristics,\ndischarge rate, and fatality rate of meta-analysis (2020). doi:10.1002/jmv.25757.\n[2] Ludvigsson JF. Systematic review of COVID-19 in children shows milder cases and a better\nprognosis than adults. Acta Paediatrica, International Journal of Paediatrics 109(March):1088–\n1095 (2020). doi:10.1111/apa.15270.\n[3] Barton M, Mehta K, Kumar K, Lu J, le Saux N, et al. COVID- 19 Infection in Children:\nEstimating Pediatric Morbidity and Mortality. medRxiv preprint pages 1–26 (2020).\n[4] NHS England. COVID-19 total announced deaths 27 May 2020. (2020).\nURL https://www.england.nhs.uk/statistics/wp-content/uploads/sites/2/2020/05/\nCOVID-19-total-announced-deaths-28-May-2020.xlsx. [Online] (Accessed: 23 June 2020).\n[5] Dong Y, Mo X, Hu Y, Qi X, Jiang F, et al. Epidemiology of COVID-19 Among Children in\nChina. Pediatrics 145(6):e20200702 (2020). doi:10.1542/peds.2020-0702.\n[6] Wang C, Liu L, Hao X, Guo H, Wang Q, et al. Evolving Epidemiology and Impact of Non-\npharmaceutical Interventions on the Outbreak of Coronavirus Disease 2019 in Wuhan, China.\nmedRxiv page 2020.03.03.20030593 (2020). doi:10.1101/2020.03.03.20030593.\n[7] Viner RM, Mytton OT, Bonell C, Melendez-Torres G, Ward JL, et al. Susceptibility to and\ntransmission of COVID-19 amongst children and adolescents compared with adults: a systematic\nreview and meta-analysis. medRxiv page 2020.05.20.20108126 (2020). doi:10.1101/2020.05.20.\n20108126.\n[8] Viner RM, Russell SJ, Croker H, Packer J, Ward J,et al. School closure and management practices\nduring coronavirus outbreaks including COVID-19: a rapid systematic review. The Lancet Child\nand Adolescent Health 4(5):397–404 (2020). doi:10.1016/S2352-4642(20)30095-X.\n[9] Zhang J, Litvinova M, Liang Y, Wang Y, Wang W, et al. Changes in contact patterns shape\nthe dynamics of the COVID-19 outbreak in China. Science 8001(April):eabb8001 (2020). doi:\n10.1126/science.abb8001.\n[10] Luo L, Liu D, Liao Xl, Wu Xb, Jing Ql, et al. Modes of contact and risk of transmission in\nCOVID-19 among close contacts. medRxiv page 2020.03.24.20042606 (2020). doi:10.1101/2020.\n03.24.20042606.\n[11] Bi Q, Wu Y, Mei S, Ye C, Zou X, et al. Epidemiology and transmission of COVID-19 in 391 cases\nand 1286 of their close contacts in Shenzhen, China: a retrospective cohort study. The Lancet\nInfectious Diseases 3099(20):1–9 (2020). doi:10.1016/S1473-3099(20)30287-5.\n[12] Streeck H, Schulte B, Kuemmerer B, Richter E, Hoeller T, et al. Infection fatality rate of\nSARS-CoV-2 infection in a German community with a super-spreading event. medRxiv page\n2020.05.04.20090076 (2020). doi:10.1101/2020.05.04.20090076.\n16\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\n[13] Stringhini S, Wisniak A, Piumatti G, Azman AS, Lauer SA, et al. Repeated seroprevalence\nof anti-SARS-CoV-2 IgG antibodies in a population-based sample from Geneva, Switzerland.\nmedRxiv page 2020.05.02.20088898 (2020). doi:10.1101/2020.05.02.20088898.\n[14] Shakiba M, Hashemi Nazari SS, Mehrabian F, Rezvani SM, Ghasempour Z, et al. Seroprevalence\nof COVID-19 virus infection in Guilan province, Iran. medRxiv page 2020.04.26.20079244 (2020).\ndoi:10.1101/2020.04.26.20079244.\n[15] Lavezzo E, Franchin E, Ciavarella C, Cuomo-Dannenburg G, Barzon L, et al. Suppression of\nCOVID-19 outbreak in the municipality of Vo, Italy. medRxiv page 2020.04.17.20053157 (2020).\ndoi:10.1101/2020.04.17.20053157.\n[16] Gudbjartsson DF, Helgason A, Jonsson H, Magnusson OT, Melsted P, et al. Early Spread of\nSARS-Cov-2 in the Icelandic Population. medRxiv page 2020.03.26.20044446 (2020). doi:10.\n1101/2020.03.26.20044446.\n[17] Office for National Statistics. Coronavirus (COVID-19) Infection Survey pilot: England,\n21 May 2020 (2020). URL https://www.ons.gov.uk/peoplepopulationandcommunity/\nhealthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/\nengland21may2020. [Online] (Accessed: 23 June 2020).\n[18] Bunyavanich S, Do A, Vicencio A. Nasal Gene Expression of Angiotensin-Converting Enzyme 2\nin Children and Adults. JAMA (2020). doi:10.1001/jama.2020.8707.\n[19] Ng K, Faulkner N, Cornish G, Rosa A, Earl C,et al. Pre-existing and de novo humoral immunity to\nSARS-CoV-2 in humans. bioRxiv page 2020.05.14.095414 (2020). doi:10.1101/2020.05.14.095414.\n[20] Grifoni A, Weiskopf D, Ramirez SI, Mateus J, Dan JM, et al. Journal Pre-proof Targets of T\ncell responses to SARS-CoV-2 coronavirus in humans with COVID-19 disease and unexposed\nindividuals. Cell 0(0) (2020). doi:10.1016/j.cell.2020.05.015.\n[21] W¨ olfel R, Corman VM, Guggemos W, Seilmaier M, Zange S,et al. Virological assessment of hos-\npitalized patients with COVID-2019. Nature pages 1–10 (2020). doi:10.1038/s41586-020-2196-x.\n[22] Jones TC, M¨ uhlemann B, Veith T, Zuchowski M, Hofmann J,et al. An analysis of SARS-CoV-2\nviral load by patient age. medRxiv 105(13) (2020).\n[23] Stoye J. A Critical Assessment of Some Recent Work on COVID-19. arXiv page\n2020.05.26.2005.10237v2 (2020). doi:arxiv:2005.10237v2.\n[24] Xu Y, Li X, Zhu B, Liang H, Fang C, et al. Characteristics of pediatric SARS-CoV-2 infection\nand potential evidence for persistent fecal viral shedding. Nature Medicine pages 1–4 (2020).\ndoi:10.1038/s41591-020-0817-4.\n[25] Xing YH, Ni W, Wu Q, Li WJ, Li GJ, et al. Prolonged viral shedding in feces of pediatric patients\nwith coronavirus disease 2019 (2020). doi:10.1016/j.jmii.2020.03.021.\n[26] Zhu N, Zhang D, Wang W, Li X, Yang B, et al. A Novel Coronavirus from Patients with Pneu-\nmonia in China, 2019. N. Engl. J. Med. 382(8):727–733 (2020). doi:10.1056/NEJMoa2001017.\n[27] Fontanet A, Tondeur L, Madec Y, Grant R, Besombes C, et al. Cluster of COVID-19 in northern\nFrance: A retrospective closed cohort study. medRxiv page 2020.04.18.20071134 (2020). doi:\n10.1101/2020.04.18.20071134.\n[28] National Centre for Immunisation Research and Surveillance. COVID-19 in schools - the expe-\nrience of NSW. (2020). URL http://ncirs.org.au/sites/default/files/2020-04/NCIRS%20NSW%\n20Schools%20COVID\nSummary FINAL%20public 26%20April%202020.pdf. [Online] (Accessed:\n23 June 2020).\n[29] Heavey L, Casey G, Kelly C, Kelly D, McDarby G. No evidence of secondary transmission of\nCOVID-19 from children attending school in Ireland, 2020. Eurosurveillance 25(21):2000903\n(2020). doi:10.2807/1560-7917.ES.2020.25.21.2000903.\n[30] Panovska-Griffiths J, Kerr CC, Stuart RM, Mistry D, Klein DJ, et al. Determining the optimal\nstrategy for reopening schools, the impact of test and trace interventions, and the risk of occur-\nrence of a second COVID-19 epidemic wave in the UK: a modelling study. Lancet Child Adolesc.\n17\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nHeal. (2020). doi:10.1016/S2352-4642(20)30250-9.\n[31] Brooks-Pollock E, Read JM, McLean AR, Keeling MJ, Danon L. Using social contact data\nto predict and compare the impact of social distancing policies with implications for school re-\nopening. medRxiv page 2020.07.25.20156471 (2020). doi:10.1101/2020.07.25.20156471.\n[32] Keeling MJ, Hill E, Gorsich E, Penman B, Guyver-Fletcher G, et al. Predictions of COVID-19\ndynamics in the UK: short-term forecasting and analysis of potential exit strategies. medRxiv\npage 2020.05.10.20083683 (2020). doi:10.1101/2020.05.10.20083683.\n[33] Keeling MJ, Dyson L, Guyver-Fletcher G, Holmes A, Semple MG, et al. Fitting to the UK\nCOVID-19 outbreak, short-term forecasts and estimating the reproductive number. medRxiv\npage 2020.08.04.20163782 (2020). doi:10.1101/2020.08.04.20163782.\n[34] Public Health England. COVID-19 Hospitalisation in England Surveillance System (CHESS)\n– daily reporting. (2020). URL https://www.england.nhs.uk/coronavirus/wp-content/uploads/\nsites/52/2020/03/phe-letter-to-trusts-re-daily-covid-19-hospital-surveillance-11-march-2020.\npdf. [Online] (Accessed: 29 July 2020).\n[35] Mossong J, Hens N, Jit M, Beutels P, Auranen K, et al. Social Contacts and Mixing Patterns\nRelevant to the Spread of Infectious Diseases. PLoS Med. 5(3):e74 (2008). doi:10.1371/journal.\npmed.0050074.\n[36] Prem K, Cook AR, Jit M. Projecting social contact matrices in 152 countries using contact surveys\nand demographic data. PLOS Comput. Biol. 13(9):e1005697 (2017). doi:10.1371/journal.pcbi.\n1005697.\n[37] Courtemanche C, Garuccio J, Le A, Pinkston J, Yelowitz A. Strong Social Distancing\nMeasures In The United States Reduced The COVID-19 Growth Rate. Health Aff. page\n10.1377/hlthaff.2020.00608 (2020). doi:10.1377/hlthaff.2020.00608.\n[38] Lemaitre JC, Perez-Saez J, Azman A, Rinaldo A, Fellay J. Assessing the impact of non-\npharmaceutical interventions on SARS-CoV-2 transmission in Switzerland. medRxiv page\n2020.05.04.20090639 (2020). doi:10.1101/2020.05.04.20090639.\n[39] The Korea Times. Calls grow to delay school opening as virus fears persist. (2020). URL https:\n//www.koreatimes.co.kr/www/nation/2020/05/181\n290297.html. [Online] (Accessed: 23 June\n2020).\n[40] Department of Health and Social Care. NHS test and trace: how it works. (2020). URL https:\n//www.gov.uk/guidance/nhs-test-and-trace-how-it-works. [Online] (Accessed: 29 July 2020).\n[41] Ismail SA, Saliba V, Lopez Bernal JA, Ramsay ME, Ladhani SN. SARS-CoV-2 infection and\ntransmission in educational settings: cross-sectional analysis of clusters and outbreaks in England.\nmedRxiv page 2020.08.21.20178574 (2020). doi:10.1101/2020.08.21.20178574.\n18\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint \n\nSupporting information items\nSupporting Text S1\nDescription of the complete system of model equations.\nSupporting Text S2\nDetails on the mechanisms underpinning social distancing measures within the model framework\nSupporting Figure S1\nPosterior distributions of key model parameters from fitting to date until 1st June. The\nleft-hand graphs show how the probability of symptoms ( da) and susceptibility (σa) varies with age;\ngiven the low value of alpha most of the age-dependence is in the displaying of symptoms. The\nright-hand graph shows the relative adherence with lockdown measures in each region; high values\ncorrespond to a dramatic reduction in the mixing matrix, while an adherence of zero returns the\nmatrix to pre-lockdown levels. This figure supplements the information in Table 1. Bars show the\n95% credible intervals from the posterior distribution.\nSupporting Figure S2\nDistribution of household symptomatic, asymptomatic and isolated cases in each age\ngroup on 1st June. Used in conjunction with Fig. 1. Bottom segments (blue shading) represent\nsymptomatic infection. Middle segments (orange shading) represent asymptomatic infection. Top\nsegments (yellow shading) represent those in isolation. Filled dots specify the fraction of the population\nwithin that age bracket.\nSupporting Figure S3\nIncrease in reproduction number, R, under eight school reopening scenarios for three\nregions in England. Estimates are depicted for the following three regions: (a) North West, (b)\nSouth East, (c) East of England. For each scenario, bars represent the mean absolute increase in\nR, compared to what we would observe if schools remained closed. We also give the 95% prediction\nintervals. Solid red lines identify the absolute increase required to raise R above 1, within each region,\nalongside 95% credible intervals (dashed red lines). Means and intervals are calculated from 1000\nreplicates sampled from the posterior parameter distributions. All scenarios are implemented on 1st\nJune and continued until 22nd July.\n19\n . CC-BY 4.0 International licenseIt is made available under a \nperpetuity. \n is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint \nThe copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}