key: cord-0300988-ed2gynla
authors: Trystan Leng, Edward M. Hill; Robin N. Thompson, Michael J. Tildesley; Matt J. Keeling, Louise Dyson
title: Assessing the impact of secondary school reopening strategies on within-school COVID-19 transmission and absences: a modelling study
date: 2021-02-12
journal: nan
DOI: 10.1101/2021.02.11.21251587
sha: 78b777ce2b1f6aff5b2fe23762068ad2792991f0
doc_id: 300988
cord_uid: ed2gynla

nan

To control the spread of SARS-CoV-2, the pathogen responsible for COVID-19, unprecedented restrictions 2 have been placed upon people's daily lives. In the UK, these non-pharmaceutical interventions (NPIs) 3 have included practising good hand hygiene, wearing of face coverings, social distancing, the prohibition 4 of households mixing socially, the restriction of a range of leisure activities, and the closure of educational 5 establishments, workplaces, pubs and restaurants. Collectively, such measures have reversed the growth in 6 infection during the first and subsequent epidemic waves.

For staff and pupils returning to secondary schools in England during January 2021, it was planned for rapid 28 coronavirus testing to be introduced using Lateral Flow Device tests (LFTs). It was originally envisaged 29 testing would be provided (as a pair of LFTs) for all secondary pupils and staff prior to a return to face- 30 to-face teaching. After this, staff would be tested once a week on an ongoing basis. Additionally, should a 31 pupil receive a positive test, all close contacts of the pupil would be tested using an LFT for the next seven 32 days. Positive tests identified during this period would trigger a further round of testing, until no new cases 33 were been identified for a period of seven days 9 . By identifying and isolating asymptomatic and presymp-34 tomatic individuals, it is hoped that a mass testing strategy would be effective in controlling transmission 35 within schools while minimising absences. Additionally, doing so may identify a large proportion of infected 36 individuals, helping to facilitate an improved test and trace strategy. 37 Mass testing strategies have been implemented in other contexts, with mixed success. Preliminary data 38 released from the field evaluation of testing in asymptomatic people in the city of Liverpool indicated just 39 48.89% of COVID-19 infections in asymptomatic people were detected with a Innova Lateral Flow SARS-40 CoV-2 antigen test, when compared with a PCR test 10 . Furthermore, the antigen test failed to detect 41 three in ten cases with the highest viral loads. Testing has also been a constituent part of guidance for the 42 movement of university students to and from universities 11 . The guidance stipulated all students should be 43 offered rapid tests before leaving and when they return to university to help identify and isolate those who 44 are asymptomatic but could spread the virus. The protocol involved two LFTs, three days apart. 45 The role of children in the spread of COVID-19, particularly in the school setting, remains unclear. Evidence 46 from a range of sources suggests that children are, in general, only mildly affected by the disease and have 47 low mortality rates 12 . This is reflected in the fact that by 27th January 2020 there had been 69, 801 48 people who had died in hospitals in England and had tested positive for COVID-19, but only 29 of those 49 were in the 0-19 year age group 13 . Additionally, SARS-CoV-2 infections and outbreaks were uncommon in 50 educational settings during the summer half-term in England 14 , with the available evidence suggesting that 51 transmission among children in schools can happen but less efficiently than other respiratory viruses such as 52 influenza 15 . Similar signals have been noted in other nations. However, a synthesis of the literature by the 53 European Centre for Disease Prevention and Control attributed moderate confidence to onward transmission 54 by adolescents occurring as often as by adults in household and community settings, given social mixing 55 patterns; they also indicated, though with weaker support, that preschool and primary school aged children 56 transmit SARS-CoV-2 less often than adolescents and adults 16 . There are complexities with balancing harms 57 associated with school openings resulting in increased transmission, with harms associated with closure of 58 educational establishments stunting the educational development and welfare of children.

To assess the potential impact of a strategies involving rapid testing on within-school transmission and 60 absences, we created an individual-based model of a secondary school formed of exclusive 'year group 61 bubbles'. By performing computational simulations corresponding to infection spread over the course of a 62 school half-term, we compared the impact of strategies involving rapid testing to a strategy of isolating year 63 group bubbles on the total number of infections within schools, the number of school days missed per pupil 64 and the proportion of infected individuals identified. By doing so, we offer an assessment of the relative 65 merits of a mass testing strategy compared to an isolation of year groups strategy. We also considered the 66 sensitivity of our results to underlying model assumptions. Consequently, we identify factors likely to have 67 the largest impact on the success of a mass testing strategy.

In this study, we used a discrete-time stochastic individual-based model, with a daily time step, to simulate 70 the spread of infection within a secondary school over a half-term of seven weeks. In our simulations, schools 71 consisted of five year groups, with each year group containing 200 pupils, equivalent to a secondary school 72 without a sixth form (ages 11-16, the inclusion of additional year groups representing a sixth form does not 73 qualitatively change results). We provide a summary of our baseline assumptions, as well as the sensitivity 74 assumptions we considered, in Table 1 . 75 We assumed that simulated schools implemented a 'bubbling' policy at the level of year groups. In our 76 baseline scenario, we assumed exclusive and effective year group bubbles, meaning that there was no trans-77 mission between year groups, but pupils mix randomly within year group bubbles. We did not explicitly 78 model teachers, siblings, or external contacts. The impact of teachers and siblings can be indirectly cap-79 tured by assuming some degree of transmission between year groups, a scenario considered in our sensitivity 80 analysis. Infected pupils' relative probability of within-school transmission since day of infection was derived 81 from data from known source-recipient pairs 17 , with an assumed incubation period distribution under the 82 assumption that the generation time and incubation period are independent. The level of onward transmis-83 sion within-school remains unclear, and is likely to be influenced by a variety of factors, including the success 84 of other within-school social distancing measures and the epidemiological characteristics of the dominant 85 strain of SARS-CoV-2 in circulation in the local area. Because of this, we considered a wide range of levels 86 of within-school transmission. We assumed that the impact of external contacts on transmission could be 87 captured by a constant external force of infection, chosen to satisfy an average of 10% of pupils becoming 88 infected by the end of the half-term under an isolation of year groups policy. When isolating, we assumed 89 that individuals adhered and effectively isolated. After 15 days, we assumed individuals were no longer 90 infectious and recover with immunity. For a more detailed summary of our model's assumptions regarding 91 transmission, see Supporting Text S1.

Informed by previous studies into the levels of asymptomatic infection within age-groups, we assumed 93 that 12-31% develop symptoms over the course of their infection 18 , with the rest of the school population 94 remaining asymptomatic. There are indications that asymptomatic individuals may be less infectious than 95 symptomatic individuals 19 . Accordingly, we assumed that asymptomatic pupils were 30-70% as infectious 96 as those that develop symptoms. Symptomatic pupils developed symptoms on a day drawn from a Gamma 97 distribution with shape 5.807 and scale 0.948 20 , corresponding to a mean time to symptom onset of 5.5 days. 98 We assumed that the relative probability of transmission of an individual and the time to symptom onset 99 were independent, though in reality these factors likely influence one another 21 . Under our assumptions, 100 approximately 50% of infectiousness occurred during an individual's presymptomatic infection phase. In line 101 with recent observations from community surveillance surveys, we assumed that the population prevalence 102 at the start of the simulation was 2% 22 and that 20% of the population had been previously infected and 103 as a result were immune from reinfection (based on an estimate from December 2020 that approximately 104 12% of the population in England would have tested positive for antibodies to SARS-CoV-2 from a blood 105 sample 23 , with an expectation the true proportion previously infected would be higher owing to waning of 106 detectable antibodies 24 ).

Upon symptom onset, infected pupils underwent a PCR test. Pupils self-isolated until they received a test 108 result, and we assumed that pupils received a result two days after taking a test. Those receiving a negative 109 result returned to school the day after receiving their result, while those testing positive entered isolation for 110 ten days. Pupils who tested positive using a LFT entered isolation, with the outcome of a confirmatory PCR 111 test then determining whether the pupil remained in isolation or was released from isolation. Accordingly, 112 we assumed that identified infected pupils did not transmit infection on the day they were tested. We used 113 previously estimated LFT and PCR test probability profiles for symptomatic individuals 25 . For asymp-114 tomatic individuals, we assumed that the probability of testing positive is equal to that of symptomatic 115 individuals until peak positive test probability, but then decays more rapidly (Supporting Text S2). We 116 assumed a PCR test specificity of 100%, in line with recent studies confirming that false positives from PCR 117 are rare 26 ). We assumed LFT specificity to be 99.7% 27 . 118 Using this model, we assessed the impact of different reopening strategies on transmission and absences 119 within schools. By simulating different school return strategies in simulations with the same set of parameter 120 values and same set of pregenerated random numbers, we could directly compare the impact each strategy 121 had for each simulation. Specifically, we produced 10,000 simulation replicates for five strategies: (i) isolation 122 of year group bubbles; (ii) serial contact testing; (iii) regular mass testing; (iv) a combination of regular 123 mass testing with serial contact testing; (v) no school-level testing or isolation of year-group bubbles. Under 124 3 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted February 12, 2021. an isolation of year group bubbles strategy, upon the identification of a case (through a symptomatic pupil 125 seeking a PCR test), all pupils within a year-group bubble were placed in isolation for ten days following 126 the last contact with the positive case. For serial contact testing, on the identification of a case (following 127 confirmation by PCR), all pupils within a year-group bubble were tested using LFT for seven days following 128 the last contact with the positive case. The period of serial contact testing is reset if another pupil in the 129 year-group bubble returned a positive LFT result. Under a regular mass testing strategy, all pupils are 130 tested once a week using LFTs. For strategies (ii), (iii), and (iv), all pupils were tested twice with LFTs in 131 the week before returning to school. We elaborate on the details of each reopening strategy in Supporting 132 Text S3.

In addition, we assessed the sensitivity of results obtained to the underlying modelling assumptions (see 134 Supporting Text S4) and we also explored the impact of altering the assumed level of within-school trans-135 mission (Supporting Text S5). For the sensitivity analysis, we generated 2000 simulation replicates for each 136 scenario. We performed the reopening strategy model simulations, sensitivity analysis and visualisation of 137 results using Matlab 2019b. 

In the majority of the 10,000 simulations (85.8%), a serial contact testing strategy was less effective at 140 reducing infections within a school than an isolation strategy. Similarly, in 89.8% of simulations, regular 141 weekly testing was less effective at reducing infections than isolating year group bubbles . However, serial 142 contact testing and regular testing combined was more effective at reducing infections than isolating year 143 group bubbles in 92.5% of simulations (Figure 1a ). 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 this this version posted February 12, 2021. ;  The average number of pupils infected over by the end of the half-term for an isolation of year-group 145 bubbles strategy was set at 10%. Slightly higher levels resulted from a serial contact testing (10.82%) or 146 regular weekly testing strategy (12.86%), whereas lower levels resulted from a combination of both measures 147 (8.20%). Without control measures, a mean of 15.21% had been infected by the end of the half-term, with 148 large outbreaks occurring much more frequently (Figure 1b) . These trends are reflected by the within-school 149 incidence at the end of the half-term; with similar within-school incidence for isolation and serial contact 150 strategies, reduced within-school incidence for a combined strategy, and substantially higher within-school 151 incidence with no control strategy (Figure 1c ).

By identifying asymptomatic and presymptomatic individuals, mass testing prior to the start of term ini-153 tially reduced mean prevalence within schools. However, prevalence quickly increased to a higher level than 154 would be obtained under an isolation of year group bubbles strategy, remaining at a higher level for weekly 155 mass testing and serial contact testing strategies from the middle of week 2 onwards (Figure 2a) . Under both 156 strategies, a considerable proportion of asymptomatic infected individuals remained unidentified through-157 out the simulation (Figure 1d, Figure 2b ). By combining serial contact testing and regular mass testing, 158 the majority of asymptomatic individuals were identified over the course of the half-term, and prevalence 159 remained low throughout the course of the half-term. 160 Serial contact tracing and mass testing strategies were more effective at reducing school absences than an 161 isolation of year group bubbles approach. By isolating year group bubbles, even uninfected pupils can spend 162 a considerable number of days absent. The average pupil spent 7.98 days isolating over the duration of 163 the half term, i.e. around 22.8% of a half-term of seven weeks. For serial contact tracing and mass testing 164 strategies, as individuals would only be absent if they had sought a PCR test, or had tested positive to 165 an LFT or PCR test, the majority (91.9% under serial contact testing, 92.8% under weekly mass testing, 166 88.0% under a combined strategy) of pupils had no days of school absence. The mean days absent for these 167 strategies was 0.39 days for a serial contact testing strategy, 0.38 days for regular weekly testing, and 0.53 168 days for those measures combined (Figure 1e) . Temporally, for a isolation of year group bubble strategy, 169 throughout the half-term a considerable portion of pupils (20-40%) may plausibly be expected to be absent. 170 For the considered strategies involving rapid testing, the fraction of students absent at any one time was 171 relatively low, remaining below 5% throughout the half-term (Figure 2c ).

Strategies involving rapid testing required a large number of tests to be implemented successfully. Over 173 the course of a half term, pupils on average undertook 13.8 LFTs under a serial contact testing strategy, 174 8.9 LFTs under a weekly mass testing strategy, and 26.3 LFTs under a combined strategy (Figure 1f ). For 175 strategies involving serial contact tracing, a high volume of testing was required throughout the half-term 176 (Figure 2d ). This high volume of testing also required many pupils to isolate over weekends, when tests 177 could not be administered.

There is considerable uncertainty surrounding many of the parametric assumptions that underpin the model. 179 Accordingly, we performed a univariate sensitivity analysis to understand the impact these assumptions have 180 on our findings (Supporting Text S4). Across the range of alternative parameterisations considered, serial 181 contact testing and regular mass testing strategies remained less effective at reducing infections than an 182 isolation of year group bubbles strategy alone, but remained more effective when combined. Of all the 183 factors considered, the sensitivity of LFTs had the largest impact on infections. Community infections, 184 captured by the external force of infection on individuals, and the level of within-school infection, had the 185 largest impact on the reduction of school days missed. We also explored the impact of altering the assumed 186 level of within-school transmission (Supporting Text S5). Different levels of within-school transmission did 187 not qualitatively change findings, but identifying asymptomatic infectious individuals had a larger benefit 188 for higher quantities of within-school transmission. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint 

Reopening strategy 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 this this version posted February 12, 2021. ; https://doi.org/10.1101/2021.02.11.21251587 doi: medRxiv preprint Figure 2 : Infection, absences, and testing over the duration of the school half-term. We display timeseries of (a) prevalence, (b) the percentage of currently infectious asymptomatic individuals identified for reopening strategies involving within-school testing. We display timeseries of (c) the percentage of pupils absent and (d) percentage of pupils tested throughout the half-term. Solid line traces correspond to the mean value attained on each daily timestep and shaded envelopes represent the 50% prediction intervals (these regions contain 50% of all simulations at each timepoint). The strategies displayed are: no control (grey), weekly mass testing (purple), serial contact testing (blue), year group bubbles strategy (orange), combined serial contact testing and mass testing (green). Results were obtained from 10,000 simulations.

In this paper, we have developed an individual-based model of a secondary school formed of exclusive 'year 191 group bubbles' and performed numerical simulations to assess the impact of a collection of postulated testing 192 and isolation-based school control strategies (against spread of SARS-CoV-2) on transmission, absences 193 and testing burden. Across the considered strategies, our findings reveal a trade-off between these three 194 measures.

Evaluating strategies on the basis of school absence, serial contact testing and regular mass testing reduce 196 absences considerably. However, these approaches adopted individually result in slightly higher levels of 197 infection than would be obtained under an isolation of year group bubbles strategy. Used together these 198 two test-based strategies can result in lower levels of infections but both strategies, particularly when 199 implemented in tandem, require a high testing capacity. Prior work performing numerical simulations 200 on complex networks has indicated a high volume of testing being required to effectively curb disease 201 spread 29 .

In comparison to isolating year group bubbles breaks chains of transmission when a positive case is identified, 203 rapid testing strategies can allow infected pupils who falsely test negative to continue to transmit infection 204 within the school setting. Under serial contact testing, asymptomatic individuals may fail to be identified 205 7 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted February 12, 2021. ;  for two reasons. Firstly, the sensitivity of LFTs means that some asymptomatic individuals would remain 206 undetected despite being tested repeatedly while infected 10 . Secondly, serial contact testing is only triggered 207 after a positive case is identified by other means. As a substantial proportion of the school population will 208 remain asymptomatic throughout their infection, there is the possibility that infection continues within the 209 school setting for a considerable period before an individual is infected who exhibits symptoms. In contrast, 210 testing before term starts, and then regularly testing throughout the half-term, reduces the risk of large 211 chains of transmission occurring unnoticed. By combining this with initiating serial contact testing, enough 212 asymptomatic and presymptomatic individuals are identified to keep incidence within the school low. 213 We have underpinned our model with relevant available data where possible and performed a sensitivity 214 analysis to understand the sensitivity of model outputs to the underlying model assumptions. Our results 215 did not qualitatively change across the range of sensitivity assumptions considered. Of all the factors 216 considered in our sensitivity analysis, the sensitivity of LFTs had the largest impact on infections. While 217 previous modelling approaches have shown that the frequency of test screening has a larger impact on 218 reducing transmission than test sensitivity 30 , our results demonstrate that the sensitivity of rapid tests may 219 still be an important determinant of the relative effectiveness of different school reopening strategies that 220 involve rapid testing at reducing transmission compared to strategies involving isolation. We believe these 221 outcomes are reconciled by the differing model approaches affecting the relative impact of test sensitivity; 222 the study by Larremore et al. 30 assumed that test results were a deterministic function of viral load, while 223 in our model the likelihood of an individual testing positive was governed by a probability distribution 224 dependent on the time since infection (inferred from observed data from UK healthcare workers 25 ). These 225 alternative approaches result in different levels of infectiousness removed through rapid testing, as under 226 the assumptions of Larremore et al. individuals with high viral loads will always test positive to LFTs. 227 This highlights the importance of continued research into the sensitivity of rapid tests, with granularity 228 to determine heterogeneity (if any) across specific age groups and in specific settings, as well as the most 229 appropriate way to capture test probability profiles in a model.

Our model makes several optimistic assumptions regarding the practicalities of testing. Schools are assumed 231 able to test pupils in an infection-secure environment, and able to effectively isolate positively identified 232 pupils from passing on infection within the school on the day of testing. We assume that the sensitivity of 233 LFTs that are self applied by pupils is comparable to that of LFTs self applied by healthcare workers 25 . In 234 our model, pupils required to isolate do so effectively, and have no risk of becoming infected while isolating. 235 All pupils comply with the school's reopening strategy, and all symptomatic pupils seek a PCR test and 236 isolate upon symptom onset. By doing so, we demonstrate the impact of reopening strategies if ideally 237 implemented. However, in reality this ideal scenario is unlikely to be met. If pupils have a substantial 238 chance of transmitting infection to other pupils when being tested in school, or do not take swabs correctly, 239 this will increase the infections that occur when implementing a serial contact testing or regular mass 240 testing strategy. Conversely, if pupils have a substantial risk of infection when they are supposed to be 241 isolating, a strategy that keeps pupils within school, where social interactions are regulated, may become 242 more beneficial. For strategies involving serial contact testing, pupils are expected to isolate on days that 243 they are due to be tested that fall on weekends. Pupils failing to isolate on serial contact test days that fall 244 on weekends will reduce the effectiveness of these approaches. The impact of other forms of non-adherence 245 will likely depend upon schools' policies regarding non-adhering pupils.

Whilst this study has focused on the impact of reopening strategies in secondary schools, results may 247 be expected to be qualitatively similar in the context of primary schools. However, there are some key 248 differences that may impact the appropriateness of applying our results directly to a primary school setting. 249 As tests within a school are expected to be self-administered, this may not be feasible for primary school 250 age children, particularly in younger years. Epidemiological and clinical factors may differ between primary 251 and secondary school aged children 16 , meaning the effectiveness of serial contact testing, which often relies 252 upon testing being initiated by a symptomatic case seeking treatment and testing positive, may be affected. 253 The relevant size of the exclusive bubbles in primary schools will typically be smaller, as pupils are often 254 partitioned into exclusive bubbles based on individual classes rather than entire year groups. Use of smaller 255 exclusive bubbles could potentially impact both transmission and testing.

An evaluation of the risk of reopening strategies to teachers and the wider community is beyond the remit 257 of this study, though this risk will be a function of the level of infections that result from different reopening 258 strategies. Capturing this aspect of transmission would require the explicit modelling of teachers and 259 external contacts of both pupils and teachers. Research into these risks would be a valuable line of enquiry 260 for future research, but as is often the case, the challenge would be the appropriate parameterisation of the 261 model. 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 this this version posted February 12, 2021. ;  In summary, we have explored the impact of different reopening strategies on both transmission and absences 263 within a secondary school setting. We find that serial contact testing and regular mass testing strategies, 264 acting alone, are less effective at reducing infections than an isolation of year group bubbles strategy, but 265 substantially reduce absences. Acting together, serial contact testing and regular mass testing can reduce 266 infections to levels lower than would occur under an isolation of year group bubbles strategy, but such a 267 policy requires a high volume of testing. Our results highlight the conflict between the goals of minimising 268 within-school transmission, minimising absences, and minimising testing burden. Amongst the strategies 269 considered here we did not identify one that minimised all three simultaneously. An assessment of the 270 relative benefits and costs of each must be made when considering future school reopening policies.

. CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted February 12, 2021. ;

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