Estimating the impact of reopening schools on the reproduction number of SARS-CoV-2 in England, using weekly contact survey data

/ 1 Estimating the impact of reopening schools on the reproduction number 2 of SARS-CoV-2 in England, using weekly contact survey data 3 James D Munday* 1a , Christopher I Jarvis* 1b , Amy Gimma 1c , Kerry LM Wong 1d , Kevin van 4 Zandvoort 1e , CMMID COVID-19 Working Group, Sebastian Funk 1f , W. John Edmunds 1g 5 1 Centre for Mathematical Modelling of Infectious Disease, London School of Hygiene and 6 Tropical Medicine. 7 a: [email protected] (Corresponding Author) 8 b: [email protected] 9 c: [email protected] 10 d: [email protected] 11 e: [email protected] 12 f: [email protected] 13 g: [email protected] 1 . CC-BY 4.0 International licenseIt 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 (which was not certified by peer review) The copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. / 14 Abstract 15 Background 16 Schools have been closed in England since the 4th of January 2021 as part of the national 17 restrictions to curb transmission of SARS-CoV-2. The UK Government plans to reopen 18 schools on the 8th of March. Although there is evidence of lower individual-level 19 transmission risk amongst children compared to adults, the combined effects of this with 20 increased contact rates in school settings are not clear. 21 Methods 22 We measured social contacts when schools were both open or closed, amongst other 23 restrictions. We combined these data with estimates of the susceptibility and infectiousness 24 of children compared with adults to estimate the impact of reopening schools on the 25 reproduction number. 26 Results 27 Our results suggest that reopening all schools could increase R from an assumed baseline 28 of 0.8 to between 1.0 and 1.5, or to between 0.9 and 1.2 reopening primary or secondary 29 schools alone. 30 Conclusion 31 Our results suggest that reopening schools is likely to halt the fall in cases observed in 32 recent months and risks returning to rising infections, but these estimates rely heavily on the 33 current estimates or reproduction number and the current validity of the susceptibility and 34 infectiousness profiles we use. 35 Keywords : School closure, SARS-CoV-2, COVID-19, Social Contacts, Reproduction 36 Number, CoMix 2 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 37 Introduction 38 School closures have been implemented in many countries as part of a broader response to 39 the COVID-19 pandemic [1] . It is well established that children are at low risk of 40 hospitalisation and death as a direct result of infection [2, 3] . Despite this lower risk, there is 41 concern that allowing transmission amongst younger age-groups increases risk of infection 42 in adults, who are at substantially higher risk. The role of schools in transmission is 43 therefore an important question. On the 4th of January 2021, a third national lockdown was 44 announced in England to curb transmission of SARS-CoV-2 [4] . This included the closure of 45 schools, a measure the UK government plans to reverse on the 8th of March. 46 The direct and indirect impact of school closures and eventual reopening is still unclear. 47 There is mixed evidence around the role of schools in community transmission. Existing 48 studies of transmission within schools have wide ranging results [5–7] . Other work 49 demonstrates an increased prevalence amongst school-aged-children when schools return 50 [8, 9] and a higher risk of infections entering households through children than adults. 51 However, the evidence that schools drive transmission in the community remains scarce [10, 52 11] . A particular challenge for many analyses is bias resulting from the age-dependence in 53 case ascertainment due to varying rates of asymptomatic infection [12] . This challenge is 54 then further complicated by changes in epidemiology due to the emergence of new variants 55 [13] . 56 The potential change in transmission of SARS-CoV-2 upon reopening schools predominantly 57 depends on a combination of two factors. Firstly, the age-specific risk of transmission upon 58 contact. Secondly, the likely increased rate of contact between members of the population 59 due to school reopening. Multiple studies aimed at understanding the relative transmission 60 risk associated with children indicate lower susceptibility [14–16] and some indicate lower 61 infectiousness [14] . However, evidence of lower transmission risk amongst children alone is 62 insufficient to quantify the impact of reopening schools. There is a need to combine the 3 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 63 estimates of reduced susceptibility and infectiousness with age specific contact patterns in 64 this age-group social contacts amongst school-aged-children. 65 There is abundant evidence that children’s contacts increase when schools are open, 66 presenting opportunities for increased infectious disease transmission which is well 67 documented in other pathogens such as influenza [17] . Nonetheless, it is important to 68 capture how these contacts vary under the specific conditions presented during the current 69 pandemic response, where social distancing and other mitigations are in effect within 70 schools. 71 CoMix is a large-scale comprehensive social contact survey which has collected data on 72 social contacts in the UK on a weekly basis since the 24th of March 2020 [18] . In this paper, 73 we estimate the impact of opening schools on the reproduction number in England, by 74 combining social-contact data collected during periods where schools were open and closed 75 [18] with estimates of age-stratified susceptibility and infectiousness [14–16] . 4 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 76 Methods 77 CoMix Data 78 CoMix is a longitudinal behavioural survey, launched on the 24 th of March 2020. The sample 79 is broadly representative of the UK adult population with data collected from approximately 80 2000 individuals per week. Participants are invited to respond to the survey once every two 81 weeks. We collected weekly data by running two alternating panels. Parents complete the 82 survey on behalf of children (17 years old or younger). Participants record direct, 83 face-to-face contacts made on the previous day, specifying certain characteristics for each 84 contact including the age and sex of the contact, whether contact was physical (skin-to-skin 85 contact), and where the contact occurred (e.g. at home, work, while undertaking leisure 86 activities, etc). Further details have been published elsewhere [18] . The contact survey is 87 based on an approach developed for the POLYMOD contact survey [19] . We provide a brief 88 descriptive analysis of the contacts recorded during the November and January lockdown 89 periods by age group and geographical region. 90 Constructing contact matrices and estimating reproduction number 91 We constructed age-stratified contact matrices for nine age-groups (0-4, 5-11, 12-17, 18-29, 92 30-39, 40-49, 50-59, 60-69, and 70+). Participants did not report exact ages of contacts, we 93 therefore sampled from the reported age-group with a weighting consistent with contacts 94 reported in the POLYMOD survey. We fitted a truncated negative binomial model to calculate 95 the mean contacts between each participant and contact age-groups. To ensure reciprocity 96 in contacts, we multiplied the matrix by population size vector for England, using United 97 Nations World Population Prospects data [20] , before taking the cross-diagonal mean and 98 then dividing by the same population vector again. 99 Profiles of Age-dependent transmission risk 100 We consider five age-dependent susceptibility and infectiousness profiles (Table 1): 5 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 101 The first profile (i) assumed equal susceptibility and infectiousness in all age groups. This is 102 unlikely to reflect reality but provides an upper limit as a reference point to compare the other 103 profiles. 104 For the second profile (ii) we used results from a mathematical modelling study by Davies et. 105 al [14] . which estimated relative susceptibility and clinical fraction in 9 age groups. The work 106 also reports estimates of 50% infectiousness of sub-clinical cases and reports clinical 107 fraction by age. We used this to calculate infectiousness per age group further detailed in 108 Table 1. 109 The third profile (iii), was based on analyses of household transmission patterns from the 110 Office for National Statistics (ONS) Community Infection Study [15] ; 50% susceptibility in 111 children relative to adults but equal infectiousness. 112 For the fourth profile (iv), we performed a meta-analysis of prevalence studies included in a 113 systematic review by Viner et al [16] . We used a random effects model based on the data 114 from Figure 4 of their paper. This resulted in 64% (51% - 81%, 95% confidence interval [CI]) 115 susceptibility in children relative to adults, we assumed equal infectiousness between 116 children and adults [16] ; 117 For the fifth profile (v), we used an independent estimate of relative susceptibility in children 118 (31%, see results section), quantified by comparing reproduction numbers estimated from 119 CoMix data and using a well-established time-series method developed by Abbott et. al [21] , 120 which uses a time-series of cases to determine the instantaneous reproduction number 121 under an assumed generation interval and infection to reporting delay distribution. 6 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 122 Table 1 Susceptibility and infectiousness profiles taken from Davies et.al. [14] , ONS reports 123 and Viner et al [16] 7 Study Age groups Susceptibility Infectiousness Clinical Fraction Davies et al 1 0-4 0.4 (0.25, 0.57) 0.61 0.29 (0.18, 0.44) 5-10 0.4 (0.25, 0.57) 0.61 0.29 (0.18, 0.44) 11-17 0.4 (0.27, 0.53) 0.61 0.21 (0.12, 0.31) 18-29 0.79 (0.59, 0.96) 0.64 0.27 (0.18, 0.38) 30-39 0.86 (0.69, 0.98) 0.67 0.33 (0.24, 0.43) 40-49 0.80 (0.61, 0.96) 0.70 0.40 (0.28, 0.52) 50-59 0.82 (0.63, 0.97) 0.75 0.49 (0.37, 0.60) 60-69 0.88 (0.70, 0.99) 0.82 0.63 (0.49, 0.76) 70+ 0.74 (0.56, 0.90) 0.85 0.69 (0.57, 0.82) Susceptibility Infectiousness ONS 2 0-4 0.5 (0.35, 0.75) 1.0 (0.7, 1.5) 5-10 0.5 (0.35, 0.75) 1.0 (0.7, 1.5) 11-17 0.5 (0.35, 0.75) 1.0 (0.7, 1.5) 18-29 1.0 1.0 30-39 1.0 1.0 40-49 1.0 1.0 50-59 1.0 1.0 60-69 1.0 1.0 70+ 1.0 1.0 Susceptibility Infectiousness Viner et al 3 0-4 0.64 (0.51, 0.81) 1.0 (assumed) 5-10 0.64 (0.51, 0.81) 1.0 (assumed) 11-17 0.64 (0.51, 0.81) 1.0 (assumed) 18-29 1.0 1.0 30-39 1.0 1.0 40-49 1.0 1.0 50-59 1.0 1.0 60-69 1.0 1.0 70+ 1.0 1.0 Susceptibility Infectiousness CoMix fit 0-4 0.31 (0.30, 0.31) 1.0 5-10 0.31 (0.30, 0.31) 1.0 11-17 0.31 (0.30, 0.31) 1.0 18-29 1.0 1.0 30-39 1.0 1.0 40-49 1.0 1.0 50-59 1.0 1.0 60-69 1.0 1.0 70+ 1.0 1.0 1 95% Credible Intervals 2 Approximate results inferred from plot in [15] unknown quantification of uncertainty 3 95% Confidence Interval . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 124 Inferring age dependent transmission risk using CoMix data 125 We established independent estimates of susceptibility and infectiousness in children 126 relative to adults. We did this by comparing estimates of R using CoMix contact data with 127 estimates of the time-varying reproduction number in England calculated using case data 128 [21] . To capture the change in contact rates as schools returned in September 2020 129 We calculated a reproduction number resulting from two-weekly rolling contact matrices C t 130 and assumed relative susceptibility and infectiousness vectors s and i to be: 131 We simplified s and i such that adult age-groups (18+) were 1.0 and child age groups were 132 equal, s and i . We inferred s and r, keeping i at 1.0 , by fitting our estimates using maximum 133 likelihood estimation to those calculated using the EpiNow2 package [21] . We assumed 134 gamma distributed uncertainty in the time-varying estimates which we parameterised using 135 the mean and standard deviation of these estimates over each survey period used to μrt σrt 136 calculate CoMix derived eigenvalues. 137 To show the likelihood surface of relative susceptibility and infectiousness, we calculated the 138 likelihood of a range of combinations of i and s while fitting r . 139 We fitted over 2 periods of time. Firstly, between 27th July and 10th October to most clearly 140 capture the impact of schools returning in the summer whilst minimising issues related to 141 gradual acquisition of natural immunity. Second, We fitted over a longer period of time 142 incorporating data from 10th June. 143 We omitted data at the end of August in both fits due to a short spike in reproduction number 144 estimates, which we believe resulted from large numbers of imported cases from 145 recreational travel. We further omitted two weeks in July when contacts were not recorded 8 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 146 for children. We assessed sensitivity to the fitted period, by using a range of fitting options 147 (Figure S4). 148 Evaluating the impact of reopening schools on Reproduction Number 149 We created contact matrices using CoMix data collected during the second lockdown, (5th 150 November to 2nd December 2020) to represent contacts during a lockdown with schools 151 open. We used data from 5th to 18th of January 2021 for contacts during a lockdown with 152 schools closed (Supplementary Figures, Figure S1). We constructed further synthetic 153 contact matrices representing opening primary or secondary schools by replacing the 154 contacts of 5-10 year-olds (primary) and 11-17 year-olds (secondary) in the ‘schools open’ 155 contact matrix (second lockdown), with those from the ‘schools closed’ contact matrix (third 156 lockdown) (Supplementary Figures, Figure S2). 157 Since the basic reproduction number scales linearly with the dominant eigenvalue of a matrix 158 of effective contact [22] , the ratio of the eigenvalues of two effective contact matrices 159 provides a relative change in reproduction number between the three scenarios considered. 160 In the case where infectiousness and susceptibility are equal in all age groups, the effective 161 contact matrix is proportional to the contact matrix itself. Under the scenarios where we 162 assumed infectiousness and susceptibility vary with age, we converted measured contact 163 matrices to effective contact matrices by taking the outer product of the estimated age 164 stratified infectiousness profile and susceptibility profile vectors and calculating the 165 eigenvalues of the Hadamard product of the resulting matrix and the contact matrices. 166 To demonstrate the potential impact of reopening schools, we estimated the relative increase 167 ( k ) in reproduction number ( R ) by calculating the ratio of dominant eigenvalues of the 168 effective contact matrix associated with the respective reopening scenario and from the 169 current lockdown period. 9 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 170 We also calculated how R varies from baseline values between 0.7 and 1.0, from official UK 171 estimates of the reproduction number from [23] . 10 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 172 Results 173 Descriptive analysis 174 Adults’ contacts were similar when comparing both periods of national lockdown, this is 175 consistent across all settings and regions. Although children’s contacts at home were similar 176 between the two periods, contacts at school and other locations were consistently higher in 177 lockdown 2 than lockdown 3. Contacts were very similar between lockdowns in all age-group 178 combinations other than those between children (Figure 1). For participants under 18 179 years-old, the mean number of contacts that were also under 18 years-old was between 6.3 180 (3.9 - 9.0, 90% CI) and 16.7 (13.1 - 20.4, 90% CI) across the regions of England during the 181 November Lockdown. Such contacts were highest in South East, South West and Yorkshire 182 and Humber and lowest in London. The mean number of contacts between children reduced 183 to between 1.8 (1.3 - 2.5, 90% CI) and 2.6 (1.9 - 3.3, 90% CI) during the January Lockdown. 184 Estimating susceptibility in children relative to adults using CoMix data. 185 Fitting the R estimates from CoMix data to time-varying R estimates over a period from 27th 186 July to 10th October we estimated susceptibility of 44% (43.5% - 0.45.4%, 95% CI) in 187 children relative to adults (Figure 2, A & C), consistent with profiles ii and iii. When we fitted 188 from the 10th June to 10th October, 2020, we estimated 31% (29.8% - 31.4%, 95% CI) 189 relative susceptibility in children compared to adults (Figure 2, B & D), near the lower range 190 of ONS and Davies et al estimates. We chose to apply the second estimate as the fifth 191 susceptibility profile (v) to represent this lower bound (Table 1) and present fits to other date 192 ranges in the supplementary material (Supplementary Figures, Figure S4). 193 Evaluation of the impact of reopening schools 194 Incorporating estimates of differential susceptibility and infectiousness of children compared 195 with adults (profiles ii - v), full school reopening increased R by a factor of between 1.3 and 196 1.9 times the baseline value across the four profiles used (including 90% CI range) (Figure 11 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 197 3, Table 2). This would result in an increase of R from 0.8 to above 1.0 for these four profiles. 198 Partial school reopening resulted in smaller increases in R from 0.8 to between 0.9 and 1.2. 199 Table 2 Expected resultant R if schools were reopened for different baseline values of R 200 reported as median (90% CI) 201 When we assumed equal infectiousness and susceptibility between all age groups (profile i), 202 reopening schools resulted in more substantial relative changes in R . Full school reopening 203 increased R by a factor of between 2.1 and 2.3 (Figure 3, Table 2), resulting in an increase 204 of R to roughly 1.7-1.9 from a baseline of 0.8 (Table 2). Partial re-opening increased R from 205 0.8 to 1.2-1.3 (Figure 3). We included these estimates for completeness but stress that 206 assuming that children are equally infectious and susceptible as adults is not compatible 207 with results from previous studies or our own estimates (Figure 2). 12 Baseline R Susceptibility/ Infectiousness Attendance 0.7 0.8 0.9 1.0 (Scale factor) 1. Equal Both 1.6 (1.5 - 1.6) 1.8 (1.7 - 1.9) 2.0 (1.9 - 2.1) 2.2 (2.1 - 2.3) Primary 1.1 (1.0 - 1.1) 1.2 (1.2 - 1.3) 1.4 (1.3 - 1.5) 1.5 (1.4 - 1.6) Secondary 1.1 (1.0 - 1.2) 1.3 (1.2 - 1.3) 1.4 (1.3 - 1.5) 1.6 (1.5 - 1.7) 2. Davies et al Both 1.1 (1.0 - 1.1) 1.2 (1.1 - 1.3) 1.4 (1.3 - 1.4) 1.5 (1.4 - 1.6) Primary 0.9 (0.8 - 0.9) 1.0 (0.9 - 1.0) 1.1 (1.1 - 1.2) 1.2 (1.2 - 1.3) Secondary 0.9 (0.8 - 0.9) 1.0 (1.0 - 1.1) 1.1 (1.1 - 1.2) 1.3 (1.2 - 1.3) 3. ONS Both 1.1 (1.1 - 1.2) 1.3 (1.2 - 1.3) 1.4 (1.4 - 1.5) 1.6 (1.5 - 1.7) Primary 0.9 (0.8 - 0.9) 1.0 (1.0 - 1.1) 1.1 (1.1 - 1.2) 1.3 (1.2 - 1.3) Secondary 0.9 (0.9 - 1.0) 1.0 (1.0 - 1.1) 1.2 (1.1 - 1.2) 1.3 (1.3 - 1.4) 4. Viner et al Both 1.3 (1.2 - 1.3) 1.4 (1.4 - 1.5) 1.6 (1.5 - 1.7) 1.8 (1.7 - 1.9) Primary 0.9 (0.9 - 1.0) 1.1 (1.0 - 1.1) 1.2 (1.1 - 1.3) 1.3 (1.3 - 1.4) Secondary 1.0 (0.9 - 1.0) 1.1 (1.1 - 1.2) 1.2 (1.2 - 1.3) 1.4 (1.3 - 1.4) 5. CoMix fit Both 0.9 (0.9 - 1.0) 1.1 (1.0 - 1.1) 1.2 (1.2 - 1.3) 1.4 (1.3 - 1.4) Primary 0.8 (0.8 - 0.9) 0.9 (0.9 - 1.0) 1.1 (1.0 - 1.1) 1.2 (1.1 - 1.2) Secondary 0.8 (0.8 - 0.9) 1.0 (0.9 - 1.0) 1.1 (1.0 - 1.1) 1.2 (1.2 - 1.3) . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 208 Discussion 209 The potential impact of reopening schools on transmission of SARS-CoV-2 is uncertain. 210 Although there have been many attempts to quantify the relative susceptibility and 211 infectiousness of children and adults, these estimates need to be assessed alongside rates 212 of contact to give an indication of the overall risk of transmission in any given setting. We 213 combined social contact data from a large-scale survey in England during two periods of 214 national lockdown, one with schools open and the other with schools closed, with estimates 215 of relative susceptibility of children and adults. We used these data to quantify the potential 216 impact of reopening schools on reproduction number. 217 Whereas adults’ contacts were generally similar between the two periods of lockdown, there 218 was markedly higher contact between children during the November lockdown, when 219 schools were open. We observed the change in contacts at school but also in other contacts 220 outside of the home. Increased contact outside of school and home settings includes 221 contacts in wrap around care, which would be expected to rise, however it could also 222 indicate reduced overall adherence amongst children when attending schools physically. 223 The differences in contacts suggest that reopening all schools is highly likely to increase R 224 above 1.0, from an assumed current value 0.8. Reopening primary or secondary is likely to 225 increase R above 1.0. This would be expected to stop or reverse the fall in cases that has 226 been observed since January 2021 [24] . The risk of cases increasing following the reopening 227 of schools is highly dependent on the current value of R . Although cases of the current 228 dominant variant (B.1.1.7) appeared to be increasing whilst national lockdown was still in 229 place in November [10, 13] , the latest national serology surveys suggest that immunity levels 230 have substantially increased across the UK [24] , resultant from both infections and the 231 national COVID-19 vaccination program. These changes in overall immunity should be 232 reflected in the current estimates of R, but these estimates are lagged due to delays in 233 reporting [25] . 13 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 234 In November, when schools were open, there was substantial variation in contacts between 235 children by region. We have not presented regional estimates of the impact of reopening 236 schools on R due to low numbers of observations between the lower-level age-group 237 aggregation used in the construction of contact matrices, however the variation in mean 238 contacts points to potential geographical variation in the impact of reopening schools, which 239 may be lower in London than other parts of the country. 240 There are a number of important limitations to this work: Contacts in different settings likely 241 contribute differently to transmission, but we assumed all contacts make equal contributions 242 to transmission, as these differences are not well quantified in the context of control 243 measures. If contacts at school are lower risk than those outside of school the impact of 244 reopening schools would be lower. The age-stratified susceptibility profile is likely to change 245 over time as natural immunity is acquired in the population. The profiles we used each reflect 246 a single point in time. Changes in the relative immunity in children would alter the relative 247 impact of school contacts on overall transmission. We assume adult contacts revert to those 248 observed when all schools were open, which is conservative, in reality, particularly for partial 249 reopening scenarios, adult contacts may not fully return to the same levels. Furthermore, 250 there may also be differences in adherence to restrictions between the two lockdowns, 251 unrelated to school closure. However, the change in adults’ contacts between the two 252 periods was relatively small. The proportion of children in school varied over time due to 253 exclusion-based control measures during the autumn, though the proportion attending 254 school remained high during the November lockdown (Supplementary Figures, Figure S3). 255 Contacts of children are reported by parents, which may impact their reliability, particularly in 256 school, where parents are unlikely to witness students’ behaviour, it is unclear whether this 257 would lead to systematic bias in reporting either more or fewer contacts. 258 Our work evaluates the impact of reopening schools on the reproduction number in England, 259 which gives an indication of how transmission may be affected. However, there are other 260 factors that reopening schools may introduce, such as the potential for children’s contact at 14 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 261 school to provide routes of transmission between households, facilitating long chains of 262 transmission that would be otherwise impossible [26] . We are not able to capture these 263 network effects in this analysis, however they may play an important role in the change in 264 epidemiology between school closure and reopening. Second, there is evidence for lower 265 prevalence in primary school than secondary schools [8] . Our framework has not captured 266 these differences suggesting there may be additional factors that reduce the impact of 267 reopening primary schools relative to secondary schools. Furthermore, additional 268 management strategies such as mass testing of school children, may serve to reduce the 269 risk that a contact in a school results in infection beyond those implemented last year. 270 Importantly, with the recent emergence of new variants, particularly B.1.1.7 [27] , the baseline 271 R will depend on proportions of these variants as well as contact patterns. Furthermore, 272 these proportions are likely to change, potentially altering the implications of reopening 273 schools. 274 Our results suggest reopening schools is likely to increase R close to or above 1.0, which 275 would stop the decrease in cases observed in recent months. However, precise estimates 276 rely heavily on the baseline values of R and the profiles of susceptibility, generally assuming 277 lower susceptibility and no greater infectiousness in children relative to adults. 15 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 278 List of abbreviations 279 CI Confidence Interval 280 ONS Office for National Statistics 281 UK United Kingdom 282 Declarations 283 Ethics approval and consent to participate 284 Participation in this opt-in study was voluntary, and all analyses were carried out on 285 anonymised data. The study and method of informed consent was approved by the ethics 286 committee of the London School of Hygiene & Tropical Medicine Reference number 21795. 287 Consent to publish 288 Not applicable 289 Availability of data and materials 290 Although it is not possible to share the contact survey data used to generate the contact 291 matrices used in this analysis. The analysis code and contact matrices used are available in 292 an online repository here: https://github.com/jdmunday/CoMix_schools_reopening 293 Competing interests 294 None 295 Funding 296 CoMix is funded by the EU Horizon 2020 Research and Innovations Programme - project 297 EpiPose (Epidemic Intelligence to Minimize COVID-19’s Public Health, Societal and 298 Economical Impact, No 101003688) and by the Medical Research Council (Understanding 299 the dynamics and drivers of the COVID-2019 epidemic using real-time outbreak analytics 300 MC_PC 19065). 16 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 301 The following funding sources are acknowledged as providing funding for the named 302 authors. Elrha R2HC/UK FCDO/Wellcome Trust/This research was partly funded by the 303 National Institute for Health Research (NIHR) using UK aid from the UK Government to 304 support global health research. The views expressed in this publication are those of the 305 author(s) and not necessarily those of the NIHR or the UK Department of Health and Social 306 Care (KvZ). This project has received funding from the European Union's Horizon 2020 307 research and innovation programme - project EpiPose (101003688: AG, WJE). 308 FCDO/Wellcome Trust (Epidemic Preparedness Coronavirus research programme 309 221303/Z/20/Z: KvZ). This research was partly funded by the Global Challenges Research 310 Fund (GCRF) project 'RECAP' managed through RCUK and ESRC (ES/P010873/1: CIJ). 311 NIHR (PR-OD-1017-20002: WJE). UK MRC (MC_PC_19065 - Covid 19: Understanding the 312 dynamics and drivers of the COVID-19 epidemic using real-time outbreak analytics: WJE). 313 Wellcome Trust (210758/Z/18/Z: JDM, SFunk). Department of Health and Social Care 314 School Infection Study (PHSEZU7510) (JDM, WJE). No funding (KW). 315 The following funding sources are acknowledged as providing funding for the working group 316 authors. BBSRC LIDP (BB/M009513/1: DS). This research was partly funded by the Bill & 317 Melinda Gates Foundation (INV-001754: MQ; INV-003174: KP, MJ, YL; INV-016832: SRP; 318 NTD Modelling Consortium OPP1184344: CABP, GFM; OPP1139859: BJQ; OPP1183986: 319 ESN; OPP1191821: MA). BMGF (INV-016832; OPP1157270: KA). EDCTP2 320 (RIA2020EF-2983-CSIGN: HPG). ERC Starting Grant (#757699: MQ). This project has 321 received funding from the European Union's Horizon 2020 research and innovation 322 programme - project EpiPose (101003688: KP, MJ, PK, RCB, YL). FCDO/Wellcome Trust 323 (Epidemic Preparedness Coronavirus research programme 221303/Z/20/Z: CABP). This 324 research was partly funded by the Global Challenges Research Fund (GCRF) project 325 'RECAP' managed through RCUK and ESRC (ES/P010873/1: TJ). HDR UK 326 (MR/S003975/1: RME). HPRU (This research was partly funded by the National Institute for 327 Health Research (NIHR) using UK aid from the UK Government to support global health 328 research. The views expressed in this publication are those of the author(s) and not 17 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 329 necessarily those of the NIHR or the UK Department of Health and Social Care200908: 330 NIB). MRC (MR/N013638/1: NRW). Nakajima Foundation (AE). NIHR (16/136/46: BJQ; 331 16/137/109: BJQ, FYS, MJ, YL; Health Protection Research Unit for Modelling Methodology 332 HPRU-2012-10096: TJ; NIHR200908: AJK, RME; NIHR200929: FGS, MJ, NGD; 333 PR-OD-1017-20002: AR). Royal Society (Dorothy Hodgkin Fellowship: RL; RP\EA\180004: 334 PK). UK DHSC/UK Aid/NIHR (PR-OD-1017-20001: HPG). UK MRC (MC_PC_19065 - Covid 335 19: Understanding the dynamics and drivers of the COVID-19 epidemic using real-time 336 outbreak analytics: NGD, RME, SC, TJ, YL; MR/P014658/1: GMK). Authors of this research 337 receive funding from UK Public Health Rapid Support Team funded by the United Kingdom 338 Department of Health and Social Care (TJ). UKRI Research England (NGD). Wellcome Trust 339 (206250/Z/17/Z: AJK, TWR; 206471/Z/17/Z: OJB; 208812/Z/17/Z: SC, SFlasche; 340 210758/Z/18/Z: JH, KS, SA, SRM). No funding (AMF, AS, CJVA, DCT, JW, KEA, YWDC). 341 Authors contributions 342 JDM, CIJ, WJE conceived of and planned the analysis; JDM and CIJ performed the main 343 analysis with input from WEJ and SF; SF provided estimates of time-varying reproduction 344 number; CIJ, KvZ, and WEJ designed the CoMix contact survey, CIJ, AG, KW, and KvZ 345 cleaned and managed the contact survey data; All authors wrote and reviewed the 346 manuscript. The CMMID COVID-19 Working Group provided discussion and comments. 347 Acknowledgements 348 The authors wish to thank Dr Thomas House for his support with interpretation of the ONS 349 susceptibility estimates. We also thank members of SPI-M for their useful discussion which 350 helped shape the final version of this work. We would like to thank the team at Ipsos, who 351 have been excellent in running the survey, collecting the data and allowing for the CoMix 352 study to be implemented rapidly. Finally, we thank Katie Collis for proof reading and 353 excellent discussions. 18 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 354 The following authors were part of the Centre for Mathematical Modelling of Infectious Disease 355 COVID-19 Working Group. Each contributed in processing, cleaning and interpretation of data, 356 interpreted findings, contributed to the manuscript, and approved the work for publication: Yang Liu, 357 Joel Hellewell, Nicholas G. Davies, C Julian Villabona-Arenas, Rosalind M Eggo, Akira Endo, Nikos I 358 Bosse, Hamish P Gibbs, Carl A B Pearson, Fiona Yueqian Sun, Mark Jit, Kathleen O'Reilly, Yalda 359 Jafari, Katherine E. Atkins, Naomi R Waterlow, Alicia Rosello, Yung-Wai Desmond Chan, Anna M 360 Foss, Billy J Quilty, Timothy W Russell, Stefan Flasche, Simon R Procter, William Waites, Rosanna C 361 Barnard, Adam J Kucharski, Thibaut Jombart, Graham Medley, Rachel Lowe, Fabienne Krauer, 362 Damien C Tully, Kiesha Prem, Jiayao Lei, Oliver Brady, Frank G Sandmann, Sophie R Meakin, Kaja 363 Abbas, Gwenan M Knight, Matthew Quaife, Mihaly Koltai, Sam Abbott, Samuel Clifford. 364 Additional Files 365 Supplementary Figures 19 . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint / 366 Figure Captions 367 Figure 1. Contacts in the national lockdown periods in November (Lockdown 2) and 368 January (Lockdown 3) . A) the distribution of the number of reported contacts in Home, 369 Work, School and Other locations for Adult (> 17 years old) and Child (<= 17 years old) 370 participants. B) Mean contacts reported between Children and Adults in each region of 371 England. Error bars show the 90% CI (bootstrapped, 1000 samples). 372 Figure 2: R estimates using CoMix data fit to time-varying reproduction number 373 estimates based on the time series of cases [21] . Transformed likelihood for different 374 combinations of relative susceptibility and infectiousness based on data from A) August to 375 October and B) June to October and the corresponding R estimates in C) and D) 376 respectively. 90% CI of the estimates are shown by Grey rectangles for CoMix and the red 377 ribbon for the time-varying reproduction number estimates from case data, red bars show 378 their mean for the CoMix survey periods. Grey shaded areas indicate fitted periods. 379 Figure 3: The impact of reopening schools on the reproduction number. A) the relative 380 increase in R (the ratio of dominant eigenvalues between contact matrices for each 381 reopening scenario and that for current contact patterns) under different estimates of the age 382 profile of susceptibility and infectiousness. B) The estimated R after reopening schools 383 (points, 90% CI bars) from baseline R of 0.7, 0.8, 0.9 and 1.0 (vertical line). Dashed vertical 384 lines show R = 1.0. 20 . 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(which was not certified by peer review) The copyright holder for this preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 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● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Home Work School Other Adult ParticipantChild Participant 1 10 100 1000 1 10 100 1000 1 10 100 1000 1 10 100 1000 1 10 100 1000 1 10 100 1000 No. Contacts Participants A ●● ●● ●● ●●● ●●● ●● ● ●●● ● ●● ●● ● ● ●● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ●● ●● Adult Contact Child Contact Adult ParticipantChild Participant East Midlands East of England Greater London North East North West South East South West West Midlands Y orkshire and The Humber East Midlands East of England Greater London North East North West South East South West West Midlands Y orkshire and The Humber 5 10 15 20 5 10 15 20 Region Mean Contacts Period ● ●Lockdown 2 Lockdown 3 B . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint ● 0.25 0.50 0.75 1.00 1.25 0.25 0.50 0.75 1.00 1.25 Relative Susceptibility Relative Infectiousness Study: ● 1. Equal 2. Davies et al 3. ONS 4. Viner et al 0.5 1.0 1.5 2.0 exp(−ll/1000) A ● 0.25 0.50 0.75 1.00 1.25 0.25 0.50 0.75 1.00 1.25 Relative Susceptibility Relative Infectiousness Study: ● 1. Equal 2. Davies et al 3. ONS 4. Viner et al 0.25 0.50 0.75 1.00 exp(−ll/1000) B 0.4 0.8 1.2 1.6 2.0 Aug Sep Oct Nov Dec Jan date R estimate C 0.4 0.8 1.2 1.6 2.0 Jun Jul Aug Sep Oct Nov Dec Jan date R estimate D . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint Secondary Primary Both 1.0 1.5 2.0 2.5 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Relative increase in R Study: 1. Equal 2. Davies et al 3. ONS 4. Viner et al 5. CoMix fit A ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Baseline R = 1 Baseline R = 0.9 Baseline R = 0.8 Baseline R = 0.7 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Primary Secondary Both Primary Secondary Both Primary Secondary Both Primary Secondary Both R B . CC-BY 4.0 International licenseIt 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 preprintthis version posted March 8, 2021. ; https://doi.org/10.1101/2021.03.06.21252964doi: medRxiv preprint