The impact of school reopening on the spread of COVID-19 in England

By mid-May, cases of COVID-19 in the UK had been declining for over a month; a multi-phase emergence from lockdown was planned, including a scheduled partial reopening of schools on 1st June. Although evidence suggests that children generally display mild symptoms, the size of the school-age population means the total impact of reopening schools is unclear. Here, we present work from mid- May that focused on the imminent opening of schools and consider what these results imply for future policy. We compared eight strategies for reopening primary and secondary schools in England. Modifying a transmission model fitted to UK SARS-CoV-2 data, we assessed how reopening schools affects contact patterns, anticipated secondary infections and the relative change in the reproduction number, R. We determined the associated public health impact and its sensitivity to changes in social-distancing within the wider community. We predicted reopening schools with half-sized classes or focused on younger children was unlikely to push R above one. Older children generally have more social contacts, so reopening secondary schools results in more cases than reopening primary schools, while reopening both could have pushed R above one in some regions. Reductions in community social-distancing were found to outweigh and exacerbate any impacts of reopening. In particular, opening schools when the reproduction number R is already above one generates the largest increase in cases. Our work indicates that while any school reopening will result in increased mixing and infection amongst children and the wider population, reopening schools alone in June was unlikely to push R above one. Ultimately, reopening decisions are a difficult trade-off between epidemiological conse- quences and the emotional, educational and developmental needs of children. Into the future, there are difficult questions about what controls can be instigated such that schools can remain open if cases increase. 1 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.

1 The emergence of a novel strain of coronavirus, now named SARS-CoV-2, in Wuhan city, China, in 2 late 2019, has resulted in a global pandemic that spread to every region in the world. When the SARS- 3 CoV-2 virus infects humans it can result in COVID-19 disease, with symptoms including a fever, a 4 continuous dry cough, a shortness of breath and a loss of sense of taste and smell [1]. In severe cases, 5 the symptoms can require hospitalisation and admission to intensive care, with ventilation required in 6 the most severe cases in order to assist with breathing. 7 As the number of confirmed cases increased both nationally and globally, there was a concern that 8 hospital and intensive care capacities would be rapidly overwhelmed without the introduction of in- 9 terventions to curb the spread of infection. With this in mind, many countries introduced a range of 10 social distancing measures, such as the closing of workplaces, pubs and restaurants, the restriction of 11 leisure activities and the closing of schools. In the UK, the introduction of many of these measures 12 was announced during the week of 16th March, with schools, along with the hospitality sector, closing 13 on Friday 20th March. Full lockdown measures were subsequently introduced three days later, on the 14 evening of Monday 23rd March. When we completed this work in late May, over 270 , 000 people in 15 the UK had been confirmed to have been infected with COVID-19, with over 37, 500 confirmed deaths 16 of individuals who had tested positive for infection. 17 The decision to close schools is a balance between the risk associated with transmission in the school 18 environment and the educational and welfare impact upon children of shutting down education es- 19 tablishments. Evidence from a range of sources suggests that children are, in general, only mildly 20 affected by the disease and have low mortality rates [2, 3]. This is reflected in the fact that by 27th 21 May 2020 there had been 26 , 235 COVID-19 associated deaths in hospitals in England, but only 16 22 of those were in the 0-19 year age group [4]. In a retrospective study of 2 , 135 paediatric COVID-19 23 cases in China [5], 89.7% of children had mild or moderate disease while 5 .8% were severe or critical; 24 similarly low levels of severe disease are reported in other regions [3, 6]. The health risks of school 25 attendance for any individual child is therefore thought to be low. 26 However, there is less certainty regarding children’s role in the transmission of SARS-CoV-2 [7, 8]. 27 This can be broken down into two key questions: (i) how likely are children to become infected, and 28 (ii) once infected, are children likely to transmit infection? 29 A meta-analysis concluded that children and young people under the age of 20 may be less likely to 30 become infected: the odds ratio for becoming infected upon contact with an index case compared to 31 adults (> 20 years old) is 0 .44 (CI 0.29, 0.69) [7]. This conclusion is based on pooling the results of 32 contact tracing and population-screening studies, most of which find evidence that the attack rate in 33 children may be lower than in adults [9, 10], but one does not (Bi et al. [11]). All contact tracing 34 studies are hampered by the problem that symptom-based surveillance is likely to systematically under 35 detect cases in children [11]. Seroprevalence surveys so far do not find any significant effect of age on 36 the probability of possessing antibodies against COVID-19, although those under the age of five are 37 not always included in surveys [12–14]. Two cross sectional PCR studies hint at lower susceptibility 38 in children, since they found no SARS-CoV-2 PCR positive children under the age of 10 [15, 16], but 39 a PCR-based survey by the UK Office for National Statistics found no difference in the probability of 40 infection between age classes [17]. Further, large-scale seroprevalence studies which fully sample all 41 age groups will be necessary to fully resolve these questions. Overall the balance of evidence cautiously 42 suggests that children may have a lower inherent susceptibility. If it exists, such lower susceptibility 43 could be physiological [18] or could be due to cross reactive immune responses from other childhood 44 infections, with cross-protection between other human coronaviruses and SARS-CoV-2 hinted at by 45 recent studies [19, 20]. 46 2 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint There is little evidence from contact tracing and clinical investigations about the relative infectiousness 47 of children. Children hospitalised with COVID-19 readily shed the virus above the likely transmission 48 threshold [21–23], with detection of virus in nasopharyngeal (nasal) swabs, oropharyngeal (throat) 49 swabs, sputum, or faeces [24, 25]. However, in their review of contact tracing and population-screening 50 studies, Viner et al. [7] found just one relevant study comparing infectiousness by age: Zhu et al. [26], 51 which shows that children make up a low proportion of index cases in households. As pointed out by 52 Viner et al. , this particular result could be explained by children being less likely to get infected in 53 the first place rather than children being less infectious once they have actually contracted the virus. 54 There is also evidence suggesting that mild cases in adults could be less infectious than severe or 55 critical cases [10], but it remains unknown whether this result extends to asymptomatic or mild cases 56 in children. Thus, children with severe symptoms are likely infectious, but it is harder to determine 57 how transmissible the virus may be from children with few or no symptoms. 58 As of May 2020, we were aware of three reported studies of SARS-CoV-2 infection within the school 59 environment. A retrospective serology study of 661 individuals with links to a school-based outbreak in 60 Oise, France, showed that the infection spread readily within and outside the school to reach students, 61 teachers, staff, and families [27]. In contrast, an Australian government study of cases in schools in 62 Western Australia [28] identified nine children and nine adults who tested positive for SARS-CoV-2 63 (located across different schools), but found only two secondary cases when testing a third of the 64 close contacts of these cases (288 samples). In Ireland, six SARS-CoV-2 cases were identified who 65 had attended or taught in schools. None of 924 school related child contacts or 101 school related 66 adult contacts showed any symptoms, but asymptomatic cases could have been missed [29]. The 67 Australian school cases were identified between 5th March and 3rd April, and the first Irish school 68 case was identified at the beginning of March. The first Oise school cases, by contrast, were identified 69 on the 2nd February 2020. The greater awareness of COVID-19 by March, during which the WHO 70 declared COVID-19 as a global pandemic, likely helped to control the Australian and Irish school-based 71 outbreaks sooner than in Oise. 72 In the UK, during late May 2020, cases of COVID-19 were declining and there was strong evidence to 73 suggest that the effective reproduction number (R ) had dropped below 1 across the country. A multi- 74 phase relaxation plan for the country to emerge from lockdown began on 13th May, with a greater 75 emphasis on returning to work if practical. We present here research formulated to address policy 76 questions in May, to help inform the expected impact of various groups returning to the classroom. 77 In particular, we investigate the epidemiological impacts of reopening schools in England, focusing 78 on different combinations of year groups. We extend a previously developed dynamic transmission 79 model for SARS-CoV-2, which is fit (on a regional basis for the UK) to real-time data on confirmed 80 cases requiring hospital care and mortality. We compare and contrast multiple possible strategies for 81 reopening both primary and secondary schools, focusing upon determining the effect of given year 82 groups returning to school upon future epidemic behaviour. By elucidating the risks associated with 83 particular age groups returning to school, we seek to contribute to the evidence base on the likely 84 role of schools in the containment and control of this outbreak. Unlike other modelling studies [30], 85 we decouple school reopening from other measures (such as a greater return to work); we feel this 86 generates a clearer picture of the roles of school children and adults [31]. 87 In England, primary schools partially reopened on 1st June: reception, year 1 and year 6 children 88 initially returned, with an emphasis on maintaining social distancing measures where possible. In 89 September (August in Scotland), the majority of schools reopened with generally high levels of atten- 90 dance. We therefore discuss the implications for this work both in terms of the likely effects of schools 91 on the unfolding epidemic and their role in any future imposition of additional control measures. 92 3 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint

93 Transmission model 94 In order to perform the analysis of school reopening, we extended a previously-developed determinis- 95 tic, age-structured compartmental SARS-CoV-2 transmission model [32]. The model was matched to 96 a variety of data sources including hospitalisations, ICU occupancy and deaths, while age-dependent 97 parameters were scaled to achieve agreement with the early age-distributions [33]. We stratified the 98 population according to current disease status, following a susceptible-exposed-infectious-recovered 99 (SEIR) paradigm (Fig. 1). We assumed the latent period to be Erlang distributed, modelled within 100 the compartmental framework via division of the latent state into three stages. Infectious cases were 101 partitioned by presence of symptoms, meaning we tracked symptomatic and asymptomatic individuals 102 separately. Additional layers of complexity included differentiating by isolation and household status. 103 We provide a listing of model parameters in Table 1, with a description of the model equations given 104 in Supporting Text S1. We use the predicted number of symptomatic individuals to estimate the 105 number of hospital admissions, ICU admissions and deaths, by estimating the proportion of symp- 106 tomatic individuals requiring hospitalisation, ICU admission and the proportion that eventually die, 107 and the distribution of times through each of these states. For hospital admissions and cases requiring 108 treatment in ICU, the proportions going through each state and the distribution of times taken were 109 drawn from the COVID-19 Hospitalisation in England Surveillance System (CHESS) data set that 110 collects detailed data on patients infected with COVID-19 [34]. The risk of death was also captured 111 with an age-dependent probability, while the distribution of delays between hospital admission and 112 death was assumed to be age-independent, with both these two quantities determined from the Public 113 Health England (PHE) death records. 114 With the inclusion of age-structure, transmission was governed through age-dependent mixing ma- 115 trices, based on UK social mixing patterns [35, 36], scaled by an age-dependent susceptibility that 116 was determined to produce the early age-distribution of symptomatic cases. To capture the effects of 117 social distancing measures that were introduced in the UK to reduce transmission, we scaled down 118 the mixing matrices associated with schools, work and other activities while increasing the within 119 household transmission matrix (see Supporting Text S2). 120 In a refinement to the base model, we imposed an amended age-stratification of the population. Whilst 121 in previous work the population was stratified into five year age brackets, for this study we separated 122 those aged between 0 and 19 years old into single year cohorts, with the remainder of the population 123 stratified into five year age brackets as before (20-24yrs, 25-29yrs and so on). The final age category 124 corresponded to those aged 100 years or above. This fine-scale structure for those younger than 20 is 125 important to be able to capture different policy questions; however resolution at a single year of age is 126 not captured within the mixing matrices [35, 36]. We therefore generally retain the mixing structure 127 based on five year age groups (Fig. 2), but assume that 70% of mixing within the same five year age 128 group comes from interactions within the same school year. 129 Modelling school reopening scenarios 130 We used this model framework to evaluate eight strategies for reopening schools from 1st June. The 131 eight school reopening options we considered assumed that, from the 1st June, the following school 132 year groups would return to school: 133 (i) reception (year 0), year 1 and year 6 (full class sizes); 134 (ii) reception, year 1 and year 6 (half class sizes); 135 (iii) all primary schools; 136 (iv) reception, years 1, 6, 10 and 12 (full class sizes); 137 4 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint Fig. 1: Disease states and transitions. We stratified the population into susceptible, exposed, detectable infectious, undetectable infectious, and removed states. Solid lines correspond to disease state transitions, with dashed lines representing mapping from detectable cases to severe clinical cases that require hospital treatment, critical care (ICU), or result in death. We separated those aged between 0 and 19 years old into single years, with the remainder of the population stratified into five year age brackets. See Table 1 for a listing of model parameters. Note, we have not included quarantining or household status on this depiction of the system. (v) reception, years 1, 6, 10 and 12 (half class sizes); 138 (vi) primary schools plus year groups 10 and 12; 139 (vii) all secondary schools; 140 (viii) all schools. 141 For clarity, in all the strategies considered here we assumed that children of key workers continued to 142 attend school at the currently observed level. 143 We assessed the school reopening scenarios at a regional scale, modelling the population of England 144 aggregated to seven regions (East of England, London, Midlands, North East and Yorkshire, North 145 West England, South East England, South West England). This involved the use of region-specific 146 posterior parameters obtained in our prior work, where we fit our base transmission model on a region- 147 by-region basis, using a Monte Carlo Markov Chain (MCMC) fitting scheme, to four timeseries: (i) new 148 hospitalisations; (ii) hospital bed occupancy; (iii) ICU bed occupancy; (iv) daily deaths (using data on 149 the recorded date of death, wherever possible) [32]. The inference was performed from epidemiological 150 data until 12th May 2020. 151 Our assessment of school reopening strategies comprised of three strands. Firstly, we quantified how 152 the process of opening schools and year groups affected contact patterns and anticipated secondary 153 infections. Secondly, we related the scale of school opening to the relative change in R, assuming 154 the same transmission patterns in the rest of the population as during the strict lockdown phase. 155 Finally, we gauged the estimated change in clinical case and its sensitivity to changes in community 156 transmission following the easing of lockdown measures on 13th May. We outline each item in further 157 detail below. 158 5 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint Table 1: Key model parameters Parameter Description Value Source β Age-dependent transmission, split into household, school, work and other Derived from POLYMOD matrices [36] ϵ Rate of progression to infectious disease (1/ϵ is the duration in the exposed class) ∼ 0.2 Fitted as part of MCMC process γ Recovery rate, changes with τ, the rel- ative level of transmission from unde- tected asymptomatics compared to de- tected symptomatics ∼ 0.5 Fitted from early age- stratified UK case data α Scales the degree to which age-structured heterogeneity is due to age-dependent probability of symptoms ( α = 0) or age- dependent susceptibility (α = 1) 0.137(0.1150.146) Fitted as part of MCMC process τ Relative level of transmission from asymp- tomatic compared to symptomatic infec- tion 0.138(0.135 − 0.145) Fitted as part of MCMC process da Age-dependent probability of displaying symptoms (and hence being detected), changes with α and τ 0-1 Fitted from early age- stratified UK case data (see of MCMC process or varied according to sce- nario (see Supporting Fig- ure S1) σa Age-dependent susceptibility, changes with α and τ 0.4-1 Fitted from early age- stratified UK case data (see of MCMC process or varied according to sce- nario (see Supporting Fig- ure S1) φR Adherence to the lockdown restrictions 0.3 − 0.8 Fitted as part of MCMC process or varied according to scenario (see Supporting Figure S1) H R Household quarantine proportion 0 − 1 Can be varied according to scenario N R a Population size of a given age By region ONS Contacts and secondary infections 159 Any school reopening plan will inherently alter age-group contact patterns compared to contact struc- 160 tures observed during the lockdown. We attempted to resolve how these alterations in social in- 161 teractions propagated into the transmission dynamics by tracking secondary infections arising from 162 symptomatic index cases and infected index cases (either symptomatic or asymptomatic), respec- 163 tively. 164 Specific to this aspect of the analysis we focused on a single region, namely the Midlands and the 165 posterior parameter set with the maximum likelihood. We first assess the contact structure and 166 transmission under two distinct lockdown assumptions (‘strict closure’ and our default assumption of 167 ‘weaker closure’). The ‘strict closure’ scenario assumed that there was no additional mixing between 168 6 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint school-age groups during the lockdown period. ‘Weaker closure’ assumed there was more limited 169 adherence, leading to higher mixing between school-age groups compared to the ‘strict closure’ setting. 170 We also consider six of the eight reopening strategies (omitting those with half class sizes as these are 171 bounded above by the full-class strategy). For each we show the age-mixing matrix between age-groups; 172 the transmission matrix from a symptomatic infectious individual; the transmission matrix from an 173 average infectious individual (recognising the many will be asymptomatic or in household quarantine); 174 and the expected number of secondary cases an average infectious individual of a particular age-group 175 will generate. 176 Reproduction number analysis 177 The reproduction ratio or number (R) has become a universally recognised quantity in the description 178 of COVID-19 dynamics; it is defined as the average number of secondary cases from an average index 179 case — where the second average is important as it samples across all infectious states including 180 asymptomatics and those currently under household isolation. To prevent the occurrence of a second 181 phase of exponential growth in infection, it is crucial that relaxation of social distancing measures 182 do not result in the value of R rising above 1. On these grounds, there is interest in predicting the 183 magnitude of a rise in R that could result from the reopening of schools, and our confidence in this 184 result. 185 We considered all eight school reopening scenarios and examined the increase in R per region under 186 each of the eight strategies. To compute R, we used the contact matrices associated with the given 187 choice of school reopening and accounting for the regional population structure, whilst assuming the 188 same level of mixing in the rest of the population as during the strict lockdown; therefore any changes in 189 R are driven by changes in school-age mixing. We calculated means and intervals from 1000 simulation 190 replicates with parameter sets sampled from the posterior parameter distributions. 191 Clinical case impact 192 The prior methods focused on the reproduction numberR, which is both an instantaneous measure (R 193 can be calculated at any or every time point) and a long-term calculation (as it utilises an eigenvalue 194 approach to generate the asymptotic R). Calculation of quantities of public health interest requires 195 the simulation of the full temporal dynamics from the start of the outbreak to the closing of schools 196 for the summer holidays on 22nd July. In addition, we considered the sensitivity of reopening schools 197 to other potential changes in population mixing patterns (and hence different values of R) driven by 198 other changes to the lockdown since 13th May. These changes to population mixing were generated 199 by reducing the adherence with lockdown measures, bringing the mixing matrices closer to the pre- 200 pandemic norm. 201 We performed these simulations, using the full dynamic model to generate estimates of the symp- 202 tomatic cases, deaths and ICU admissions between 1st June and 22nd July, for each of the eight 203 school-opening strategies. We compared these measures, aggregated over this 52-day period, to a 204 scenario where school closures remain in place beyond the 1st June. 205 For each reopening strategy and each region, we performed a total of 1000 replicates. In each replicate 206 we sampled parameter values randomly from all posterior parameter distributions, with the exception 207 of the adherence level. The potential reduction in adherence values, from 13th May, inevitably gen- 208 erates different R values at the point of school reopening (measured by the observed growth rate of 209 the outbreak in the model simulation). As a consequence, for comparative purposes we segregated 210 the estimated increases in epidemiological quantities (comparing different school opening strategies for 211 fixed underlying parameters) into three categories according to the R value before school reopening: 212 below 0.8, between 0.8 and 1, or between 1 and 1.2. 213 7 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint

214 Choice of reopening strategy influences contact structure and secondary infection risk 215 We first investigated the impact of alternate strategies for reopening schools upon contact patterns be- 216 tween individuals and the effect of this upon transmission of SARS-CoV-2 and occurrences of COVID- 217 19 infection. Our results for the Midlands, and the posterior parameter-set derived in May that 218 maximises the likelihood (giving R ≈ 0.78), are summarised in Fig. 2. For all scenarios investigated 219 we observe several common trends. Contacts are most common between individuals of the same, 220 or similar ages (Fig. 2, first row [36]). There was also greater contact between children and adults 221 between the ages of 25 and 55, reflecting interactions between children and their parents, as well as 222 between elderly people [36]. This increased likelihood of contact within and between those age groups 223 is reflected in the risk of secondary infections occurring (Fig. 2, second and third rows). The second 224 row accounts for age-dependent susceptiblity, and shows the expected number of secondary infections 225 in each age (y-axis) from a symptomatic index case of a particular age (x-axis). The third row incor- 226 porates the likely state of an index infection (symptomatic, asymptomatic or in household quarantine 227 - as predicted by the underlying ODEs) thereby reducing the potential transmission from particular 228 age-groups (Supporting Figure S2). 229 If schools remain closed, with a high level of adherence to the lockdown within this younger age-group 230 (Fig. 2, first column) we observe that contact between children, and therefore the risk of secondary 231 infection occurring, is extremely low. Should adherence to lockdown be weaker (Fig. 2, second column), 232 we observe a higher rate of mixing between children and a slight increase in risk of secondary infections 233 occurring. For both of these scenarios the average number of secondary infections per index infection 234 is below 1 for all age groups and the value of R remains significantly below 1. 235 We now investigate the impact of various strategies for school reopenings. We first investigate the 236 scenario of reception, year 1 and year 6 children returning to school – the policy that is scheduled to 237 be implemented on 1st June in England (Fig. 2, third column). In this scenario, we observe a slight 238 increase in contacts compared to the “weaker closure” scenario, with increased transmission between 239 individuals in these age groups. However, crucially, even within these age groups, the total number 240 of secondary infections per index case remains below one (third column, final row, red bars) and the 241 overall reproduction number value ofR was only observed to have slightly increased from the scenarios 242 in which schools remain closed. A slight increase in mixing, and hence R, was again observed when 243 all primary schools are opened (Fig. 2, fourth column), but we predict that R remains below 1. 244 To conclude this segment of the analysis, we investigated the impact of school reopening strategies 245 that involved some, or all, secondary school children returning to the classroom. If children from key 246 years of 10 and 12 return to school (in addition to some or all primary school children), a significant 247 increase in mixing was observed within those age groups; the number of secondary infections as a 248

of index infections in secondary schools was predicted to be above one (Fig. 2, fifth and sixth 249 columns). However, this expected number of cases is distributed across multiple age-groups thereby 250 dissipating the worst effects. In general, we found secondary schools to represent a higher risk of 251 increased transmission potential than primary schools. This could lead to higher values of R when all 252 secondary schools are opened; but for all scenarios investigated, even the scenario in which all schools 253 are opened, we found strong support for R remaining below 1 in the Midlands (Fig. 2, final column) 254 assuming that all other transmission patterns remain unchanged. 255 8 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint Fig. 2: Mixing matrices and their implications for onwards transmission. We consider the effect on contact structures between different age groups under (first column) strict school closure, (second column) weak closure, (third column) years 0 (reception), 1 and 6 returning to school, (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 years 10 and 12 at school, (seventh column) all secondary school children at school and (eighth column) all children in school. For each school closure we show: (first row) the average number of contacts by age for each index age group [36]; (second row) the average number of secondary infections for a symptomatic infected individual by age (combining the mixing matrix with age-susceptibility); and (third row) the average number of secondary infections for each infected individual by age combining the mixing matrix, age-susceptibility and the impact of asymptomatic transmission). (Fourth row) The total number of secondary infections for each infected index age group. Green bars indicate school year groups who remain at home, whilst red bars indicate year groups who return to school. 9 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint Effect of school reopening on reproduction number 256 Next, we sought to estimate changes in R that may result from school reopenings alone - assuming 257 the transmission patterns in the rest of the population are maintained at strict lockdown phase levels. 258 In contrast to the the first part of the analysis, which focused on a single set of parameters and a 259 single region (Fig. 2), here we explore the full parameter uncertainty and compare different parts of 260 the country. 261 For all school opening scenarios, within the seven regions of England, we observe an increase in R 262 compared to what we predict for keeping schools closed until the end of the academic year (Fig. 3 and 263 Supporting Figure S3). This is to be expected, given the increase in contact between children that 264 such reopening scenarios would allow. However, the magnitude of increase is predicted to be relatively 265 low, depending on the age-groups that return to school. In general, the more year groups allowed to 266 return to school at one time, the greater the effect on R, with the return of secondary school children 267 having the greatest impact. 268 The impact of allowing multiple year groups to return to school can still be small: opening a fraction 269 of the age-cohorts in each school generally leads to a moderate (less than 0.05) increase inR, especially 270 if children can be taught in smaller class sizes which is assumed to lead to a proportionate reduction 271 in within school transmission. 272 There is however considerable variation between the regions and here we focus on four exemplars. 273 For London and North East England & Yorkshire, the increase in R was considerably less than that 274 for East of England and the Midlands across all reopening scenarios. For the former, even allowing 275 all age groups to return to school (while maintaining tight control in other age-groups) was highly 276 unlikely to increase R above 1, with both means and 95% prediction intervals falling well below this 277 threshold (Figs. 3(a) and 3(b), the 95% prediction intervals, as the name suggests, contain 95% of 278 all predicted values across the entire posterior distribution of parameters). This low R value was 279 especially true for London, which saw the most abrupt rise and subsequent decline in cases. However, 280 this was not the case for the East of England (Fig. 3(c)) and the Midlands (Fig. 3(d)). In these regions, 281 allowing schools to fully reopen could increaseR above 1, with such an occurrence lying within the 95% 282 prediction intervals. We attribute these regional differences to both heterogeneity in the observed rate 283 of epidemic decline and the differential proportion of school age children in each region; the Midlands 284 has the highest proportion of older teenagers in the country. 285 Quantifying clinical case impact stemming from the re-opening of schools 286 Our final piece of analysis examined the extent to which each of the eight school reopening strategies 287 may contribute to clinical case outcomes, using the full dynamic model. We also considered the 288 sensitivity of reopening schools to other potential changes in population mixing patterns (and hence 289 different values of R) driven by other changes to the lockdown since 13th May. 290 In each scenario, reopening schools increased the absolute number of cases, ICU admissions and deaths 291 as a result of increased transmission (Fig. 4). Note that these increases will not be restricted to the 292 children that return to school, since the greater transmission will lead to increased cases in other age 293 groups. Echoing our earlier findings, strategies in which a larger number of children return to school 294 generally resulted in larger increases. In addition, older children had a greater effect, so that reopening 295 secondary schools results in larger increases than only reopening primary schools. 296 The opening of schools on 1st June was just one of a collection of changes in a short space of time, 297 which began from 13th May. In the previous sections we focused on school reopening, assuming 298 that mixing (and hence transmission) within the wider population remained unchanged. Here we 299 allowed the relaxation of lockdown measures to precipitate an increase of R within the community 300 10 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint and calculate the additional change from the opening of schools. We consistently found that school 301 reopening had a larger impact when R in the community was high, leading to a greater increase in 302 cases, ICU admissions and deaths. However, by far the largest increase in any of these key quantities 303 was driven by the underlying change in R due to relaxations other than the reopening of schools 304 (Figs. 4(b), 4(d) and 4(f)). 305 (a) (b) (c) (d) Fig. 3: Increase in reproduction number, R, under eight school reopening scenarios for four regions in England. Estimates are depicted for the following four regions: (a) London (R ≈ 0.69), (b) North East and Yorkshire (R ≈ 0.71, (c) East of England (R ≈ 0.74), (d) the Midlands (R ≈ 0.78). For each scenario, bars represent the mean absolute increase in R, compared to what we would observe if schools remained closed. We also give the 95% prediction intervals. Solid red lines identify the absolute increase required to raiseR above 1, within each region, alongside 50% and 95% intervals (shaded red areas). Means and intervals are calculated from 1000 replicates sampled from the posterior parameter distributions. All scenarios are implemented on 1st June and continued until 22nd July. 11 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint (a) (b) (c) (d) (e) (f) Fig. 4: Increase in disease burden and clinical case outcomes from 1st June to 22nd July under the eight different scenarios representing various combinations of school years return to school. (a,b) Cases; (c,d) ICU admissions and (e,f) deaths. For each scenario, the three coloured bars give the increase relative to if no schools returned for low (red), intermediate (yellow) and high (purple) reproduction numbers, while the clear bar (in panels a, c and e) is the mean across all reproduction numbers. Prediction intervals are given for each scenario representing the uncertainty in the predicted values. In panels b, d and f, we also display (in lighter colours) the increase in each quantity that is associated with the change in R from the current low situation. 12 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint

306 In this paper, we have described a mathematical model used in May 2020 to consider the implications 307 of various potential strategies for reopening schools in England. We have compared the different 308 strategies by presenting mixing matrices and discussing their implication for onward transmission, and 309 by analysing the increase in the reproduction number and absolute number of cases, ICU admissions 310 and deaths compared to those predicted if schools remain closed. Given that in May all regions were 311 estimated to have reproduction numbers ( R) below 0.8, we predicted that, in the absence of other 312 changes, the complete opening of all schools was unlikely to raise the reproduction number above one. 313 It must be noted that even though R remains below one, the slight increase in transmission resulting 314 from school reopening subsequently leads to a small increase in the absolute number of cases, ICU 315 admissions and deaths. If the reopening of schools is part of a wider policy of relaxing controls, then 316 the impact of these additional changes must also be factored into the analysis [30, 31]. 317 Reopening schools, in any form, inevitably leads to more mixing between children, an increase in R 318 and thus more transmission of the disease. However, we can constrain and potentially minimise the 319 extent of this increase by selecting a subset of year-groups to return to school. In doing so, we restrict 320 the increase in R to very low levels and, crucially, avoid any possibility of increasingR above 1. These 321 findings are in agreement with studies applied to other nations suggesting that school settings are 322 not a major driver of SARS-CoV-2 transmission. A statistical study in US counties looking at the 323 relationship between the reduction in growth rate and the timing of different state and local government 324 social distancing interventions found school closures to not be statistically significant [37]. Further, in 325 terms of suppressing spread of SARS-CoV-2, a mechanistic transmission model evaluating the impact 326 of non-pharmaceutical interventions in Switzerland, by their potential to reduceR below 1 at a national 327 level, predicted school closures alone would typically be insufficient to induce control [38]. 328 In choosing a specific reopening policy, decision-makers must weigh-up the benefits to both children and 329 parents that are gained from allowing more year groups to return to school, with the risks associated 330 with increased transmission. In light of the variation in effects onR between regions, reopening policies 331 may benefit from heterogeneity across the country, in order to allow the most children possible to 332 return to school without threatening a resurgence of disease prevalence. Our results also highlighted 333 the benefit to be gained from small class sizes and hence maintaining such measures of social distancing, 334 with the impact of this form of non-pharmaceutical intervention within the school environment difficult 335 to infer without explicit data. 336 Our results also predicted a higher risk of increased transmission associated with reopening secondary 337 schools compared to the reopening of primary schools. Such a relationship may be partly attributed 338 to the observed larger number of contacts of secondary school children compared to primary school 339 children [36]. Additionally, other contributory factors include differences between age groups in terms 340 of susceptibility and, if infected, displaying symptoms [7, 8]. These may consequently lead to secondary 341 school children having a larger contribution to overall transmission throughout the population. This 342 could potentially be offset by the greater ability of older pupils to understand and abide by social 343 distancing advice. 344 Increasing levels of contacts between school children inevitably leads to greater absolute numbers of 345 infections, detected cases, ICU admissions and, regrettably, deaths, even if the reproduction number 346 is not raised above one. For this reason, we also estimate the increase in these outcomes as a result 347 of reopening schools using the different strategies. The ranking of the different strategies for these 348 outcomes mirrors the ranking in terms of increases in R. The epidemiological impact of reopening 349 schools also depends on the behaviour of the wider population. If there is more mixing within the adult 350 (and elderly) population, the effect of reopening schools will be exacerbated by the generally higher 351 infection levels and contacts in the community. Reopening schools will then lead to greater increases in 352 13 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint case numbers over and above the increases due to greater mixing. In general, we found that even small 353 changes inR due to the behaviour of the general population swamp the impacts of reopening schools. 354 We would stress that, such increases must be viewed in the context of the restrictions currently placed 355 on pupils and parents. Ultimately, it is a societal decision to balance the benefits to pupils’ welfare 356 and education against the epidemiological consequences. 357 To consider the effects of specific school years returning, this work made some simplifying assumptions, 358 and our results therefore have limitations. In particular, in this paper we consider only an England- 359 specific context. The devolved administrations employ a different school system from England, includ- 360 ing different school term dates, which may affect the outcome of reopening schools. Future work could 361 incorporate such differences, some of the epidemic variability between nations will be captured by the 362 model parameter fits that are already performed for all the devolved nations. In our analysis of schools 363 we have made the pessimistic assumption that there will be limited non-pharmaceutical intervention 364 within the school setting, however, we have ignored the potentially greater mixing of parents or other 365 adults when taking younger children to school. Also, the model is deterministic, and captures the 366 return to school in terms of increased mixing between school ages; it cannot capture the inevitable 367 heterogeneity between schools, with some schools experiencing many cases while others have none. 368 Similarly, we make no attempt to replicate the reactive closure of classes to prevent further spread 369 once cases are identified. 370 As we have shown, the context in which school reopening happens will also have an impact on its 371 effect. While we consider different population level mixing patterns, this exploration is necessarily 372 constrained; for example it may also be the case that the opening of schools allows more parents to 373 return to work, increasing their risk of infection [30]. Indeed, a surge in cases in Seoul, South Korea 374 linked to a distribution centre, has identified at least one SARS-CoV-2 positive high-school student, 375 whose family member worked at the centre; this was followed by the re-implementation of localised 376 lockdown and social distancing measures, including the closure of 251 schools, days after their phased 377 reopening [39]. It is also be important to consider the impact of school re-openings in combination 378 with other concurrent measures, such as the NHS test and trace system in England (that began on 379 28th May) [40], which aims to trace close recent contacts of anyone who tests positive for SARS-CoV-2 380 and, if necessary, notify them to self-isolate at home to prevent onward transmission. Effective contact 381 tracing breaks transmission chains, but may also subject school classes to tracing and isolation. Even 382 without national-scale relaxation in the lockdown measures, the behaviour of the general population 383 is likely to change over time, in ways that are difficult to predict. Beyond these considerations, we 384 have also neglected the many possible side effects of reopening schools, such as parents interacting at 385 the school gates, teachers’ exposure while travelling to school (or in the staff room), or the effects of 386 school reopening on children mixing outside of school. 387 These analyses, performed in May, indicated that it should have been feasible to reopen all schools 388 in June. Reopening schools (for June and July) while other measures remained constant would have 389 allowed accurate information regarding the impact of children returning to the classroom for a rela- 390 tively short period, and would have provided invaluable evidence on the role of younger age-groups 391 in transmission. In practice, there was only a partial reopening on 1st June, with reception (year 0), 392 year 1 and year 6 returning to primary schools, and the sporadic return of some years 10 and 12 to 393 senior schools from 15th June. We predicted that the general return of just three primary school years 394 would have a minimal impact on R, and very few school-based outbreaks were reported before the 395 main summer holidays [41]. Unfortunately, before the return of all children to school in September, 396 multiple regions (notably Leicester, Manchester and the North West) of England experienced high 397 case numbers, while R continued to rise - such that it was likely to be above 1 before the reopening of 398 schools. However, our modelling still generates some useful predictions. School reopening is predicted 399 to have a larger impact in September than it would have done in June, although the impact is still 400 14 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint relatively small compared to other relaxations of lockdown. Our work also suggests that measures to 401 mitigate the rise in cases as we approach winter would be best focused on other routes of transmission, 402 as even when R is significantly above 1, the effect of opening or closing schools is minimal. 403

404 The authors would like to thank Massimiliano Tamborrino for contributing to data curation, and the 405 RAMP Rapid Review Group for their useful comments on this manuscript. 406 Author contributions 407 Conceptualisation: Matt J. Keeling. 408 Data curation: Matt J. Keeling; Glen Guyver-Fletcher; Alexander Holmes. 409 Formal analysis: Matt J. Keeling. 410 Investigation: Matt J. Keeling. 411 Methodology: Matt J. Keeling. 412 Software: Matt J. Keeling; Edward M. Hill; Louise Dyson; Michael J. Tildesley. 413 Validation: Matt J. Keeling; Edward M. Hill; Benjamin D. Atkins; Louise Dyson; Michael J. Tildes- 414 ley. 415 Visualisation: Matt J. Keeling. 416 Writing - original draft: Michael J. Tildesley; Edward M. Hill; Louise Dyson; Benjamin D. Atkins; 417 Matt J. Keeling; Bridget Penman; Erin Gorsich; Emma Southall. 418 Writing - review & editing: Matt J. Keeling; Edward M. Hill; Louise Dyson; Benjamin D. Atkins; 419 Erin E. Gorsich; Bridget Penman; Glen Guyver-Fletcher; Alexander Holmes; Hector McKimm; Emma 420 Southall; Michael J. Tildesley. 421 Financial disclosure 422 This work has been funded by the Engineering and Physical Sciences Research Council through the 423 MathSys CDT [grant number EP/S022244/1] and by the Medical Research Council through the 424 COVID-19 Rapid Response Rolling Call [grant number MR/V009761/1]. The funders had no role in 425 study design, data collection and analysis, decision to publish, or preparation of the manuscript. 426 Ethical considerations 427 The data were supplied from the CHESS database after anonymisation under strict data protection 428 protocols agreed between the University of Warwick and Public Health England. The ethics of the 429 use of these data for these purposes was agreed by Public Health England with the Government’s 430 SPI-M(O) / SAGE committees. 431 15 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint Data availability 432 Data on cases were obtained from the COVID-19 Hospitalisation in England Surveillance System 433 (CHESS) data set that collects detailed data on patients infected with COVID-19. Data on COVID- 434 19 deaths were obtained from Public Health England. These data contain confidential information, 435 with public data deposition non-permissible for socioeconomic reasons. The CHESS data resides with 436 the National Health Service (www.nhs.gov.uk) whilst the death data are available from Public Health 437 England (www.phe.gov.uk). 438 Competing interests 439 All authors declare that they have no competing interests. 440

[1] Li Lq, Huang T, Wang Yq, Wang Zp, Liang Y, et al. COVID-19 patients’ clinical characteristics, discharge rate, and fatality rate of meta-analysis (2020). doi:10.1002/jmv.25757. [2] Ludvigsson JF. Systematic review of COVID-19 in children shows milder cases and a better prognosis than adults. Acta Paediatrica, International Journal of Paediatrics 109(March):1088– 1095 (2020). doi:10.1111/apa.15270. [3] Barton M, Mehta K, Kumar K, Lu J, le Saux N, et al. COVID- 19 Infection in Children: Estimating Pediatric Morbidity and Mortality. medRxiv preprint pages 1–26 (2020). [4] NHS England. COVID-19 total announced deaths 27 May 2020. (2020). URL https://www.england.nhs.uk/statistics/wp-content/uploads/sites/2/2020/05/ COVID-19-total-announced-deaths-28-May-2020.xlsx. [Online] (Accessed: 23 June 2020). [5] Dong Y, Mo X, Hu Y, Qi X, Jiang F, et al. Epidemiology of COVID-19 Among Children in China. Pediatrics 145(6):e20200702 (2020). doi:10.1542/peds.2020-0702. [6] Wang C, Liu L, Hao X, Guo H, Wang Q, et al. Evolving Epidemiology and Impact of Non- pharmaceutical Interventions on the Outbreak of Coronavirus Disease 2019 in Wuhan, China. medRxiv page 2020.03.03.20030593 (2020). doi:10.1101/2020.03.03.20030593. [7] Viner RM, Mytton OT, Bonell C, Melendez-Torres G, Ward JL, et al. Susceptibility to and transmission of COVID-19 amongst children and adolescents compared with adults: a systematic review and meta-analysis. medRxiv page 2020.05.20.20108126 (2020). doi:10.1101/2020.05.20. 20108126. [8] Viner RM, Russell SJ, Croker H, Packer J, Ward J,et al. School closure and management practices during coronavirus outbreaks including COVID-19: a rapid systematic review. The Lancet Child and Adolescent Health 4(5):397–404 (2020). doi:10.1016/S2352-4642(20)30095-X. [9] Zhang J, Litvinova M, Liang Y, Wang Y, Wang W, et al. Changes in contact patterns shape the dynamics of the COVID-19 outbreak in China. Science 8001(April):eabb8001 (2020). doi: 10.1126/science.abb8001. [10] Luo L, Liu D, Liao Xl, Wu Xb, Jing Ql, et al. Modes of contact and risk of transmission in COVID-19 among close contacts. medRxiv page 2020.03.24.20042606 (2020). doi:10.1101/2020. 03.24.20042606. [11] Bi Q, Wu Y, Mei S, Ye C, Zou X, et al. Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study. The Lancet Infectious Diseases 3099(20):1–9 (2020). doi:10.1016/S1473-3099(20)30287-5. [12] Streeck H, Schulte B, Kuemmerer B, Richter E, Hoeller T, et al. Infection fatality rate of SARS-CoV-2 infection in a German community with a super-spreading event. medRxiv page 2020.05.04.20090076 (2020). doi:10.1101/2020.05.04.20090076. 16 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint [13] Stringhini S, Wisniak A, Piumatti G, Azman AS, Lauer SA, et al. Repeated seroprevalence of anti-SARS-CoV-2 IgG antibodies in a population-based sample from Geneva, Switzerland. medRxiv page 2020.05.02.20088898 (2020). doi:10.1101/2020.05.02.20088898. [14] Shakiba M, Hashemi Nazari SS, Mehrabian F, Rezvani SM, Ghasempour Z, et al. Seroprevalence of COVID-19 virus infection in Guilan province, Iran. medRxiv page 2020.04.26.20079244 (2020). doi:10.1101/2020.04.26.20079244. [15] Lavezzo E, Franchin E, Ciavarella C, Cuomo-Dannenburg G, Barzon L, et al. Suppression of COVID-19 outbreak in the municipality of Vo, Italy. medRxiv page 2020.04.17.20053157 (2020). doi:10.1101/2020.04.17.20053157. [16] Gudbjartsson DF, Helgason A, Jonsson H, Magnusson OT, Melsted P, et al. Early Spread of SARS-Cov-2 in the Icelandic Population. medRxiv page 2020.03.26.20044446 (2020). doi:10. 1101/2020.03.26.20044446. [17] Office for National Statistics. Coronavirus (COVID-19) Infection Survey pilot: England, 21 May 2020 (2020). URL https://www.ons.gov.uk/peoplepopulationandcommunity/ healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/ england21may2020. [Online] (Accessed: 23 June 2020). [18] Bunyavanich S, Do A, Vicencio A. Nasal Gene Expression of Angiotensin-Converting Enzyme 2 in Children and Adults. JAMA (2020). doi:10.1001/jama.2020.8707. [19] Ng K, Faulkner N, Cornish G, Rosa A, Earl C,et al. Pre-existing and de novo humoral immunity to SARS-CoV-2 in humans. bioRxiv page 2020.05.14.095414 (2020). doi:10.1101/2020.05.14.095414. [20] Grifoni A, Weiskopf D, Ramirez SI, Mateus J, Dan JM, et al. Journal Pre-proof Targets of T cell responses to SARS-CoV-2 coronavirus in humans with COVID-19 disease and unexposed individuals. Cell 0(0) (2020). doi:10.1016/j.cell.2020.05.015. [21] W¨ olfel R, Corman VM, Guggemos W, Seilmaier M, Zange S,et al. Virological assessment of hos- pitalized patients with COVID-2019. Nature pages 1–10 (2020). doi:10.1038/s41586-020-2196-x. [22] Jones TC, M¨ uhlemann B, Veith T, Zuchowski M, Hofmann J,et al. An analysis of SARS-CoV-2 viral load by patient age. medRxiv 105(13) (2020). [23] Stoye J. A Critical Assessment of Some Recent Work on COVID-19. arXiv page 2020.05.26.2005.10237v2 (2020). doi:arxiv:2005.10237v2. [24] Xu Y, Li X, Zhu B, Liang H, Fang C, et al. Characteristics of pediatric SARS-CoV-2 infection and potential evidence for persistent fecal viral shedding. Nature Medicine pages 1–4 (2020). doi:10.1038/s41591-020-0817-4. [25] Xing YH, Ni W, Wu Q, Li WJ, Li GJ, et al. Prolonged viral shedding in feces of pediatric patients with coronavirus disease 2019 (2020). doi:10.1016/j.jmii.2020.03.021. [26] Zhu N, Zhang D, Wang W, Li X, Yang B, et al. A Novel Coronavirus from Patients with Pneu- monia in China, 2019. N. Engl. J. Med. 382(8):727–733 (2020). doi:10.1056/NEJMoa2001017. [27] Fontanet A, Tondeur L, Madec Y, Grant R, Besombes C, et al. Cluster of COVID-19 in northern France: A retrospective closed cohort study. medRxiv page 2020.04.18.20071134 (2020). doi: 10.1101/2020.04.18.20071134. [28] National Centre for Immunisation Research and Surveillance. COVID-19 in schools - the expe- rience of NSW. (2020). URL http://ncirs.org.au/sites/default/files/2020-04/NCIRS%20NSW% 20Schools%20COVID Summary FINAL%20public 26%20April%202020.pdf. [Online] (Accessed: 23 June 2020). [29] Heavey L, Casey G, Kelly C, Kelly D, McDarby G. No evidence of secondary transmission of COVID-19 from children attending school in Ireland, 2020. Eurosurveillance 25(21):2000903 (2020). doi:10.2807/1560-7917.ES.2020.25.21.2000903. [30] Panovska-Griffiths J, Kerr CC, Stuart RM, Mistry D, Klein DJ, et al. Determining the optimal strategy for reopening schools, the impact of test and trace interventions, and the risk of occur- rence of a second COVID-19 epidemic wave in the UK: a modelling study. Lancet Child Adolesc. 17 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint Heal. (2020). doi:10.1016/S2352-4642(20)30250-9. [31] Brooks-Pollock E, Read JM, McLean AR, Keeling MJ, Danon L. Using social contact data to predict and compare the impact of social distancing policies with implications for school re- opening. medRxiv page 2020.07.25.20156471 (2020). doi:10.1101/2020.07.25.20156471. [32] Keeling MJ, Hill E, Gorsich E, Penman B, Guyver-Fletcher G, et al. Predictions of COVID-19 dynamics in the UK: short-term forecasting and analysis of potential exit strategies. medRxiv page 2020.05.10.20083683 (2020). doi:10.1101/2020.05.10.20083683. [33] Keeling MJ, Dyson L, Guyver-Fletcher G, Holmes A, Semple MG, et al. Fitting to the UK COVID-19 outbreak, short-term forecasts and estimating the reproductive number. medRxiv page 2020.08.04.20163782 (2020). doi:10.1101/2020.08.04.20163782. [34] Public Health England. COVID-19 Hospitalisation in England Surveillance System (CHESS) – daily reporting. (2020). URL https://www.england.nhs.uk/coronavirus/wp-content/uploads/ sites/52/2020/03/phe-letter-to-trusts-re-daily-covid-19-hospital-surveillance-11-march-2020. pdf. [Online] (Accessed: 29 July 2020). [35] Mossong J, Hens N, Jit M, Beutels P, Auranen K, et al. Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases. PLoS Med. 5(3):e74 (2008). doi:10.1371/journal. pmed.0050074. [36] Prem K, Cook AR, Jit M. Projecting social contact matrices in 152 countries using contact surveys and demographic data. PLOS Comput. Biol. 13(9):e1005697 (2017). doi:10.1371/journal.pcbi. 1005697. [37] Courtemanche C, Garuccio J, Le A, Pinkston J, Yelowitz A. Strong Social Distancing Measures In The United States Reduced The COVID-19 Growth Rate. Health Aff. page 10.1377/hlthaff.2020.00608 (2020). doi:10.1377/hlthaff.2020.00608. [38] Lemaitre JC, Perez-Saez J, Azman A, Rinaldo A, Fellay J. Assessing the impact of non- pharmaceutical interventions on SARS-CoV-2 transmission in Switzerland. medRxiv page 2020.05.04.20090639 (2020). doi:10.1101/2020.05.04.20090639. [39] The Korea Times. Calls grow to delay school opening as virus fears persist. (2020). URL https: //www.koreatimes.co.kr/www/nation/2020/05/181 290297.html. [Online] (Accessed: 23 June 2020). [40] Department of Health and Social Care. NHS test and trace: how it works. (2020). URL https: //www.gov.uk/guidance/nhs-test-and-trace-how-it-works. [Online] (Accessed: 29 July 2020). [41] Ismail SA, Saliba V, Lopez Bernal JA, Ramsay ME, Ladhani SN. SARS-CoV-2 infection and transmission in educational settings: cross-sectional analysis of clusters and outbreaks in England. medRxiv page 2020.08.21.20178574 (2020). doi:10.1101/2020.08.21.20178574. 18 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint Supporting information items Supporting Text S1 Description of the complete system of model equations. Supporting Text S2 Details on the mechanisms underpinning social distancing measures within the model framework Supporting Figure S1 Posterior distributions of key model parameters from fitting to date until 1st June. The left-hand graphs show how the probability of symptoms ( da) and susceptibility (σa) varies with age; given the low value of alpha most of the age-dependence is in the displaying of symptoms. The right-hand graph shows the relative adherence with lockdown measures in each region; high values correspond to a dramatic reduction in the mixing matrix, while an adherence of zero returns the matrix to pre-lockdown levels. This figure supplements the information in Table 1. Bars show the 95% credible intervals from the posterior distribution. Supporting Figure S2 Distribution of household symptomatic, asymptomatic and isolated cases in each age group on 1st June. Used in conjunction with Fig. 1. Bottom segments (blue shading) represent symptomatic infection. Middle segments (orange shading) represent asymptomatic infection. Top segments (yellow shading) represent those in isolation. Filled dots specify the fraction of the population within that age bracket. Supporting Figure S3 Increase in reproduction number, R, under eight school reopening scenarios for three regions in England. Estimates are depicted for the following three regions: (a) North West, (b) South East, (c) East of England. For each scenario, bars represent the mean absolute increase in R, compared to what we would observe if schools remained closed. We also give the 95% prediction intervals. Solid red lines identify the absolute increase required to raise R above 1, within each region, alongside 95% credible intervals (dashed red lines). Means and intervals are calculated from 1000 replicates sampled from the posterior parameter distributions. All scenarios are implemented on 1st June and continued until 22nd July. 19 . CC-BY 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted September 16, 2020. ; https://doi.org/10.1101/2020.06.04.20121434doi: medRxiv preprint