key: cord-339164-xhyqg5u2
authors: Keeling, M. J.; Tildesley, M. J.; Atkins, B. D.; Penman, B.; Southall, E.; Guyver-Fletcher, G.; Holmes, A.; McKimm, H.; Gorsich, E. E.; Hill, E. M.; Dyson, L.
title: The impact of school reopening on the spread of COVID-19 in England
date: 2020-06-05
journal: nan
DOI: 10.1101/2020.06.04.20121434
sha: 
doc_id: 339164
cord_uid: xhyqg5u2

Background: In the UK, cases of COVID-19 have been declining since mid-April and there is good evidence to suggest that the effective reproduction number has dropped below 1, leading to a multi-phase relaxation plan for the country to emerge from lockdown. As part of this staggered process, primary schools are scheduled to partially reopen on 1st June. Evidence from a range of sources suggests that children are, in general, only mildly affected by the disease and have low mortality rates, though there is less certainty regarding children's role in transmission. Therefore, there is wide discussion on the impact of reopening schools. Methods: We compare eight strategies for reopening primary and secondary schools in England from 1st June, focusing on the return of particular year groups and the associated epidemic consequences. This is assessed through model simulation, modifying a previously developed dynamic transmission model for SARS-CoV-2. We quantify how the process of reopening schools affected contact patterns and anticipated secondary infections, the relative change in R according to the extent of school reopening, and determine the public health impact via estimated change in clinical cases and its sensitivity to decreases in adherence post strict lockdown. Findings: Whilst reopening schools, in any form, results in more mixing between children, an increase in R and hence transmission of the disease, the magnitude of that increase can be low dependent upon the age-groups that return to school and the behaviour of the remaining population. We predict that reopening schools in a way that allows half class sizes or that is focused on younger children is unlikely to push R above one, although there is noticeable variation between the regions of the country. Given that older children have a greater number of social contacts and hence a greater potential for transmission, our findings suggest reopening secondary schools results in larger increases in case burden than only reopening primary schools; reopening both generates the largest increase and could push R above one in some regions. The impact of less social-distancing in the rest of the population, generally has far larger effects than reopening schools and exacerbates the impacts of reopening. Discussion: Our work indicates that any reopening of schools will result in increased mixing and infection amongst children and the wider population, although the opening of schools alone is unlikely to push the value of R above one. However, impacts of other recent relaxations of lockdown measures are yet to be quantified, suggesting some regions may be closer to the critical threshold that would lead to a growth in cases. Given the uncertainties, in part due to limited data on COVID-19 in children, school reopening should be carefully monitored. Ultimately, the decision about reopening classrooms is a difficult trade-off between increased epidemiological consequences and the emotional, educational and developmental needs of children.

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. At the time of writing, over 270, 000 people in the UK have been 15 confirmed to have been infected with COVID-19, with over 37, 500 confirmed deaths of individuals 16 who have 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 recent meta-analysis concludes that children and young people under the age of 20 may be less likely 30 to become infected: the odds ratio for becoming infected upon contact with an index case compared 31 to adults (> 20 years old) is 0.44 (CI 0.29, 0.69) [7] . This conclusion is based on pooling the results 32 of contact tracing and population-screening studies, most of which find evidence that the attack rate 33 in 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] [13] [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 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] [22] [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 We are aware of three reported studies of SARS-CoV-2 infection within the school environment. A 59 retrospective serology study of 661 individuals with links to a school-based outbreak in Oise, France, 60 showed that the infection spread readily within and outside the school to reach students, teachers, 61 staff, and families [27] . In contrast, an Australian government study of cases in schools in Western 62 Australia [28] identified nine children and nine adults who tested positive for SARS-CoV-2 (located 63 across different schools), but found only two secondary cases when testing a third of the close contacts 64 of these cases (288 samples). In Ireland, six SARS-CoV-2 cases were identified who had attended 65 or taught in schools. None of 924 school related child contacts or 101 school related adult contacts 66 showed any symptoms, but asymptomatic cases could have been missed [29] . The Australian school 67 cases were identified between 5th March and 3rd April, and the first Irish school case was identified at 68 the beginning of March. The first Oise school cases, by contrast, were identified on the 2nd February 69 2020. The greater awareness of COVID-19 by March, during which the WHO declared COVID-19 70 as a global pandemic, likely helped to control the Australian and Irish school-based outbreaks sooner 71 than in Oise.

In the UK, at the time of writing (late May 2020), cases of COVID-19 are declining and there is strong 73 evidence to suggest that the effective reproduction number has dropped below 1 across the country. 74 A multi-phase relaxation plan for the country to emerge from lockdown began on 13th May, with a 75 greater emphasis on returning to work if practical. As part of this staged process, primary schools 76 in England are scheduled to partially reopen on 1st June; reception, year 1 and year 6 children are 77 initially due to return to the classroom, with an emphasis on maintaining social distancing measures 78 where possible.

In this paper we investigate the epidemiological impacts of reopening schools in England, focusing 80 on different combinations of year groups. We extend a previously developed dynamic transmission 81 model for SARS-CoV-2, which is fit (on a regional basis for the UK) to real-time data on confirmed 82 cases requiring hospital care and mortality. We compare and contrast multiple possible strategies for 83 reopening both primary and secondary schools, focusing upon determining the effect of given year 84 groups returning to school upon future epidemic behaviour. By elucidating the risks associated with 85 particular age groups returning to school, we seek to contribute to the evidence base on the likely role 86 3 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 5, 2020. . https://doi.org/10.1101/2020.06.04.20121434 doi: medRxiv preprint of schools in the containment and control of this outbreak.

Transmission model 89 In order to perform the analysis of school reopening, we extended a previously-developed determin-90 istic, age-structured compartmental SARS-CoV-2 transmission model [30] . This model stratifies the 91 population according to current disease status, following a susceptible-exposed-infectious-recovered 92 (SEIR) paradigm (Fig. 1) . We assumed the latent period to be Erlang distributed, modelled within 93 the compartmental framework via division of the latent state into three stages. Infectious cases were 94 partitioned by presence of symptoms, meaning we tracked symptomatic and asymptomatic individuals 95 separately. Additional layers of complexity included differentiating by isolation and household status. 96 We provide a listing of model parameters in Table 1 , with a description of the model equations given 97 in Supporting Text S1. We use the predicted number of symptomatic individuals to estimate the 98 number of hospital admissions, ICU admissions and deaths, by estimating the proportion of symp-99 tomatic individuals requiring hospitalisation, ICU admission and the proportion that eventually die, 100 and the distribution of times through each of these states. For hospital admissions and cases requiring 101 treatment in ICU, the proportions going through each state and the distribution of times taken were 102 drawn from the COVID-19 Hospitalisation in England Surveillance System (CHESS) data set that 103 collects detailed data on patients infected with COVID-19 [31] . The risk of death was also captured 104 with an age-dependent probability, while the distribution of delays between hospital admission and 105 death was assumed to be age-independent, with both these two quantities determined from the Public 106 Health England (PHE) death records.

With the inclusion of age-structure, transmission was governed through age-dependent mixing ma-108 trices, based on UK social mixing patterns [32, 33] , and age-dependent susceptibility. To capture 109 the effects of social distancing measures that were introduced in the UK to reduce transmission, we 110 scaled down the mixing matrices associated with schools, work and other activities while increasing 111 the within household transmission matrix (see Supporting Text S2).

In a refinement to the base model, we imposed an amended age-stratification of the population. Whilst 113 in previous work the population was stratified into five year age brackets, for this study we separated 114 those aged between 0 and 19 years old into single year cohorts, with the remainder of the population 115 stratified into five year age brackets as before (20-24yrs, 25-29yrs and so on). The final age category 116 corresponded to those aged 100 years or above.

Modelling school reopening scenarios 118 We used this model framework to evaluate eight strategies for reopening schools from 1st June. The 119 eight school reopening options we considered assumed that, from the 1st June, the following school 120 year groups would return to school: CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 5, 2020. .

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.

For clarity, in all the strategies considered here we assumed that children of key workers continued to 130 attend school at the currently observed level. 131 We assessed the school reopening scenarios at a regional scale, modelling the population of England 132 aggregated to seven regions (East of England, London, Midlands, North East and Yorkshire, North 133 West England, South East England, South West England). This involved the use of region-specific 134 posterior parameters obtained in our prior work, where we fit our base transmission model on a region-135 by-region basis, using a Monte Carlo Markov Chain (MCMC) fitting scheme, to four timeseries: (i) new 136 hospitalisations; (ii) hospital bed occupancy; (iii) ICU bed occupancy; (iv) daily deaths (using data on 137 the recorded date of death, wherever possible) [30] . The inference was performed from epidemiological 138 data until 12th May 2020.

Our assessment of school reopening strategies comprised three strands. Firstly, we quantified how 140 the process of opening schools and year groups affected contact patterns and anticipated secondary 141 infections. Secondly, we related the scale of school opening to the relative change in R, assuming 142 the same transmission patterns in the rest of the population as during the strict lockdown phase. 143 Finally, we gauged the estimated change in clinical case and its sensitivity to changes in community 144 transmission following the easing of lockdown measures on 13th May. We outline each item in further 145 detail below.

Contacts and secondary infections 147 Any school reopening plan will inherently alter age-group contact patterns compared to contact struc-148 tures observed during the lockdown. We attempted to resolve how these alterations in social in-149 teractions propagated into the transmission dynamics by tracking secondary infections arising from 150 5 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 5, 2020. . https://doi.org/10.1101/2020.06.04.20121434 doi: medRxiv preprint 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 symptomatic index cases and infected index cases (either symptomatic or asymptomatic), respec-151 tively.

Specific to this aspect of the analysis we focused on a single region, namely the Midlands and the 153 posterior parameter set with the maximum likelihood. We first assess the contact structure and 154 transmission under two distinct lockdown assumptions ('strict closure' and our default assumption of 155 'weaker closure'). The 'strict closure' scenario assumed that there was no additional mixing between 156 school-age groups during the lockdown period. 'Weaker closure' assumed there was more limited 157 adherence, leading to higher mixing between school-age groups compared to the 'strict closure' setting. 158 We also consider six of the eight reopening strategies (omitting those with half class sizes as these are 159 bounded above by the full-class strategy). For each we show the age-mixing matrix between age-groups; 160 6 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 5, 2020. . the transmission matrix from a symptomatic infectious individual; the transmission matrix from an 161 average infectious individual (recognising the many will be asymptomatic or in household quarantine); 162 and the expected number of secondary cases an average infectious individual of a particular age-group 163 will generate. 164 Reproductive number analysis 165 The reproductive ratio or number (R) has become a universally recognised quantity in the description 166 of COVID-19 dynamics; it is defined as the average number of secondary cases from an average index 167 case -where the second average is important as it samples across all infectious states including 168 asymptomatics and those currently under household isolation. To prevent the occurrence of a second 169 phase of exponential growth in infection, it is crucial that relaxation of social distancing measures 170 do not result in the value of R rising above 1. On these grounds, there is interest in predicting the 171 magnitude of a rise in R that could result from the reopening of schools, and our confidence in this 172 result. 173 We considered all eight school reopening scenarios and examined the increase in R per region under 174 each of the eight strategies. To compute R, we used the contact matrices associated with the given 175 choice of school reopening and accounting for the regional population structure, whilst assuming the 176 same level of mixing in the rest of the population as during the strict lockdown; therefore any changes in 177 R are driven by changes in school-age mixing. We calculated means and intervals from 1000 simulation 178 replicates with parameter sets sampled from the posterior parameter distributions.

Clinical case impact 180 The prior methods focused on the reproductive ratio R, which is both an instantaneous measure (R 181 can be calculated at any or every time point) and a long-term calculation (as it utilises an eigenvalue 182 approach to generate the asymptotic R). Calculation of quantities of public health interest requires 183 the simulation of the full temporal dynamics from the start of the outbreak to the closing of schools 184 for the summer holidays on 22nd July. In addition, we considered the sensitivity of reopening schools 185 to other potential changes in population mixing patterns (and hence different values of R) driven by 186 other changes to the lockdown since 13th May. These changes to population mixing were generated 187 by reducing the adherence with lockdown measures, bringing the mixing matrices closer to the pre-188 pandemic norm. 189 We performed these simulations, using the full dynamic model to generate estimates of the symp-190 tomatic cases, deaths and ICU admissions between 1st June and 22nd July, for each of the eight 191 school-opening strategies. We compared these measures, aggregated over this 42-day period, to a 192 scenario where school closures remain in place beyond the 1st June.

For each reopening strategy and each region, we performed a total of 1000 replicates. In each replicate 194 we sampled parameter values randomly from all posterior parameter distributions, with the exception 195 of the adherence level. The potential reduction in adherence values, from 13th May, inevitably gen-196 erates different R values at the point of school reopening (measured by the observed growth rate of 197 the outbreak in the model simulation). As a consequence, for comparative purposes we segregated 198 the estimated increases in epidemiological quantities (comparing different school opening strategies for 199 fixed underlying parameters) into three categories according to the R value before school reopening: 200 below 0.8, between 0.8 and 1, or between 1 and 1.2. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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Choice of reopening strategy influences contact structure and secondary infection risk 203 We first investigated the impact of alternate strategies for reopening schools upon contact patterns be-204 tween individuals and the effect of this upon transmission of SARS-CoV-2 and occurrences of COVID-205 19 infection. Our results for the Midlands, and the posterior parameter set that maximises the 206 likelihood, are summarised in Fig. 2 . For all scenarios investigated we observe several common trends. 207 Contact is most common between individuals of the same, or similar ages (Fig. 2, first row) . There was 208 also greater contact between children and adults between the ages of 25 and 55, reflecting interactions 209 between children and their parents, as well as between elderly people. This increased likelihood of 210 contact within and between those age groups is reflected in the risk of secondary infections occurring 211 (Fig. 2, second and third rows) . The second row accounts for age-dependent susceptiblity, and shows 212 the expected number of secondary infections in each age (y-axis) from a symptomatic index case of a 213 particular age (x-axis). The third row incorporates the likely state of an index infection (symptomatic, 214 asymptomatic or in household quarantine -as predicted by the underlying ODEs) thereby reducing 215 the potential transmission from particular age-groups (Supporting Figure S2 ).

If schools remain closed, with a high level of adherence to the lockdown within this younger age-group 217 (Fig. 2 , first column) we observe that contact between children, and therefore the risk of secondary 218 infection occurring, is extremely low. Should adherence to lockdown be weaker (Fig. 2, second column) , 219 we observe a higher rate of mixing between children and a slight increase in risk of secondary infections 220 occurring. For both of these scenarios the average number of secondary infections per index infection 221 is below 1 for all age groups and the value of R remains significantly below 1.

We now investigate the impact of various strategies for school reopenings. We first investigate the 223 scenario of reception, year 1 and year 6 children returning to school -the policy that is scheduled to 224 be implemented on 1st June in England (Fig. 2, third column) . In this scenario, we observe a slight 225 increase in contacts compared to the "weaker closure" scenario, with increased transmission between 226 individuals in these age groups. However, crucially, even within these age groups, the total number 227 of secondary infections per index case remains below one (third column, final row, red bars) and the 228 overall reproduction number value of R was only observed to have slightly increased from the scenarios 229 in which schools remain closed. A slight increase in mixing, and hence R, was again observed when 230 all primary schools are opened (Fig. 2, fourth column) , but we predict that R remains below 1.

To conclude this segment of the analysis, we investigated the impact of school reopening strategies 232 that involved some, or all, secondary school children returning to the classroom. If children from key 233 years of 10 and 12 return to school (in addition to some or all primary school children), a significant 234 increase in mixing was observed within those age groups; the number of secondary infections as a 235 result of index infections in secondary schools was predicted to be above one (Fig. 2 , fifth and sixth 236 columns). However, this expected number of cases is distributed across multiple age-groups thereby 237 dissipating the worst effects. In general, we found secondary schools to represent a higher risk of 238 increased transmission potential than primary schools. This could lead to higher values of R when all 239 secondary schools are opened; but for all scenarios investigated, even the scenario in which all schools 240 are opened, we found strong support for R remaining below 1 in the Midlands (Fig. 2, final column) 241 assuming that all other transmission patterns remain unchanged. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted June 5, 2020. . https://doi.org/10.1101/2020.06.04.20121434 doi: medRxiv preprint Effect of school reopening on reproductive number 243 Next, we sought to estimate changes in R that may result from school reopenings alone -assuming 244 the transmission patterns in the rest of the population are maintained at strict lockdown phase levels. 245 In contrast to the the first part of the analysis, which focused on a single set of parameters and a 246 single region (Fig. 2) , here we explore the full parameter uncertainty and compare different parts of 247 the country.

For all school opening scenarios, within the seven regions of England, we observe an increase in R 249 compared to what we predict for keeping schools closed until the end of this academic year (Fig. 3 and 250 Supporting Figure S3 ). This is to be expected, given the increase in contact between children that 251 such reopening scenarios would allow. However, the magnitude of increase is predicted to be relatively 252 low, depending on the age-groups that return to school. In general, the more year groups allowed to 253 return to school at one time, the greater the effect on R, with the return of secondary school children 254 having the greatest impact.

The impact of allowing multiple year groups to return to school can still be small: opening a fraction 256 of the age-cohorts in each school generally leads to a moderate (less than 0.05) increase in R, especially 257 if children can be taught in smaller class sizes which is assumed to lead to a proportionate reduction 258 in within school transmission.

There is however considerable variation between the regions and here we focus on four exemplars. For 260 London and North East England & Yorkshire, the increase in R is considerably less than that for 261 East of England and the Midlands across all reopening scenarios. For the former, even allowing all 262 age groups to return to school (while maintaining tight control in other age-groups) is highly unlikely 263 to increase R above 1, with both means and 95% prediction intervals falling well below this threshold 264 (Figs. 3(a) and 3(b) , the 95% prediction intervals, as the name suggests, contain 95% of all predicted 265 values across the entire posterior distribution of parameters). This low R value is especially true for 266 London, which saw the most abrupt rise and subsequent decline in cases. However, this is not the case 267 for the East of England (Fig. 3(c) ) and the Midlands (Fig. 3(d) ). In these regions, allowing schools 268 to fully reopen could increase R above 1, with such an occurrence lying within the 95% prediction 269 intervals. We attribute these regional differences to both heterogeneity in the observed rate of epidemic 270 decline and the differential proportion of school age school in each region; the Midlands has the highest 271 proportion of older teenagers in the country.

Quantifying clinical case impact stemming from the re-opening of schools 273 Our final piece of analysis examined the extent to which each of the eight school reopening strategies 274 may contribute to clinical case outcomes, using the full dynamic model. We also considered the 275 sensitivity of reopening schools to other potential changes in population mixing patterns (and hence 276 different values of R) driven by other changes to the lockdown since 13th May.

In each scenario, reopening schools increased the absolute number of cases, ICU admissions and deaths 278 as a result of increased transmission (Fig. 4) . Note that these increases will not be restricted to the 279 children that return to school, since the greater transmission will lead to increased cases in other age 280 groups. Echoing our earlier findings, strategies in which a larger number of children return to school 281 generally resulted in larger increases. In addition, older children had a greater effect, so that reopening 282 secondary schools results in larger increases than only reopening primary schools.

The opening of schools on 1st June, is just one of a number of changes that began on 13th May. In 284 the previous sections we focused on school reopening, assuming that mixing (and hence transmission) 285 within the wider population has remained unchanged. Here we allow the relaxation of lockdown 286 measures to precipitate an increase of R within the community and calculate the additional change 287 10 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 5, 2020. . from the opening of schools. We consistently find that school reopening has a larger impact when R 288 in the community is high, leading to a greater increase in cases, ICU admissions and deaths. However, 289 by far the largest increase in any of these key quantities is driven by the underlying change in R due 290 to relaxations other than the reopening of schools (Figs. 4(b) , 4(d) and 4(f)). We also give the 95% prediction intervals. Solid red lines identify the absolute increase required to raise R 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.

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In this paper, we have used a mathematical model to consider the implications of various potential 293 strategies for reopening schools in England. We have compared the different strategies by presenting 294 mixing matrices and discussing their implication for onward transmission, and by analysing the increase 295 in the reproduction number and absolute number of cases, ICU admissions and deaths compared to 296 those predicted if schools remain closed. In the absence of other changes, the complete opening of all 297 schools is not predicted to raise the reproductive ratio above one. It must be noted that even in the 298 case where R remains below one, the increased transmission resulting from school reopening will likely 299 lead to a small increase in the absolute number of cases, ICU admissions and deaths.

Reopening schools, in any form, is going to result in more mixing between children, an increase in R 301 and thus, equivalently, more transmission of the disease. However, we can constrain and potentially 302 minimise the extent of this increase by selecting a subset of year groups to return to school. In doing 303 so, we restrict the increase in R to very low levels and, crucially, avoid the possibility of increasing R 304 above 1. These findings are in agreement with studies applied to other nations showing an apparent 305 non-primary role of school settings as a driver of SARS-CoV-2 transmission. A statistical study 306 in US counties looking at the relationship between the reduction in growth rate and the timing of 307 different state and local government social distancing interventions found school closures to not be 308 statistically significant [34] . Further, in terms of suppressing spread of SARS-CoV-2, a mechanistic 309 transmission model judging the impact of non-pharmaceutical interventions in Switzerland, by their 310 potential to reduce R below 1 at a national level, predicted school closures alone would typically be 311 insufficient [35] .

In choosing a specific reopening policy, one must weigh up the benefits to both children and parents 313 that are gained from allowing more year groups to return to school, with the risks associated with 314 increased transmission. In light of the variation in effects on R between regions, reopening policies may 315 benefit from heterogeneity across the country, in order to allow the most children possible to return to 316 school without threatening a resurgence of disease prevalence. Our results also highlight the benefit 317 to be gained from small class sizes and hence maintaining such measures of social distancing. 318 We also discerned a higher risk of increased transmission potential for reopening secondary schools 319 versus the reopening of primary schools. Such a relationship may be partly attributed to the observed 320 larger number of contacts of secondary school children compared with primary school children [33] . 321 On the other hand, other contributory factors include differences between age classes in susceptibility 322 and, if infected, displaying symptoms [7, 8] . These may consequently lead to secondary school children 323 having a larger contribution to overall transmission throughout the population.

Increasing levels of contacts between school children also inevitably leads to greater absolute numbers 325 of infections, detected cases, ICU admissions and, regrettably, deaths, even if the reproductive ratio is 326 not raised above one. For this reason, we also estimate the increase in the numbers of these outcomes 327 as a result of reopening schools using the different strategies. The ranking of the different strategies 328 for these outcomes mirrors the ranking in terms of increases in R. The impact of reopening schools 329 also depends on the behaviour of the wider population. If there is more mixing within the adult 330 (and elderly) population, the effect of reopening schools will be exacerbated by the generally higher 331 infection levels and contacts in the community. Reopening schools will then lead to greater increases 332 in case numbers over and above the increases due to greater mixing. In general we find that even small 333 changes in R due to the behaviour of the general population swamp the impacts of reopening schools. 334 We would stress that, such increases must be viewed in the context of the restrictions currently placed 335 on pupils and parents. Ultimately, it is a societal decision to balance the benefits to pupils' welfare 336 and education against the epidemiological consequences. 337 

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To consider the effects of specific school years returning, this work made some simplifying assump-338 tions, and our results therefore have limitations. In particular, in this paper we consider only an 339 England-specific context. The devolved administrations employ a different school system from Eng-340 land, including different school term dates, which may affect the outcome of reopening schools on 341 specific dates. Future work could incorporate such differences, some of the epidemic variability be-342 tween nations will be captured by the model parameter fits that are already performed for all the 343 devolved nations.

As we have shown, the context in which school reopening happens will also have an impact on its 345 effect. While we consider different population level mixing patterns, this exploration is necessarily 346 constrained; for example it may also be the case that the opening of schools allows more parents to 347 return to work, increasing their risk of infection. Indeed, a recent surge in cases in Seoul, South Korea 348 linked to a distribution centre, has identified at least one SARS-CoV-2 positive high-school student, 349 whose family member worked at the centre. This was followed by the re-implementation of localised 350 lockdown and social distancing measures, including the closure of 251 schools, days after their phased 351 reopening [36] . It will also be important to consider the impact of school re-openings in combination 352 with other concurrent measures, such as the recently rolled out NHS test and trace system in England 353 (beginning on 28th May) [37] , which aims to trace close recent contacts of anyone who tests positive 354 for SARS-CoV-2 and, if necessary, notify them to self-isolate at home to prevent onward transmission. 355 Effective contact tracing breaks transmission chains, but may also subject school classes to tracing 356 and isolation. Even without national-scale relaxation in the lockdown measures, the behaviour of the 357 general population is likely to change over time, in ways that are difficult to predict. Beyond these 358 considerations, we have also neglected the many possible side effects of reopening schools, such as 359 parents interacting at the school gates, teachers' exposure while travelling to school (or in the staff 360 room), or the effects of school reopening on children mixing outside of school.

The decision to gradually reopen schools in England, starting on 1st June with reception, year 1 and 362 year 6, has caused significant debate amongst scientists, policy makers, teachers and parents regarding 363 the risks associated with such a change in policy. Our work provides evidence suggesting that the 364 reopening of primary schools will result in only a small change to the value of R, indicating that the 365 risk associated with this policy change is low. As more children return to school, we would expect 366 the value of R to rise further, although our forecasts indicate that school reopening alone is unlikely 367 to push R above 1. However, given the number of other changes that have occurred over the past 368 month and are scheduled for the coming months, there is the potential for a gradual increase in R; it 369 is therefore vital that all epidemiological indicators are monitored closely during this relaxation phase 370 and measures reinstated should there be a significant rise in cases in the future. 371 14 .

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The copyright holder for this preprint this version posted June 5, 2020. The data were supplied from the CHESS database after anonymisation under strict data protection 394 protocols agreed between the University of Warwick and Public Health England. The ethics of the 395 use of these data for these purposes was agreed by Public Health England with the Government's 396 SPI-M(O) / SAGE committees.

Data availability 398 Data on cases were obtained from the COVID-19 Hospitalisation in England Surveillance System 399 (CHESS) data set that collects detailed data on patients infected with COVID-19. Data on COVID-400 19 deaths were obtained from Public Health England. These data contain confidential information, 401 with public data deposition non-permissible for socioeconomic reasons. The CHESS data resides with 402 the National Health Service (www.nhs.gov.uk) whilst the death data are available from Public Health 403 England (www.phe.gov.uk). 404 

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Supporting Text S1

Description of the complete system of model equations.

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 (d a ) and susceptibility (σ a ) 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.

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.

Increase in reproductive 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.

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All authors declare that they have no competing interests. 406