{"paper_id":"01fc0f3d-d063-4e55-aba6-4cca2ebeb310","body_text":"Within and between classroom transmission patterns of 1 \nseasonal influenza among primary school students in 2 \nMatsumoto city, Japan 3 \nAkira Endo1,2,3,4,*, Mitsuo Uchida5, Naoki Hayashi6,7, Yang Liu1,2, Katherine E. Atkins1,2,8, Adam J. 4 \nKucharski1,2, Sebastian Funk1,2 5 \n1. Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical 6 \nMedicine, London, WC1E 7HT, United Kingdom 7 \n2. The Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & 8 \nTropical Medicine, WC1E 7HT, United Kingdom 9 \n3. The Alan Turing Institute, London, NW1 2DB, United Kingdom 10 \n4. School of Tropical Medicine and Global Health, Nagasaki University, Nagasaki, 852-8523, Japan 11 \n5. Graduate School of Medicine, Gunma University, Gunma, 371-8511, Japan 12 \n6. Simulation & Mining Division, NTT DATA Mathematical Systems Inc., Tokyo, 160–0016, Japan 13 \n7. Department of Mathematical and Computing Science, School of Computing, Tokyo Institute of 14 \nTechnology, Tokyo, 152–8552, Japan 15 \n8. Centre for Global Health Research, Usher Institute, University of Edinburgh, Edinburgh, EH16 16 \n4UX, United Kingdom 17 \n* Correspondence to: akira.endo@lshtm.ac.uk 18 \nSignificance 19 \nEmpirical evidence on detailed transmission patterns of influenza among students within and between 20 \nclasses and grades and how they are shaped by school population structure (e.g. class and school 21 \nsizes) has been limited to date. We analysed a detailed dataset of seasonal influenza incidence in 29 22 \nprimary schools in Japan and found that the reproduction number at school did not show any clear 23 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n\nassociation with the size or the number of classes. Our findings suggest that the interventions that only 24 \nfocus on reducing the number of students in class at any moment in time (e.g. reduced class sizes and 25 \nstaggered attendance) may not be as effective as measures that aim to reduce within-class risk (e.g. 26 \nmask-wearing and vaccines).  27 \nAbstract 28 \nSchools play a central role in the transmission of many respiratory infections. Heterogeneous social 29 \ncontact patterns associated with the social structures of schools (i.e. classes/grades) are likely to 30 \ninfluence the within-school transmission dynamics, but data-driven evidence on fine-scale 31 \ntransmission patterns between students has been limited. Using a mathematical model, we analysed a 32 \nlarge-scale dataset of seasonal influenza outbreaks in Matsumoto city, Japan to infer social 33 \ninteractions within and between classes/grades from observed transmission patterns. While the 34 \nrelative contribution of within-class and within-grade transmissions to the reproduction number varied 35 \nwith the number of classes per grade, the overall within-school reproduction number, which 36 \ndetermines the initial growth of cases and the risk of sustained transmission, was only minimally 37 \nassociated with class sizes and the number of classes per grade. This finding suggests that 38 \ninterventions that change the size and number of classes, e.g. splitting classes and staggered 39 \nattendance, may have limited effect on the control of school outbreaks. We also found that 40 \nvaccination and mask-wearing of students were associated with reduced susceptibility (vaccination 41 \nand mask-wearing) and infectiousness (mask-wearing) and hand washing with increased 42 \nsusceptibility. Our results show how analysis of fine-grained transmission patterns between students 43 \ncan improve understanding of within-school disease dynamics and provide insights into the relative 44 \nimpact of different approaches to outbreak control. 45 \nBackground 46 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\n Influenza virus and other directly transmitted pathogens typically spread over social contact 47 \nnetworks involving frequent conversational or physical contacts (1–4). There is evidence that schools 48 \nare important social environments that can facilitate the transmission of influenza via close contacts 49 \nbetween students (5–9). Previous studies have collected contact data between students using 50 \nquestionnaires and wearable sensor devices and found strong assortativity of contact rates within 51 \nclasses and grades (10–14), which is likely relevant to the within-school transmission dynamics of 52 \nrespiratory infections and the effectiveness of school-based interventions. However, such insights 53 \nfrom contact data also need to be validated with real-world outbreak data because contacts as 54 \nmeasured in those studies may not necessarily be fully representative of the types of contacts that lead 55 \nto transmission (e.g. with regards to proximity and duration). In this light, the differential transmission 56 \nrates of influenza associated with classes and grades have also been estimated from empirical 57 \noutbreak data in a few studies (6, 15, 16). However, those studies are limited to the analysis of only 58 \none or two schools and included a relatively small number of cases (< 300). Therefore, robust findings 59 \nacross schools with different structures that capture the full range of heterogeneity in within-school 60 \ntransmission dynamics have remained a crucial knowledge gap.  61 \nUnderstanding how school population structures (e.g. class and school sizes) shape 62 \ntransmission dynamics is key to making predictions about outbreak dynamics and interventions in 63 \nthese settings. Modelling studies of school outbreaks often require a choice between the ‘density-64 \ndependent mixing’ and ‘frequency-dependent mixing’ assumptions (17). The density-dependent 65 \nmixing assumes that the transmission rate between a pair of students is constant regardless of the 66 \nclass/school sizes, while the frequency-dependent mixing assumes an inverse proportionality between 67 \nthem. As a result, the reproduction number is expected to increase with class/school size with the 68 \ndensity-dependent mixing assumption and remain stable with the frequency-dependent mixing 69 \nassumption. Whether the transmission is best characterised by the density-dependent mixing, 70 \nfrequency-dependent mixing or any other alternative assumption may vary between different modes 71 \nof transmission and exposure settings (18–22). However, choices between the assumptions made by 72 \nexisting studies of school outbreaks vary widely and are not based on a clear empirical concensus (9, 73 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\n23–26). These makes it challenging to interpret simulation studies evaluating school-based 74 \ninterventions (e.g. reduced class sizes) because the estimated effect sizes can heavily rely on the 75 \nassumed mixing patterns (27–31). 76 \nTo fill this knowledge gap in heterogeneous transmission dynamics at school, we applied a 77 \nmathematical model of influenza virus transmission to a large-scale dataset from the 2014-15 season 78 \nin Matsumoto city, Japan, which included diagnosed influenza reports among 10,923 primary school 79 \nstudents and their household members. The model accounted for within-school transmissions as well 80 \nas introductions to and from households and risk from the general community, which constitute key 81 \nsocial layers of transmission (32–34). Using this model, we estimated fine-scale heterogeneous 82 \ntransmission patterns among students within and between classes and grades, as well as determinants 83 \nof transmission rates including school structures and precautionary measures. 84 \nResults 85 \nWe analysed citywide survey data of 10,923 primary school students (5–12 years old) in 86 \nMatsumoto city, Japan in 2014/15, which included 2,548 diagnosed influenza episodes among 87 \nstudents (Figure 1A). The dataset was obtained from 29 schools with a range of class structures (sizes 88 \nand the number of classes per grade), allowing for detailed analysis of within and between class 89 \ntransmission patterns (Figure 1B). The attack ratio (i.e. the cumulative proportion diseased) in each 90 \nschool (excluding three distinctively small schools with fewer than 15 students per class) showed 91 \nweak to null negative correlations with the mean class size and the mean number of classes per grade 92 \n(Figure 1C). The onset dates of students showed a temporal clustering pattern associated with school 93 \nstructure (Figure 1D). When the students were partitioned into different levels of groupings (i.e. by 94 \nclass, grade, school and overall), the deviation of onset dates from the within-group mean tended to be 95 \nsmaller with finer groupings.  96 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\n 97 \nFigure 1. Transmission dynamics of seasonal influenza in primary schools in Matsumoto city, Japan and estimated effects of 98 \ninterventions for SARS-CoV-2. (A) Epidemic curve of seasonal influenza by illness onset in primary schools in Matsumoto 99 \ncity, 2014/15. Colours represent different schools. Month names denote the 1st day of the month. (B) Scatterplot of the class 100 \nsizes and the number of classes per grade in the dataset. Each dot represents a class in the dataset. Dots are jittered along the 101 \nx-axis. Three schools had classes of fewer than 15 students (denoted by dotted horizontal line) and were excluded from the 102 \nmodel fitting. (C) The scatterplots of the school attack ratio (%) against the mean class size and the mean number of classes 103 \nper grade. The correlation indices (r) and the 95% confidence intervals are also shown. (D) Temporal clustering patterns of 104 \nstudents’ onset dates with different levels of groupings reproduced from the school transmission model. The distributions of 105 \nthe deviance of each student’s onset from the group mean are displayed at overall, school, grade and class levels. The 106 \nstandard deviation (SD) of each distribution is also shown.  107 \n 108 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nThe temporal clustering shown in Figure 1D supports the hypothesis that the transmission is 109 \nmore likely within-class, followed by within-grade and within-school. We explored this further by 110 \nestimating reproduction numbers within school. Using a mathematical model that accounts for 111 \ndifferent levels of interaction within and between classrooms and grades as well as introductions from 112 \nhouseholds and community, we estimated the within-school effective reproduction number RS of 113 \nseasonal influenza in primary schools along with the breakdown of transmission risks associated with 114 \nclass/grade relationships (Figure 2). The relationship between any pair of students in the same school 115 \nwas classified as either “classmates”, “grademates” (in the same grade but not classmates) or 116 \n“schoolmates” (not in the same grade). The estimated RS was broken down as a sum of the 117 \ncontributions from these students, where the class size (n) and the number of classes per grade (m) 118 \nwere assumed to affect the risk of transmission. The reconstructed overall RS in a 6-year primary 119 \nschool was estimated to be around 0.7–0.9 and was not significantly associated with n or m (Figure 120 \n2A). Namely, an infected student was suggested to generate a similar number of secondary cases 121 \nirrespective of the class structure; although our estimates of RS were about 15% smaller for the class 122 \nsize of 40 than 201, the posterior p-value did not suggest a statistical significance (p ~ 0.15 or above). 123 \nAs RS was likely below 1 across class structures, school outbreaks may not have been sustained 124 \nwithout continuous introductions from households and community. Transmission to classmates 125 \naccounted for about two-thirds of RS when each grade has only one class and was partially replaced 126 \nby transmission to grademates as the number of classes per grade increases, while the sum of within-127 \ngrade transmission (i.e. transmission to either classmates or grademates) remained stable (Figures 2B 128 \nand 2C). Around 20–30% of overall RS was explained by transmission to schoolmates throughout. We 129 \nalso obtained qualitatively similar results throughout our sensitivity analysis (Figure S3). In a 6-year 130 \nschool with 3 classes of 30 students, the risk of transmission was estimated to be 1.8% (95% credible 131 \ninterval (CrI): 1.4–2.5) from a given infected classmate of the same sex, 1.6% (1.2–2.1) the opposite 132 \nsex, 0.13% (0.08–0.19) from a given infected grademate and 0.040% (0.029–0.055) from a given 133 \n \n1 For example, the estimated relative reduction was 17% (95% credible interval: -16%–40%) for m = 3. \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\ninfected schoolmate (Table S2). The cumulative risk of infection from the community was estimated 134 \nto be 2.2% (1.7–2.7) over the season. 135 \n 136 \nFigure 2. The estimated within-school transmission patterns of seasonal influenza among primary school students in 137 \nMatsumoto city, Japan. (A) The overall school reproduction number (RS) under different class structures. Whiskers represent 138 \nthe 95% credible intervals (B) The breakdown of RS corresponding to each type of within-school relationships. Whiskers 139 \nrepresent the 95% credible intervals. Bottom panels: stacked graph of RS based on the median estimates.  140 \n 141 \nWe incorporated a log-linear regression (35) into the above estimation of RS to account for 142 \ncovariates that may affect the susceptibility or infectiousness of students. The results suggested that 143 \nvaccines were associated with reduced susceptibility while mask wearing was associated with both 144 \nreduced susceptibility and infectiousness (Table 1). Conversely, hand washing was associated with 145 \nincreased susceptibility. Reduced chance of transmission during the winter break (27 December 146 \n2014–7 January 2015) was captured as a 75% estimated decline in the infectiousness of cases whose 147 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nonset dates were during the break. School grade, which serves as a proxy of students’ age, did not 148 \nshow a significant association with either susceptibility (relative value 1.10; CrI: 0.88–1.38) or 149 \ninfectiousness (relative value 0.78; CrI: 0.59–1.04). 150 \nTable 1. Covariates and effects estimated in the log-linear regression 151 \nCovariate Frequency in data Relative susceptibility Relative infectiousness \nSchool grade (1 year \nincrease) \n— 1.10 (0.88–1.38) 0.78 (0.59–1.04) \nVaccine 47.7% 0.88* (0.81–0.96) 0.97 (0.82–1.18) \nMask wearing 51.4% 0.77* (0.71–0.85) 0.65* (0.55–0.78) \nHand washing 80.1% 1.54* (1.36–1.76) 1.25 (0.96–1.65) \nOnset in winter break 5.9% (of cases) — 0.25* (0.15–0.39) \nValues are median estimates and 95% credible intervals. 152 \n* Estimates with 95% credible intervals not crossing 1. 153 \n 154 \nWe estimated the breakdown of the source of infection for student cases based on the 155 \nconditional probability predicted by the model and parameter estimates. The epidemic curve stratified 156 \nby the estimated source of infection suggested that within-school transmission accounted for the 157 \nmajority of student cases while schools were open and that the within-household transmission was 158 \nresponsible for most of the cases reported during the winter break and shortly after (Figure 3A). The 159 \naggregated relative contribution suggested that 54.6% (CrI: 53.5–55.7), 38.7% (CrI: 37.9–39.5) and 160 \n6.7% (CrI: 5.9–7.5) of the student cases were acquired from school, household and community, 161 \nrespectively (Figure 3B).We estimated the possible relative effects of interventions altering the school 162 \npopulation structure on the school reproduction number RS. We assumed that the estimated relative 163 \ncontributions of class/grade relationship to the transmission risk reflect the contact patterns between 164 \nstudents which may also be relevant to  the dynamics of another influenza outbreak at school (and 165 \npotentially those of directly-transmitted disease outbreaks in general) and that the responses to 166 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\ninterventions can be captured by the estimated relationship between RS and the changes in the 167 \nvariables n and m according to each intervention (Table 2). Specifically, in the ‘split class’ scenario, 168 \neach class was assumed to be split in half and taught simultaneously in separate classrooms, while in 169 \nthe ‘staggered attendance’ scenarios only half of the students attend school at the same time by 170 \nintroducing two different time schedules, e.g. morning and evening classes. The estimated relative 171 \neffects of school-based interventions on RS in a hypothetical setting of 6-year school with 2 classes 172 \nper grade (40 students each) showed that splitting classes or staggered attendance alone was unlikely 173 \nto reduce RS (or may even be counteractive) (Figure 1D), which is consistent with the aforementioned 174 \nestimates of RS minimally associated with class sizes and the number of classes. By reducing 175 \ninteractions between students from different classes (so-called ‘bubbling’ or ‘cohorting’) by 90%, RS 176 \ncould be reduced by up to around 20%. Combining split classes/staggered attendance with reduced 177 \ninteractions outside classes did not suggest incremental benefit in reducing RS. Given that these 178 \ninterventions typically require additional resources including staff and classrooms, the overall benefit 179 \nto changing class structures for influenza control may be limited. 180 \nTable 2. Summary of interventions that changes the size/number of classes 181 \nInterventions Class size \n(n) \n# classes per \ngrade (m) \nAssumption \nBaseline (‘no change’) 40 2 Students contact within and between \nclasses and grades proportionally to the \nestimated transmission patterns in \nFigure 2. \nSplit class 20 4 Each class is split into two and taught \nsimultaneously in separate classrooms. \nStudents may contact each other \nbetween classes. \nStaggered attendance \n(within class) \n20 2 Each class is split into two and taught \nseparately in two different time slots \n(e.g. morning and evening). Students in \ndifferent time slots do not contact each \nother and thus RS is calculated for \nstudents in one slot. \nStaggered attendance \n(between class) \n40 1 Each class is allocated (as a whole) to \neither of the two different time slots and \ntaught separately. Students in different \ntime slots do not contact each other and \nthus RS is calculated for students in one \nslot. \n 182 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\n 183 \nFigure 3. Reconstruction of students’ source of infection. (A) Epidemic curve stratified by the reconstructed source of 184 \ninfection. The conditional probability of infection from different sources was computed for each student and aggregated by 185 \ndate of illness onset. (B) Breakdown of the reconstructed source of infection. For each student, the source of infection was 186 \nsampled based on the conditional probability to provide the proportion of students infected from each source. Bars denote 187 \nposterior median and whiskers 95% credible intervals. (C) Expected relative changes in the school reproduction number 188 \nunder school-based interventions changing the structure of classes. Dots represent medians and whiskers 95% credible 189 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nintervals. Reduced outside-class transmissions (i.e. from grademates or schoolmates) were also considered (50% reduction: 190 \nblue; 90% reduction: green). 191 \n 192 \nDiscussion 193 \n We used a mathematical model that stratified transmission within and between classes/grades 194 \nto understand the dynamics of influenza transmission among primary school students. The inferred 195 \ntransmission dynamics of seasonal influenza in Matsumoto city, Japan, 2014-15 season suggested that 196 \nthe within-school reproduction number RS stayed relatively constant regardless of the size or the 197 \nnumber of classes (suggesting ‘frequency-dependent mixing’ (36)), in contrast to common modelling 198 \nassumptions. The estimated RS of 0.8–0.9, more than half of which was attributable to within-class 199 \ntransmissions, is consistent with a previous study in the United States (15). This value is also in line 200 \nwith the reported R0 of 1.2–1.3 for seasonal influenza (37)  because our previous study estimated that 201 \nthe students in this dataset had infected 0.3–0.4 household members on average during this 2014-15 202 \nseason (note that R0 corresponds to the overall number of secondary transmissions per student, 203 \nincluding at school and household) (18). The value of RS below 1 suggests that an outbreak cannot 204 \nsustain itself within a school alone and that interactions through importing and exporting infections 205 \nbetween households and the general community is likely to play a crucial role in the overall 206 \ntransmission dynamics. We estimated that school, household and community accounted for 55%, 39% 207 \nand 7% of the source of infection for student cases, respectively. The attributable proportion was 208 \nlower for schools and higher for households than the previous study (15), which may be explained by 209 \ndifferent scales of outbreaks in schools and households. In the Matsumoto city dataset, the overall 210 \nattack ratio at school was lower (19%), students had larger households (average size 5.5) and there 211 \nwere more household cases than student cases (3996 vs 2548), as opposed to 35%, size of 3.4 and 141 212 \nvs 129 cases in (15). 213 \nThe estimated breakdown of RS revealed a number of notable patterns. As the number of 214 \nclasses per grade increased, the contribution of within-class transmission risk declined and was 215 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nreplaced by within-grade transmission. Combined with the almost constant overall RS, this might 216 \nindicate that contact behaviour between students that contributed to transmission was only minimally 217 \naffected by the student population density. That is, students may have had a certain number of ‘close 218 \nfriends’ with whom they had more intimate interactions that could facilitate transmission. In a school 219 \nwith more classes per grade, some of such friendship may have come from grademates instead of 220 \nclassmates, but the total number of close friends may have remained similar. This interpretation is in 221 \nline with published evidence of influenza spreading predominantly in close proximity (38) and is 222 \nlikely to influence the expected effect of interventions not only for influenza but also other respiratory 223 \ninfectious diseases including COVID-19, which share similar routes and range of transmission (39, 224 \n40). Further disease-specific studies could elucidate the generalisability of these associations in more 225 \ndetail. 226 \nOur results suggested that interventions such as reducing class sizes or the number of students 227 \npresent (staggered attendance) may not be effective in constrast to what would be expected under the 228 \ndensity-dependent mixing assumption (27–31). If interventions altering class structures are not 229 \naccompanied by additional precaution measures and students try to resume their ‘natural’ behaviours 230 \n(i.e. the same contact patterns as those in school with the resulting class structures) through so-called 231 \nsocial contact ‘rewiring’ (41), the effect of such interventions can diminish or even reverse. For 232 \nexample, if other classes are absent due to staggered attendance, students may increase their 233 \ninteractions with classmates instead of their previous close friends in other classes. Our results are 234 \nalso consistent with a recent study of interventions against COVID-19 in US schools that did not find 235 \na significant risk reduction associated with reducing class sizes (42). Given the additional logistical 236 \nresources required to implement these interventions, we propose that reducing the class sizes or the 237 \nnumber of attending students should be considered only if they enable effective implementation of 238 \nprecaution measures such as physical distancing, environmental cleaning or forming social bubbles. 239 \nUsing a log-linear regression analysis combined with a transmission model, we identified 240 \nseveral precautionary measures associated with the susceptibility or infectiousness of students. 241 \nVaccines were associated with reduced susceptibility and masks with a reduction in both 242 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nsusceptibility and infectiousness. Influenza vaccine effectiveness in the 2014-15 season was suggested 243 \nto be particularly low in Japan due to vaccine mismatch and estimated to be 26% (95% CrI: 7–41%) 244 \nfor primary-school-age children (6–12 years old) (43). Our estimate of a relative susceptibility of 0.88 245 \n(CrI: 0.81–0.96) in vaccinated students, which translates into a vaccine effectiveness of 12% (CrI: 9–246 \n19%), is broadly consistent with this prior estimate. While existing evidence for the effectiveness of 247 \nmask policies for the control of respiratory infections is still limited (44, 45), our estimates of small 248 \nprotective effects acting on the relative susceptibility (0.77; CrI: 0.71–0.85) and infectiousness (0.65; 249 \nCrI: 0.55–0.78) lie within a plausible range based on evidence available to date (44, 46–48). Increased 250 \nsusceptibility associated with hand washing in our analysis, however, does not align with existing 251 \nfindings (49, 50). Although the underlying cause for this is unclear, the original report on the 252 \nMatsumoto city dataset also reported a higher odds ratio (1.4; CrI: 1.27–1.64; unadjusted for 253 \ndifferential exposure) and attributed it to the possible congregation of students washing hands in 254 \ncommunal settings at school (51). 255 \nSeveral limitations of this study should be noted. First, the transmission patterns within 256 \nschools were estimated from a single dataset of seasonal influenza in primary schools (aged 5-12 257 \nyears) in Matsumoto city, Japan, and it is unclear to what extent the results can be extrapolated to 258 \nother settings, e.g. secondary schools or schools in other countries. Some features of our results may 259 \nstill be relevant to transmission dynamics in different types of schools if they reflect general social 260 \ncontact behaviours of schoolchildren; however, the relative contribution of within-class/within-grade 261 \ninteractions may become smaller for older students (52). The data points used in the inference mostly 262 \nconsisted of classes of size 20-40 (those with a size smaller than 10 were excluded as they might be 263 \noperated differently) and most schools had no more than 5 classes per grade. The scope of the 264 \nestimated effect of the school-based interventions was also limited to within this range for internal 265 \nconsistency and thus may not necessarily be applicable to class structures outside this range (e.g. 266 \nsplitting a class of 20 students into two). Extrapolating the estimated transmission patterns to other 267 \nrespiratory infectious diseases also warrants caution because their epidemiological characteristics may 268 \nnot be identical, although we believe that such an approach may still be useful for diseases sharing 269 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nsimilar modes of transmission. Modelling studies using social contact data often assume 270 \nproportionality between contacts and the transmission of directly-transmitted diseases (e.g. measles, 271 \ninfluenza and COVID-19) and have many successful applications (7, 33, 53–57). Using the estimated 272 \ntransmission patterns of influenza as a proxy for other diseases essentially rests on the same 273 \nassumption, which nonetheless has limitations and should eventually be validated by disease-specific 274 \nstudies. Second, some aspect of the outbreaks may have been missing from the dataset. Since the 275 \nillness data of teachers were not available, they were not considered throughout the analysis. 276 \nHowever, their role in seasonal influenza transmission may have been minor given a large number of 277 \nstudent cases and the smaller risk in adults (58, 59). Although our student incidence data likely had 278 \ngood case ascertainment given encouraged medical attendance and confirmation by rapid diagnostic 279 \nkits (18), a certain proportion of infections (e.g. asymptomatic or very mild) may have been missing. 280 \nWe believe that students feeling unwell due to influenza mostly attended medical institutions and 281 \nreceived a test as it was encouraged by schools. Nonetheless, it should be noted that this could have 282 \nbeen a source of bias in the estimated transmission patterns. Students with very mild symptoms (e.g. 283 \nonly slight sore throat) may visit a medical institution only if they know of other classmates also 284 \ndiagnosed with influenza. If such cases were common, the contribution of within-class transmissions 285 \nin our results might have been an overestimate. Third, since the dataset was obtained from an 286 \nobservational study, the identified determinants of transmission may not be causal and should not be 287 \nviewed as conclusive evidence. The results of our log-linear regression were mostly in line with 288 \nexisting findings, however, our dataset may still be biased due to unmeasured confounders such as 289 \nhealth awareness. Our estimates of the relative effect of school-based interventions were based on the 290 \nassumption that students’ behaviours follow the fixed patterns according to the school structure even 291 \nunder interventions. That is, when the class size or the number of classes were changed by an 292 \nintervention, students were assumed to change their behaviour according to the new school structure 293 \n(as if it were the original structure) by e.g. rewiring close contacts in a timely manner. This is a 294 \nhypothetical expectation that may not exactly be observed in actual interventional settings; for 295 \nexample, it may take time for students to resume close contacts after the class is split, which can bring 296 \nRS lower than our prediction at least temporarily. We have also neglected the possible effect of the 297 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\ninterventions on the transmission outside the school. The actual effects of these interventions should 298 \nideally be validated by empirical data, as in (42). 299 \nOur analysis disentangled the transmission dynamics of seasonal influenza among primary 300 \nschool students and highlighted the relative importance of within-class and within-grade transmission. 301 \nSince class and school sizes were minimally associated with the within-school reproduction number, 302 \nschool-based interventions that change classroom structures, e.g. reduced class sizes and staggered 303 \nattendance, may have limited effectiveness. Empirical evidence on fine-grained heterogeneous 304 \ntransmission patterns at school as was obtained from this study would inform public health planning 305 \nfor future outbreaks of influenza and, potentially, other directly transmitted infectious diseases that 306 \nthrive in schools. 307 \nMaterials and methods 308 \nData 309 \nWe analysed a citywide school-based influenza survey data from the 2014/15 season. The 310 \nsurvey was conducted in Matsumoto city (population size: 242,000 (60)), Japan, enrolling 13,217 311 \nstudents from all 29 public primary schools in the city. During the survey period (from October 2014 312 \nto February 2015), the participants were asked to fill out a questionnaire when they were back from 313 \nthe suspension of attendance due to diagnosed influenza (prospective survey). In March, the 314 \nparticipants were asked to respond to another survey on their experience during the study period, 315 \nregardless of whether they had contracted influenza (retrospective survey). A total of 2,548 diagnosed 316 \ninfluenza episodes were reported in the prospective survey, which accounted for 96% of the cases 317 \nofficially recognised by the schools during the study period. Primary schools in Japan often requested 318 \nstudents suspected of influenza to seek diagnosis at a medical institution. All students reporting an 319 \ninfluenza episode in the prospective survey answered that they had received a diagnosis and at least 320 \n95% of them were noticed of type A influenza (indicating that they were lab-confirmed). In the 321 \nretrospective survey, 11,390 (86%) participants responded, among which 8,375 reported that they did 322 \nnot have influenza during the study period. 323 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nWe combined those who responded to the prospective survey (“case group”) and those who 324 \nreported no influenza experience in the retrospective survey (“control group”) and obtained a dataset 325 \nof 10,923 students. Of those, 71 students from 3 schools with less than 15 students per grade were 326 \nexcluded because they may have different schooling patterns from other schools (e.g. some students 327 \nin different grades shared classrooms). We used individual profiles (sex, school, grade, class, 328 \nhousehold composition), onset dates, influenza episodes of household members and precaution 329 \nmeasures students engaged in (vaccine, mask, hand washing) in the subsequent analysis. Further 330 \ndetails of the dataset can be found in the original studies (51, 61). 331 \nThe secondary data analysis conducted in the present study was approved by the ethics 332 \ncommittee at the London School of Hygiene & Tropical Medicine (reference number: 14599). 333 \nInference model 334 \nWe modelled within-school transmission considering class structures as follows. We defined 335 \nthe “school proximity” d between a pair of students i and j attending the same school as 336 \n𝑑 = #\n1 (different\tgrades, same\tschool)\n2 (different\tclasses, same\tgrade)\n3 (different\tsex, same\tclass)\n4 (same\tsex, same\tclass)\n (1) \nTo investigate the potential effect of reduced class sizes and the number of attending students, we 337 \nmodelled the transmission between students as a function of two variables: the class size n and the 338 \nnumber of classes per grade m (i.e. the number of students per grade is nm). Namely, we assumed that 339 \nin the absence of any individual covariate effects, the cumulative transmission rate between student i 340 \nand j in proximity d over the infectious period is represented as 341 \n𝛽!\" = 𝛽# =𝑛!,# ?\n%&!\n=𝑚!,#?\n%'!\n, (2) \nwhere 𝛽#, 𝛾#, 𝛿# are parameters to be estimated. When i and j are in the same grade (i.e. d = 2, 3, 4), 342 \nthe average class size and the number of classes in that grade were used as 𝑛!,# and 𝑚!,#. When d = 1, 343 \nthe school average was used as 𝑛!,# and 𝑚!,#. The exponent parameters within the same class were 344 \nassumed to be equal: 𝛾( = 𝛾) and 𝛿( = 𝛿). 345 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nWe modelled the daily hazard of incidence for student i as a renewal process. Let ℎ* be the 346 \nonset-based transmission hazard as a function of serial interval s (normalised such that ∑ ℎ+\n,\n+-. = 1; 347 \nℎ+ = 0 for s ≤ 0). We used a gamma distribution of a mean of 1.7 and a standard deviation of 1.0 for 348 \ninfluenza, which resulted in a mean serial interval of 2.2 days (62). The daily hazard of disease onset 349 \nattributed to school transmission is given as  350 \n𝜆!\n/(𝑇) = 𝑣! I 𝑤\"𝛽!\" ℎ0%0\"\n\"\n, (3) \nwhere vi and wi represent the relative susceptibility and infectiousness, respectively, which are 351 \nspecified for each individual by a log-linear regression model to account for covariates (see 352 \nSupplementary materials for detailed methods).  353 \nIn addition to the above within-school transmission, we also considered within-household 354 \ntransmission and general community transmission. Within-household transmission was incorporated 355 \nas the Longini-Koopman model (63) with parameters from a previous study on the same cohort of 356 \nstudents (18). General community transmission was modelled as a logistic curve fitted to the total 357 \nincidence in the dataset to reflect the overall trend of the epidemic. See Supplementary materials for 358 \nfurther details of the model. 359 \nWe constructed the likelihood function and estimated the parameters by the Markov-chain 360 \nMonte Carlo (adaptive mixture Metropolis) method. We obtained 1,000 thinned samples from 361 \n100,000 iterations after 100,000 iterations of burn-in, which yielded the effective sample size of at 362 \nleast 300 for each parameter. Using the posterior samples, we computed the proximity-specific 363 \nreproduction number Rd in a hypothetical 6-year school with given n and m (assumed to be constant 364 \nschoolwide) as 365 \n𝑅# =\n⎩\n⎨\n⎧ 5𝑛𝑚 ⋅ 𝛽.𝑛%&# 𝑚%'# \t\t\t\t\t\t\t\t\t\t\t\t\t(𝑑 = 1)\n𝑛(𝑚 − 1) ⋅ 𝛽1𝑛%&$ 𝑚%'$ \t\t\t\t\t(𝑑 = 2)\n𝑛 ⋅ 𝛽( + 𝛽)\n2 𝑛%&% 𝑚%'% \t\t\t\t\t(𝑑 = 3, 4)\n (4) \nand defined the within-school reproduction number RS as a sum of them. 366 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\n We predicted the relative reduction in RS under intervention measures changing the number of 367 \nattending students and class structures by using posterior samples. Interventions were assumed to 368 \nchange n and m as shown in Table 1, and the predictive distribution of the relative change in RS was 369 \ncomputed for each intervention. The estimated RS represents the value in a hypothetical condition 370 \nwhere an infectious student spends the whole infectious period at school; the effect of absence due to 371 \nsymptoms or the staggered attendance was not included in this reduction. 372 \nAll analysis was performed in Julia 1.5.2 and R 4.1.0. Replication code is available on 373 \nGitHub (https://github.com/akira-endo/schooldynamics_FluMatsumoto14-15). 374 \nAcknowledgement 375 \nThis research was partially funded by Lnest Grant Taisho Pharmaceutical Award. AE was financially 376 \nsupported by The Nakajima Foundation and The Alan Turing Institute. Yang Liu is supported by Bill 377 \n& Melinda Gates Foundation [INV-003174], National Institute for Health Research [16/137/109], 378 \nEuropean Commission [101003688] and UK Medical Research Council [MC_PC_19065]. KEA is 379 \nsupported by European Research Council Starting Grant [757688]. AJK [206250] and SF [210758] 380 \nare supported by the Wellcome Trust. 381 \nConflict of interest 382 \nAE received a research grant from Taisho Pharmaceutical Co., Ltd. 383 \nData and code availability 384 \nDue to potentially sensitive information included, the original dataset is not made public and is 385 \navailable from the corresponding author upon reasonable request. A processed dataset with an 386 \nincreased level of anonymity, which can still qualitatively reproduce the main study finding (i.e. 387 \nbreakdown of the school reproduction number breakdown by the class/grade relationship without 388 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint \n\nadjustment for covariates) is publicly available along with the accompanying code on a GitHub 389 \nrepository (https://github.com/akira-endo/schooldynamics_FluMatsumoto14-15). 390 \nPrior publication 391 \nEarlier version of this manuscript is available at Research Square [https://doi.org/10.21203/rs.3.rs-392 \n322366/v1]. 393 \nReferences 394 \n1.  N. A. Christakis, J. H. Fowler, Social Network Sensors for Early Detection of Contagious 395 \nOutbreaks. PLOS ONE 5, e12948 (2010). 396 \n2.  O. le Polain de Waroux, et al., Identifying human encounters that shape the transmission of 397 \nStreptococcus pneumoniae and other acute respiratory infections (2018) 398 \nhttps:/doi.org/10.1016/j.epidem.2018.05.008. 399 \n3.  S. Eubank, et al., Modelling disease outbreaks in realistic urban social networks. 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Biometrics 38, 115–126 (1982). 550 \n 551 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted July 15, 2021. ; https://doi.org/10.1101/2021.07.08.21259917doi: medRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}