key: cord-0688137-tvha3q08
authors: Lovell-Read, F. A.; Shen, S.; Thompson, R. N.
title: Estimating local outbreak risks and the effects of non-pharmaceutical interventions in age-structured populations: SARS-CoV-2 as a case study
date: 2021-04-29
journal: nan
DOI: 10.1101/2021.04.27.21256163
sha: 7e7cf8d979f6a21ea7214709665d48bb5e7a668e
doc_id: 688137
cord_uid: tvha3q08

During the COVID-19 pandemic, non-pharmaceutical interventions (NPIs) including school closures, workplace closures and social distancing policies have been employed worldwide to reduce transmission and prevent local outbreaks. However, transmission and the effectiveness of NPIs depend strongly on age-related factors including heterogeneities in contact patterns and pathophysiology. Here, using SARS-CoV-2 as a case study, we develop a branching process model for assessing the risk that an infectious case arriving in a new location will initiate a local outbreak, accounting for the age-stratification of the host population. We show that the risk of a local outbreak depends on the age of the index case, and we explore the effects of NPIs targeting individuals of different ages. Social distancing policies that reduce contacts outside of schools and workplaces and target individuals of all ages are predicted to reduce local outbreak risks substantially, whereas school closures have a more limited impact. When different NPIs are used in combination, the risk of local outbreaks can be eliminated. We also show that heightened surveillance of infectious individuals reduces the level of NPIs required to prevent local outbreaks, particularly if enhanced surveillance of symptomatic cases is combined with efforts to find and isolate nonsymptomatic infected individuals. Our results reflect real-world experience of the COVID-19 pandemic, during which combinations of intense NPIs have reduced transmission and the risk of local outbreaks. The general modelling framework that we present can be used to estimate local outbreak risks during future epidemics of a range of pathogens, accounting fully for age-related factors.

NPIs depend strongly on age-related factors including heterogeneities in contact patterns and 23 pathophysiology. Here, using SARS-CoV-2 as a case study, we develop a branching process 24 model for assessing the risk that an infectious case arriving in a new location will initiate a local 25 outbreak, accounting for the age-stratification of the host population. We show that the risk of a 26 local outbreak depends on the age of the index case, and we explore the effects of NPIs targeting 27 individuals of different ages. Social distancing policies that reduce contacts outside of schools 28 and workplaces and target individuals of all ages are predicted to reduce local outbreak risks 29 substantially, whereas school closures have a more limited impact. When different NPIs are used 30 in combination, the risk of local outbreaks can be eliminated. We also show that heightened 31 surveillance of infectious individuals reduces the level of NPIs required to prevent local 32 outbreaks, particularly if enhanced surveillance of symptomatic cases is combined with efforts to 33 find and isolate nonsymptomatic infected individuals. Our results reflect real-world experience 34 of the COVID-19 pandemic, during which combinations of intense NPIs have reduced 35 transmission and the risk of local outbreaks. The general modelling framework that we present 36 can be used to estimate local outbreak risks during future epidemics of a range of pathogens, 37

Throughout the COVID-19 pandemic, policy makers worldwide have relied on non-45 pharmaceutical interventions (NPIs) to limit the spread of SARS-CoV-2. Commonly introduced 46

NPIs have included school closures, workplace closures and population-wide social distancing 47 policies, all of which aim to reduce the numbers of contacts between individuals and disrupt 48 potential chains of transmission [1] [2] [3] [4] . Similar measures have previously been adopted for 49 countering other infectious diseases such as Ebola and pandemic influenza [5] [6] [7] , and are likely 50 to remain a key line of defence against a range of emerging pathogens that are directly 51 transmitted between hosts. NPIs are particularly important when no effective treatment or 52 vaccine is available, and they are also beneficial when vaccination programmes are being rolled 53 out [8] [9] [10] . However, the negative economic, social and non-disease health consequences of 54 these interventions have been widely discussed, with the impact of school closures on the 55 academic progress and wellbeing of school-aged individuals a particular concern [7, [11] [12] [13] [14] [15] . 56 Therefore, assessing the effectiveness of different NPIs at reducing transmission is critical for 57 determining whether or not they should be used. 58 quarter of the UK population and tend to have large numbers of contacts outside school, school 113 closures are predicted to have only a limited effect when applied as the sole NPI. 114 115 We then go on to consider the impacts of mixed strategies made up of multiple NPIs, as well as 116 additional NPIs that do not simply reduce numbers of contacts. Specifically, we show that 117 rigorous surveillance and effective isolation of infected hosts can reduce the level of contact-118 reducing NPIs required to achieve substantial reductions in the risk of local outbreaks. Although 119 we use SARS-CoV-2 as a case study, our approach can be applied more generally to explore the 120 effects of NPIs on the risk of outbreaks of any pathogen for which age-related heterogeneities 121 play a significant role in transmission dynamics. 122 123

We considered a branching process model in which the population was divided into 16 age 126 groups, denoted ! , " , … , !# . The first 15 groups represent individuals aged 0-74, divided into 127

five-year intervals (0-4, 5-9, 10-14 etc.). The final group represents individuals aged 75 and over. 128

The total number of individuals in age group $ is denoted $ . Infected individuals in each age 129 group $ are classified into compartments representing asymptomatic ( $ ), presymptomatic ( $ ) 130 7 An infected individual of any type in group $ may generate new infections in any age group. In 134 our model, the rate at which a single infected symptomatic individual in group $ generates 135 infections in group % is given by 136

Here, $ represents the infectivity of individuals in group $ , % represents the susceptibility to 138 infection of individuals in group % , $% represents the daily number of unique contacts a single 139 individual in group $ has with individuals in group % , and is a scaling factor that can be used 140 to set the reproduction number of the pathogen being considered (see Section 2.2). Since the 141 initial phase of potential local outbreaks are the focus of this study, we did not account for 142 depletion of susceptible hosts explicitly. The relative transmission rates from presymptomatic 143 and asymptomatic individuals compared to symptomatic individuals are given by the scaled 144 quantities $% and $% , respectively, where and were chosen so that the proportions of 145 transmissions generated by presymptomatic and asymptomatic hosts were in line with literature 146 estimates [56] . The parameter $ represents the proportion of asymptomatic infections in group 147 $ , so that a new infection in group $ either increases $ by one (with probability $ ) or 148 increases $ by one (with probability 1 − $ ). 149 150 A presymptomatic individual in group $ may go on to develop symptoms (transition from $ 151 to $ ) or be detected and isolated (so that $ decreases by one). A symptomatic individual in 152 group $ may be detected and isolated as a result of successful surveillance, or may be removed 153 due to self-isolation, recovery or death (so that $ decreases by one in either case). Similarly, an 154 asymptomatic individual in group $ may be detected and isolated or recover (so that $ 155 decreases by one). A schematic of the different possible events in the model is shown in Fig 1.  156 The parameter represents the rate at which presymptomatic individuals develop symptoms, so 158 that the expected duration of the presymptomatic infectious period is 1/ days in the absence of 159 surveillance of nonsymptomatic infected individuals. Similarly, the expected duration of the 160 asymptomatic infectious period in the absence of surveillance is 1/ days. The parameter 161

represents the rate at which symptomatic individuals are removed as a result of self-isolation, 162 recovery or death, so that the duration of time for which they are able to infect others is 1/ 163 days. 164

For each group $ , the rate at which symptomatic individuals are detected and isolated as a result 166 of enhanced surveillance is determined by the parameter $ . Analogously, the parameter $ 167 governs the rate at which presymptomatic and asymptomatic individuals in $ are detected and 168 isolated. We assumed that surveillance measures targeted towards nonsymptomatic hosts are 169 equally effective for those who are presymptomatic and those who are asymptomatic, and 170 therefore used the same rate of isolation due to surveillance for both of these groups. 171 172 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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The effective reproduction number, , represents the expected number of secondary infections 179 generated by a single infected individual during their entire course of infection, accounting for 180 interventions that are in place: 181

182 where = ! + ⋯ + !# is the total population size. This expression is an average of the 183 expected number of secondary infections generated by individuals in each age group, weighted 184 by the proportions of the population belonging to each age group. This corresponds to the 185 assumption that the initial infected host is more likely to belong to an age group containing more 186 individuals than an age group with fewer individuals. For an individual in age group $ , the 187 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint expected number of secondary infections is the sum of the expected number of transmissions 188 from a host who begins in the asymptomatic class and a host who begins in the presymptomatic 189 class, respectively weighted by the probabilities $ and 1 − $ that an infected host experiences 190 an asymptomatic or a symptomatic course of infection. Transmissions arising from a host who 191 begins in the presymptomatic class comprise those which occur during the presymptomatic 192 period and those which occur during the symptomatic period, accounting for the possibility that 193 the individual is isolated before developing symptoms. In the absence of interventions, i.e. when 194 susceptibility was assumed to vary with age but the proportion of asymptomatic infections is 217 independent of age. In scenario C, we allowed both susceptibility and the asymptomatic 218 proportion to vary with age. The values used for the parameters $ and $ in each of these three 219 scenarios are shown in Table 1 (see also [30] ). 220

In all scenarios considered, the inherent infectivity was not assumed to be age-dependent (i.e. 222 $ = 1 for all values of ). In other words, the expected infectiousness of infected hosts in 223 different age groups was governed solely by the proportion of asymptomatic infections in that 224 age group. We chose the scaling factors and for the relative transmission rates from 225 presymptomatic and asymptomatic individuals compared to symptomatic individuals so that the 226 proportions of infections arising from each of these groups were in line with literature estimates 227 (see Table 3 and [56]). 228

In the absence of enhanced isolation, we set the expected duration of the presymptomatic 230 infectious period and the time for which symptomatic individuals are able to infect others to be 231 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint 1/ = 2 days and 1/ = 8 days, respectively [58-61]. The asymptomatic infectious period was 232 then chosen so that all infected individuals are expected to be infectious for the same period (i.e. 233 1/ = 10 days). Initially, we set the isolation rates $ and $ equal to 0 for all ; later, we 234 considered the effects of increasing these rates. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) 

The probability that an infected individual in a particular age group initiates a local outbreak 254 when they are introduced into the population was calculated using the branching process model, 255 as follows. 256 257 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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The probability of a local outbreak not occurring (i.e. pathogen fadeout occurs), starting from a 258 single symptomatic (or presymptomatic, asymptomatic respectively) infectious individual in age 259 group $ was denoted by $ ( $ , $ ). Beginning with a single symptomatic individual in $ , the 260 possibilities for the next event are as follows: 261

1. The infected individual in $ infects a susceptible individual in % , so that either % 262 increases by one (with probability % ) or % increases by one (with probability (1 − % ). 263

This occurs with probability 264

2. The infected individual in $ recovers, dies or is isolated before infecting anyone else, so 266 that $ decreases to zero (and there are no infected individuals left in the population). 267

This occurs with probability 268

If there are no infectious hosts present in the population, then a local outbreak will not occur. 270 Therefore, assuming that chains of transmission arising from infectious individuals are 271 independent, the probability that no local outbreak occurs beginning from a single symptomatic 272 individual in $ is 273

Similarly, beginning instead with a single presymptomatic individual in $ , the possibilities for 276 the next event are: 277 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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1. The presymptomatic infected individual in $ infects a susceptible individual in % , so 278 that as before either % increases by one (with probability % ) or % increases by one (with 279 probability (1 − % ). This occurs with probability 280

. 281 2. The infected individual in $ develops symptoms (transitions from $ to $ ). This occurs 282 with probability 283

. 284

3. The infected individual in $ is isolated before infecting anyone else, so that $ decreases 285 by one. This occurs with probability 286

Therefore, the probability that no local outbreak occurs beginning from a single presymptomatic 288 individual in $ is 289

Similarly, the probability $ that a local outbreak does not occur starting from a single 291 asymptomatic individual in $ satisfies the equation 292

where 294

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The system of simultaneous equations (2) − (4) can be solved numerically to obtain $ , $ and 297 $ (specifically, we take the minimal non-negative solution, as is standard when calculating 298 extinction probabilities using branching process models [54, 66]). Then, for each , the 299 probability of a local outbreak occurring beginning from a single symptomatic (or 300 presymptomatic, asymptomatic respectively) individual in group $ is given by

Throughout, we consider the probability $ of a local outbreak occurring beginning from a single 304 nonsymptomatic individual in group $ arriving in the population at the beginning of their 305 infection: 306

The average local outbreak probability, , which is defined as the probability of a local outbreak 309 when the index case is chosen randomly from the population, is also considered. The value of 310 is therefore a weighted average of the $ values, where the weights correspond to the proportion 311 of the population represented by each group: 312

This reflects an assumption that the index case is more likely to come from an age group with 314 more individuals than an age group with fewer individuals. 315 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint We first considered the probability that a single infected individual in a particular age group $ 328 initiates a local outbreak when introduced into a new host population. This quantity was 329 calculated for each of the three scenarios A, B and C (Fig 3) . 330

In scenario A, the variation in the outbreak risk for introduced cases of different ages is driven 332 solely by the numbers of contacts between age groups. As a result, due to their higher numbers 333 of daily contacts, school-and working-age individuals are more likely to trigger an outbreak than 334 children under five or adults over 60, with index cases aged 15-19 posing the highest risk (0.596) 335 ( Fig 3A) . These findings do not change significantly when susceptibility is allowed to vary with 336 age in scenario B ( Fig 3B) . However, in scenario C, assuming that the clinical fraction also 337 varies between age groups significantly alters the age-dependent risk profile. This is because 338 asymptomatic individuals are assumed to be less infectious than symptomatic individuals, and 339 therefore an index case in an age group with a high proportion of asymptomatic infections is less 340 likely to trigger a local outbreak. In this scenario, index cases aged 40 or over had a 341 disproportionately high probability of generating a local outbreak, with individuals aged 70-74 342 presenting the highest risk (0.598). These older individuals are more likely to develop symptoms 343 than younger individuals (Table 1) , leading to a higher expected infectiousness. In contrast, 344 individuals below the age of 40 had a below average probability of generating a local outbreak, 345 with individuals aged 10-14 presenting the lowest risk (0.284). Noticeably, individuals aged 5-346 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint 19 presented relatively low risks, despite the high numbers of contacts occurring among these 347 age groups (Fig 2B) . In this scenario, the large number of contacts was offset by the fact that 348 individuals in these age groups are more likely to be asymptomatic and consequently less 349 infectious than older individuals (Table 1) . Therefore, an index case in one of these age groups is 350 likely to lead to fewer secondary transmissions. Furthermore, the contact patterns between 351 individuals in these age groups are highly assortative with respect to age ( Fig 2B) . Therefore, in 352 addition to the index case being less infectious, a high proportion of the contacts they make are 353 with individuals who are also likely to be less infectious, as well as being less susceptible to 354 infection in the first place. 355

We performed our subsequent analyses for each of the three scenarios A, B and C, with 357 qualitatively similar results. The figures shown in the main text are for scenario C, since we 358 deem this scenario to be the most realistic for SARS-CoV-2 transmission, but the analogous 359 results for scenarios A and B are presented in Supplementary Figs S1-6. 360 361 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The analogous figure to A but for scenario B, in which clinical fraction is assumed constant across 367 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint all age groups but susceptibility varies with age (Table 1 ). C. The analogous figure to A but for 368 scenario C, in which both susceptibility and clinical fraction vary with age (Table 1) .

We next considered the effects of NPIs that reduce the number of contacts between individuals 372 on the probability that an introduced case will lead to a local outbreak. To approximate the 373 relative effects of school closures, workplace closures and population-wide social distancing 374 policies, we calculated the age-dependent risk profiles when each of these types of contact were 375 excluded from the overall contact matrix. 376 377 First, we removed all 'school' contacts from the total contact matrix (Fig 4A) . For scenario C, 378 removing 'school' contacts led to a 4.2% reduction in the average probability of a local outbreak, 379 from 0.449 to 0.430. This small reduction is unsurprising for scenario C, since in that scenario 380 school-aged infected individuals are assumed more likely to be asymptomatic than other infected 381 individuals, and therefore their expected infectiousness is lower. However, even for scenarios A 382 and B, in which school-aged individuals present the greatest risk of triggering an outbreak, the 383 effectiveness of removing 'school' contacts alone at reducing the local outbreak probability was 384 limited (reductions of 7.2% and 4.75% respectively; see Supplementary Figs S1A, S4A). In each 385 scenario, the reduction in risk was predominantly for school-aged index cases, with the risk from 386 index cases of other ages only slightly reduced. Second, we considered the effects of removing 387 'work' contacts from the total contact matrix (Fig 4B) . This led to a more substantial 25.4% 388 reduction in the average probability of a local outbreak for scenario C (with corresponding 389 reductions of 19.0% and 24.0% for scenarios A and B respectively; see Supplementary Figs S1B, 390 S4B). As well as reducing the risk of an outbreak from an index case of working age, removing 391 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint 'work' contacts also reduced the probability of a local outbreak occurring starting from a school-392 aged individual. This is because closing workplaces helps to block chains of transmission that 393 begin with an infected child. For example, a transmission chain involving a child transmitting to 394 an adult at home, followed by subsequent spread around the adult's workplace, will be less likely 395 to occur. Third, we investigated the effect of removing all 'other' contacts, reflecting perfect 396 social distancing being observed outside of the home, school or workplace ( Fig 4C) . This had the 397 most significant effect of the three types of contact-reducing intervention considered, reducing 398 the probability of a local outbreak by 41.7% for scenario C (and 30.7% or 33.2% for scenarios A 399 and B, respectively). 400 401 In the three cases described above, we considered complete reductions in 'school', 'work' and 402 'other' contacts, respectively. In practice, such complete elimination of contacts is unfeasible. 403

We therefore also considered partial reductions in 'school', 'work' and 'other' contacts, and 404 compared the resulting reductions in the local outbreak probability (Fig 4D) . Next, we considered the effects of combining reductions in 'school', 'work' and 'other' contacts 425 on the local outbreak probability (Fig 5; analogous results for scenarios A and B are shown in 426 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint Supplementary Figs S2 and S5) . We allowed reductions in 'school' and 'work' contacts to vary 427 between 0% and 100% whilst 'other' contacts were reduced by 25%, 50% or 75% (Fig 5A,B CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint Finally, keeping the enhanced isolation rate of symptomatic individuals equal to $ = 485 1/2 days )! , we increased the isolation rate of nonsymptomatic individuals to $ = 1/7 days )! . 486

In this case, the local outbreak probability without contact-reducing NPIs fell by 59.4% 487 compared to a situation without enhanced surveillance (Fig 6E) , and the reductions in 'work' and 488 'other' contacts needed to bring the local outbreak probability below 0.01 were significantly 489 smaller ( Figure 6F ). For example, if 'work' contacts can be reduced by 50%, then 'other' 490 contacts only need to be reduced by 43%. This indicates that effective surveillance of both 491 symptomatic and nonsymptomatic individuals can substantially lower the extent of contact-492 reducing NPIs that are required to achieve substantial reductions in local outbreak risks. 493

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The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint when the isolation rate of symptomatic individuals is ! = 1/2 days '" , without contact-reducing NPIs or surveillance (as in Fig 3C) . D. The effect of reducing 'work' and 'other' contacts when the isolation rate CoV-2 as a case study, we demonstrated that the risk that an introduced case initiates a local 526 outbreak depends on these age-related factors and on the age of the introduced case (Fig 3) , as 527 well as the age-structure of the local population. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint reductions in all three types of contact were required to eliminate the risk of local outbreaks 548 entirely ( Fig 5D) . However, implementing effective surveillance to identify infected hosts led to 549 substantial reductions in the risk of local outbreaks even in the absence of other control measures 550 (Figs 6A,B) . With an efficient surveillance strategy in place, significantly smaller reductions in 551 'work' and 'other' contacts were needed to render the outbreak probability negligible, even when 552 'school' contacts were not reduced at all (Figs 6C-F) . This supports the use of surveillance that 553 targets both symptomatic and nonsymptomatic individuals, such as contact tracing and isolation 554 strategies or population-wide diagnostic testing, to prevent local outbreaks [54] . 555 556 Although here we used SARS-CoV-2 as a case study, our model provides a framework for 557 estimating the risk of local outbreaks in age-structured populations that can be adapted for other 558 pathogens, provided sufficient data are available to parametrise the model appropriately. The 559 effects of age-structure on local outbreak risks may vary for pathogens with different 560 epidemiological characteristics. For influenza-A viruses, for example, susceptibility to infection 561 tends to decreases with age, whilst the risk of developing severe symptoms is greater both for the 562 elderly and for the very young [30, 70, 71] . This is in contrast to SARS-CoV-2, for which 563 children are more likely to experience subclinical courses of infection. In this study, we used age 564 demographic and contact data for the UK, but equivalent data for other countries are available 565 and can easily be substituted into our model to estimate outbreak risks elsewhere [16, 57] . 566 567 One caveat of the results for SARS-CoV-2 presented here is that, although the epidemiological 568 parameters of our model were chosen to be consistent with reported literature estimates, there is 569 considerable variation between studies. In particular, the precise age-dependent variation in 570 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint susceptibility and clinical fraction remains unclear, and the relative infectiousness of 571 asymptomatic, presymptomatic and symptomatic hosts has not been determined exactly. 572 Furthermore, the inherent transmissibility of SARS-CoV-2 is now higher than in the initial stage 573 of the pandemic, due to the appearance of new variants such as B.1.1.7. We therefore also 574 conducted sensitivity analyses to explore the effects of varying the parameters of the model on 575 our results ( Supplementary Figs S1-12) . In each case that we considered, our main conclusions 576 were unchanged: the probability that an introduced case initiates a local outbreak depends on 577 age-dependent factors affecting pathogen transmission and control, with widespread 578 interventions and combinations of NPIs reducing the risk of local outbreaks most significantly. 579 580 An important limitation of our approach to modelling contact-reducing NPIs is that we made a 581 standard assumption that 'school', 'work' and 'other' contacts are independent [26, 30, 46] . In 582 other words, reducing the numbers of contacts in one location did not affect the numbers of 583 contacts occurring in another. In reality, this is unlikely to be the case. For example, closing 584 schools is also likely to affect workplace contacts, as adults may then work from home in order 585 to fulfil childcare requirements. Additionally, the contact data that we used represent the number 586 of unique contacts per day and do not include possible repeated contacts with the same person, 587 which affect the risk of transmission between individuals. These assumptions could in principle 588 be removed, if relevant data become available -for example, data describing the effects of 589 school closures on numbers of contacts in other locations. 590 591 Despite these simplifications, our model provides a useful framework for estimating the risk of 592 local outbreaks and the effects of NPIs. Different measures can be considered in combination in 593 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint dependent probability of a local outbreak with enhanced surveillance of both symptomatic and 960 nonsymptomatic infected hosts ( ! = 1/2 days '" and ! = 1/7 days '" ), without contact-reducing NPIs 961 (purple bars and solid line). Pale grey bars and black dash-dotted line represent the local outbreak 962 probabilities without any contact-reducing NPIs or enhanced surveillance (as in Fig S8A) . 

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The copyright holder for this preprint this version posted April 29, 2021. ; https://doi.org/10.1101/2021.04.27.21256163 doi: medRxiv preprint text: the probability that a single infected individual in any given age group triggers a local outbreak (grey 'work' contacts are reduced by 100% (solid line). D. Analogous to Fig 6E in probabilities without any contact-reducing NPIs or enhanced surveillance (as in Fig S10A) .

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Systematic review of COVID-19 in children shows milder cases and 715 a better prognosis than adults

COVID-19 Among Children in China

Online ahead of print. COVID-19 in 721 childhood: Transmission, clinical presentation, complications and risk factors

SARS-CoV-2 725 (COVID-19): What Do We Know About Children? A Systematic Review

With Coronavirus Disease 2019 in the Republic of Korea

Asymptomatic transmission of covid-19

Occurrence and transmission potential of asymptomatic and 735 presymptomatic SARS-CoV-2 infections: A living systematic review and meta-analysis

Estimating the extent of asymptomatic COVID-19 and its potential for community transmission: 739 Systematic review and meta-analysis

What do we know about SARS-CoV-2 742 transmission? A systematic review and meta-analysis of the secondary attack rate and associated 743 risk factors

Transmission of SARS-CoV-2: A Systematic Review and Meta-analysis

Defining the 748 role of asymptomatic and pre-symptomatic SARS-CoV-2 transmission -a living systematic 749 review

Demographic risk 752 factors for COVID-19 infection, severity, ICU admission and death: a meta-analysis of 59 753 studies

Estimates of the severity of 756 coronavirus disease 2019: a model-based analysis

COVID-19) in Wuhan, China: A Single-Centered, Retrospective Study

The effect of control strategies to reduce 764 social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study

Effects of non-768 pharmaceutical interventions on COVID-19 cases, deaths, and demand for hospital services in 769 the UK: a modelling study

Cluster infections play 772 important roles in the rapid evolution of COVID-19 transmission: A systematic review

What settings have 775 been linked to SARS-CoV-2 transmission clusters?

A framework for identifying regional outbreak and spread of 779 COVID-19 from one-minute population-wide surveys

Ebola virus disease 782 outbreak in Nigeria: Transmission dynamics and rapid control

Sustained transmission of Ebola in new 785 locations: more likely than previously thought

Novel Coronavirus Outbreak

Surveillance Is Vital for Preventing Sustained Transmission in New Locations

Feasibility of controlling COVID-19 792 outbreaks by isolation of cases and contacts

Interventions targeting nonsymptomatic cases can be important to prevent local outbreaks: 796 SARS-CoV-2 as a case-study

Assortativity and the Probability of 798

Epidemic Extinction: A Case Study of Pandemic Influenza A (H1N1-2009)

Quantifying SARS-CoV-2 transmission suggests epidemic control 802 with digital contact tracing

United Nations, Department of Economic and Social Affairs, Population Division

Transmission of SARS-CoV-2 -Singapore

Presymptomatic SARS-CoV-2 Infections 811 and Transmission in a Skilled Nursing Facility

Predicting Infectious Severe Acute Respiratory 815

Syndrome Coronavirus 2 From Diagnostic Samples

Virological assessment of 819 hospitalized patients with COVID-2019

Severe acute respiratory 822 syndrome coronavirus 2 (SARS-CoV-2) and coronavirus disease-2019 (COVID-19): The 823 epidemic and the challenges

The reproductive number of 826 COVID-19 is higher compared to SARS coronavirus

The epidemiology, diagnosis 829 and treatment of COVID-19

Preliminary estimation of the basic reproduction number of novel coronavirus 833 (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the 834 outbreak

Markov Chains (Cambridge Series in Statistical and Probabilistic 836

nonpharmaceutical interventions on influenza and other respiratory viral infections in New 840

Estimating the effects of non-pharmaceutical 843 interventions on COVID-19 in Europe

Closing Schools in Response to the

Influenza A H1N1 Virus in New York City: Economic Impact on Households