key: cord-0824553-033d0pxx
authors: Hill, E. M.; Atkins, B. D.; Keeling, M. J.; Dyson, L.; Tildesley, M. J.
title: A network modelling approach to assess non-pharmaceutical disease controls in a worker population: An application to SARS-CoV-2
date: 2020-11-20
journal: nan
DOI: 10.1101/2020.11.18.20230649
sha: 55dc889aca259a04499af0e3efaaabad3441d69a
doc_id: 824553
cord_uid: 033d0pxx

Background: As part of a concerted pandemic response to protect public health, businesses can enact non-pharmaceutical controls to minimise exposure to pathogens in workplaces and premises open to the public. Amendments to working practices can lead to the amount, duration and/or proximity of interactions being changed, ultimately altering the dynamics of disease spread. These modifications could be specific to the type of business being operated. Methods: We use a data-driven approach to parameterise an individual-based network model for transmission of SARS-CoV-2 amongst the working population, stratified into work sectors. The network is comprised of layered contacts to consider risk of spread in multiple encounter settings (workplaces, households, social and other). We analyse several interventions targeted towards working practices: mandating a fraction of the population to work from home, using temporally asynchronous work patterns and introducing measures to create `COVID-secure' workplaces. We also assess the general role of adherence to (or effectiveness of) isolation and test and trace measures and demonstrate the impact of all these interventions across a variety of relevant metrics. Results: The progress of the epidemic can be significantly hindered by instructing a significant proportion of the workforce to work from home. Furthermore, if required to be present at the workplace, asynchronous work patterns can help to reduce infections when compared with scenarios where all workers work on the same days, particularly for longer working weeks. When assessing COVID-secure workplace measures, we found that smaller work teams and a greater reduction in transmission risk led to a flatter temporal profile for both infections and the number of people isolating, and reduced the probability of large, long outbreaks. Finally, following isolation guidance and engaging with contact tracing alone is an effective tool to curb transmission, but is highly sensitive to adherence levels. Conclusions: In the absence of sufficient adherence to non-pharmaceutical interventions, our results indicate a high likelihood of SARS-CoV-2 spreading widely throughout a worker population. Given the heterogeneity of demographic attributes across worker roles, in addition to the individual nature of controls such as contact tracing, we demonstrate the utility of a network model approach to investigate workplace-targeted intervention strategies and the role of test, trace and isolation in tackling disease spread.

Globally, many countries have employed social distancing measures and non-pharmaceutical interven-2 tions (NPIs) to curb the spread of SARS-CoV-2 [1] . For many individuals, infection develops into 3 COVID-19 disease, with symptoms including fever, shortness of breath and altered sense of taste and 4 smell, potentially escalating to a more severe state which may include pneumonia, sepsis, and kidney 5 failure [2] . In the United Kingdom (UK), the enaction of lockdown on 23rd March 2020 saw the 6 closure of workplaces, pubs and restaurants, and the restriction of a range of leisure activities. As the 7 number of daily confirmed cases went into decline during April, May and into June [3] , measures to 8 ease lockdown restrictions began, with the re-opening of some non-essential businesses and allowing 9 small groups of individuals from different households to meet up outdoors, whilst maintaining social 10 distancing. 11 By the end of September 2020, exponential growth had returned in almost all regions of the UK [4, 5] , 12 with subsequent attempts to curtail growth by introducing stricter controls. Whilst lockdown has been 13 a strategy used around the world to reduce the public health impacts of COVID-19, it is important 14 to recognise that such strategies are very disruptive to multiple elements of society [6, 7] , especially 15 given that restrictions are largely unpredictable to the local populous and businesses. 16 As part of collective efforts to protect public health by disrupting viral transmission, businesses also 17 need to act appropriately by taking all reasonable measures to minimise exposure to coronavirus in 18 workplaces and premises open to the public. In the UK, each of the four nations (England, Wales, 19 Scotland, Northern Ireland) has published guidance to help employers, employees and the self-employed 20 to work safely [8] [9] [10] [11] . Adjustments in working practices can result in changes to the amount, duration 21 and/or proximity of interactions, thereby altering the dynamics of viral spread. These modifications 22 could be variable depending upon the type of business being operated and may include limiting 23 the number of workers attending a workplace on any given day, as well as introducing measures to 24 make a workplace COVID-secure, such as compulsory mask wearing and the use of screens. For 25 this particular paper, we are interested in how interventions targeting workplace practices may affect 26 infectious disease control efforts, whilst accounting for the variation in employee demographics across 27 working sectors. 28 As part of the response to the COVID-19 pandemic, modelling analyses have been carried out pertain- 29 ing to transmission of SARS-CoV-2 within specific parts of society, including health care workers [12] , 30 care homes [13] , university students [14] [15] [16] and school pupils and staff [17] [18] [19] . Similarly to these stud- 31 ies, we may view the contact structure for the adult workforce as being comprised of several distinct 32 layers. Knowledge of the structure of the network allows models to compute the epidemic dynamics 33 at the population scale from the individual-level behaviour of infections [20] . More generally, such 34 models of infectious disease transmission are a tool that can be used to assess the impact of options 35 seeking to control a disease outbreak. 36 In this study, we outline an individual-based network model for transmission of SARS-CoV-2 amongst 37 the working population. Informed by UK data, the model takes into account work sector, workplace 38 size and the division of time between work and home. In addition to workplace interactions, contacts 39 also occur in household and social settings. Given the heterogeneity of demographic attributes across 40 worker roles, as well as the individual-based NPIs such as contact tracing, we demonstrate the utility 41 of a network model approach in investigating workplace-targeted control measures against infectious 42 disease spread. 44 We used simulations of an epidemic process over a network model to explore the impact of workplace-45 targeted non-pharmaceutical interventions in suppressing transmission of SARS-CoV-2 within a popu-46 lation of workers. In this section we detail: (i) the structure of the network model; (ii) the data sources 47 used to parameterise the network contact structure; (iii) the model for SARS-CoV-2 transmission and 48 COVID-19 disease progression; and (iv) the simulation protocol employed to assess the scenarios of 49 interest. 50 Network model description 51 We used a multi-layered network model to encapsulate identifiable groupings of contacts. Our model 52 was comprised of four layers: (i) households; (ii) workplaces; (iii) social contacts; and (iv) other 53 contacts. 54 Household contact layer 55 To allocate workers to households, we sampled from an empirical distribution based on data from the 56 2011 census in England [21] . To obtain this distribution, we calculated the proportion of households 57 containing 1 to 6+ people between the ages of 20 -70 (Fig. S8) . Thus, we omit children and the 58 elderly from our analysis, an acknowledged simplification of the system. When sampling from this 59 distribution, we restricted the maximum household size to six people in an attempt to reduce the 60 amount of overestimation of the number of active workers mixing within households, which results 61 from the assumption that everyone in a household is an active worker. Within each household, members 62 formed fully connected networks.

Workplace contact layer 64 To disaggregate working sectors, we used data from the 2020 edition of the ONS 'UK business: activity, 65 size and location database' [22] . Specifically, we took counts (for the UK) of the number of workplaces 66 stratified into 88 industry divisions/615 industry classes (Standard Industrial Classifications (UK 67 SIC2007)) and by workforce size (0 -4, 5 -9, 10 -19, 20 -49, 50 -99, 100 -249, 250+). 68 We assigned the industry types into one of 41 sectors (see Table 1 for a listing of the work sectors). 69 We generated a set of workplaces and workplace sizes for each of the 41 sectors in a two-step process: 70 first, we sampled from the relevant empirical cumulative distribution function of the binned workplace 71 size data to obtain the relevant range. For a bounded range (all but the largest bin), we then sampled 72 an integer value according to a uniform distribution that spanned the selected range. Since the 73 largest data bin (250+ employees) is unbounded, in this instance we instead sampled from a shifted 74 Gamma(1,100) distribution (shape and scale parameterisation, shifted to 250). 75 We stratified workplace contacts into static contacts and dynamic contacts. For static contacts, we 76 constructed the network to allow for contacts both within a worker's workplace (most common) and to 77 other workplaces in the same industrial sector (less common). These contacts occurred every workday, 78 unless either person was working from home, and remained unchanged throughout the simulation. We 79 generated static contacts using a 'configuration model' style algorithm, allowing the specification of 80 a desired degree distribution for each sector. We adapted the standard configuration model to allow 81 a variable amount of clustering, where a higher value of clustering led to more contacts being made 82 within a workplace compared to between different workplaces. We subjectively assumed throughout 83 that the probability of making contact with an individual in another workplace compared to an 84 individual within the same workplace was 0.05. Unlike the standard configuration model, we did not 85 allow edges to be made with oneself or repeated edges. As such, the resulting degree distribution 86 was an approximation of the distribution used as an input. For the steps defining the algorithm, see 87 Section 1.1 of Supporting Text S1.

Dynamic contacts represent those that may occur between workers and non-workers, though still in 89 the workplace, for example contacts between retail workers and shoppers. These were regenerated 90 every day: for each worker (not working from home), we generated a number of dynamic contacts 91 from a sector-specific degree distribution and assigned the recipients at random. These were not 92 clustered in any way; that is, every person in the population had an equal probability of being the 93 recipient, though we do not allow repeated edges or edges with oneself. Given the number of dynamic 94 contacts per person is small compared to the size of the population, the desired degree distribution 95 was approximately preserved. Social contacts were generated in two stages. First, we generated a 'social group' for each person. We 98 used a similar configuration model style algorithm as for the generation of static workplace contacts, 99 allowing the specification of a desired degree distribution. We adapted the standard configuration 100 model to allow for greater clustering (which in this context relates to the probability that each contact 101 is made with a friend-of-a-friend, compared to someone at random, set at 0.5) and did not allow edges 102 with oneself or repeated edges. This resulted in an acceptable approximation of the desired degree 103 distribution. The second step specified who a person socialises with each day: for each individual on 104 each day, we sampled a subset of all possible social contacts to construct the social contacts made on 105 that day. The number of social contacts made per day was specified by a degree distribution (but 106 restricted by the size of their social group), which we allowed to differ between workdays and non-107 workdays. However, note that we did not enforce a correlation between the size of a person's social 108 group and the number of social contacts they made each day. We provide a description of the steps 109 for constructing the social contact layer of the network in Section 1.2 of Supporting Text S1).

Other contacts

The final contact layer sought to capture random, dynamic, contacts made each day with any other 112 individuals in the population (for example on public transport). We used a fixed daily probability of 113 each individual interacting with any other individual in the network.

Contact parameterisation 115 We characterised the network structure across the various contact layers by applying a data-driven 116 approach, using data from the University of Warwick Social Contact Survey [23, 24] . The Social 117 Contact Survey was a paper-based and online survey of 5,388 participants in the United Kingdom 118 conducted in 2010. We extracted records provided by 1,860 participants, with a total of 34,004 119 contacts (eligibility criteria are outlined in Supporting Text S2). These data informed the network 120 construction parameters for the workplace and social layers, with stratification according to the work 121 sector. We fit parameters for these contact distributions using maximum likelihood estimation via the 122 fitdistrplus package in R. We present a summary of network parameters in Table 2 .

Workplace contacts 124 We also used the Warwick Social Contact Survey to parameterise the degree distributions for both 125 4 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted November 20, 2020. ;  static and dynamic contacts occurring in workplaces. For a full description of the workplace contact 126 layer parameterisation, including the mapping between the ONS sectors and occupations listed in the 127 Contact Survey, see Section 2.1 of Supporting Text S2. 128 We found that, in general across all work sectors, the daily number of workplace contacts displayed 129 a heavy tail. Thus, we chose to fit (using maximum likelihood estimation) lognormal distributions to 130 the data, which consistently provided stronger correspondence to the data than alternative choices of 131 distribution across different occupations.

Social contacts 133 We used data from the Warwick Social Contact Survey to acquire a distribution of social group sizes 134 and estimate the daily number of social contacts on both work and non-work days. To acquire a distri-135 bution of social group sizes, we scaled up the contacts recorded in the Warwick Social Contact Survey, 136 resulting in a lognormal(3.14,1.41) distribution with a mean and standard deviation parameterisation 137 ( Fig. 1 and Table 2 , full methodological details in Section 2.2 of Supporting Text S2).

Through fitting lognormal distributions in turn to the workday and non-workday data, we obtained 139 lognormal(1.40,1.27) and lognormal(1.54,1.15) distributions for workday and non-workday social con-140 tacts, respectively ( Fig. 1 To capture individuals having other randomly occurring contacts, for each individual we sampled 144 random connections according to a fixed daily probability of interacting with any other individual in 145 the network. We parameterised the probability so each individual had, on average, one additional 146 contact per day ( Table 2 ). This results in a Poisson(1) distribution across the entire population. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 20, 2020. ; We ran a susceptible-latent-infectious-recovered (SEIR) type disease process on the network structure. 150 Once infected, we assumed infectiousness could not start immediately (i.e. on the same day), with the 151 earliest permitted moment being the following day. We assumed an Erlang-distributed incubation 152 period, with shape parameter 6 and scale parameter 0.88 [25] .

The distribution of infectiousness had a four day pre-symptomatic phase, followed by a seven day 154 symptomatic phase. This gave a total of 11 days of infectivity and a minimum 12 day infection duration 155 (for the full temporal profile, see Table 3 ). It was based on a Gamma(97.2, 0.2689) distribution, with 156 shape and scale parameterisation, shifted by 25.6 days [26, 27] . Following completion of the infectious 157 period, the individual entered the recovered state. Infected individuals could be either asymptomatic or symptomatic, with an ascribed probability deter-160 mining the chance of each individual being asymptomatic. There remains uncertainty in the fraction 161 of COVID-19 cases that are asymptomatic and how that statistic may vary with age, however com-162 munity surveillance studies have been performed to help reduce this uncertainty. Round 4 of the 163 6 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted November 20, 2020. ;

REal-time Assessment of Community Transmission-1 (REACT-1) study found approximately 70% of 164 swab-positive adults were asymptomatic at the time of swab and in the week prior [3] . To reflect the 165 uncertainty in this value, which includes a portion of the previously stated estimate being presymp-166 tomatic infected individuals who would later go on to display symptoms, and the proportion of people 167 who tested positive and were non-symptomatic being lower in round 5 at 50% [5] , in each simulation 168 we sampled the asymptomatic case probability from a uniform distribution within the interval 0.5 and 169 0.8.

There is currently limited data available to provide a robust quantitative estimate of the relative 171 infectiousness of asymptomatic and symptomatic individuals infected with SARS-CoV-2, though there 172 are some indications that asymptomatic individuals could be considered to be less infectious than 173 symptomatic individuals [28, 29] . Therefore, we set an asymptomatic individual to have a lower risk 174 of transmitting infection compared to a symptomatic individual, with the current uncertainty reflected 175 by sampling the value for the relative infectiousness of an asymptomatic in each simulation replicate 176 from a Uniform(0.3, 0.7) distribution. We applied the scaling consistently throughout the duration of 177 infectiousness for asymptomatics, meaning there was no time dependence on the scaling term over the 178 course of infectiousness.

Setting transmission risk 180 Attributing risk of transmission to any particular contact in a particular setting is complex. This 181 is partly due to the huge heterogeneity in contact types, and partly due to the different scales of 182 data: contact information is by its nature individual-based, whereas transmission rates are generally 183 measured at the population level. Therefore, whilst we can attribute a relative risk to each contact 184 type (home, work, social, other), there is an arbitrary scaling to translate these relative risks to an 185 absolute growth rate of infection in the population.

For household transmission, we attributed a household secondary attack rate to each individual based 187 on their household size. We sampled from a normal distribution whose mean value depended on the 188 household size, based on estimates of adjusted household secondary attack rates from a UK based 189 surveillance study [30] . The mean values used were: 0.48 for a household size of two, 0.40 for for a 190 household size of three, 0.33 for a household size of four, 0.22 for a household size of five or above. 191 The standard deviation of the normal distribution for households of size two or three was 0.06, and 192 for households of four or above was 0.05.

For transmission risk in other settings, we performed a mapping from the Warwick Social Contact 194 Survey [24] to obtain a relative transmission risk (see Supporting Text S3). To calibrate the relative 195 transmission risks to achieve an uncontrolled reproductive number, R t , with an average of approxi-196 mately three for the initial phase of the outbreak, we applied a universal scaling of 0.8 to all of the 197 above rates (see Supporting Text S4). Upon symptom onset, workers adhering to guidance entered isolation for ten days. At that moment, 201 fellow household members of the symptomatic case that adhere to guidance entered self-isolation for 202 14 days [31] . Individuals that are symptomatic and that will engage with the test and trace process 203 undergo a test upon symptom onset. We included a two day delay before receiving the test result.

Adherence to isolation guidance and engagement with test and trace are defined by a specified prob-205 ability that remains fixed throughout each simulation. For simplicity, we assumed that an individual 206 either both adheres to guidance and engages with test and trace, or does neither.

Once isolation periods are begun they were seen out in full unless the test result was negative (false 208 7 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted November 20, 2020. ; Proportion of cases asymptomatic Uniform(0.5, 0.8) REACT-1 study [3, 5] Relative infectiousness of an asymptomatic Uniform(0.3, 0.7) [28, 29] negative probability of 0.13 [32] ). On occasions where a negative result was given, household members 209 would be released from isolation, as long as no other symptomatic cases (that are confirmed positive 210 or awaiting test result) were present in the household. The index case remained in self-isolation if they 211 had independently been identified via contact tracing as a contact of a known infected; otherwise, that 212 individual also left self-isolation.

Forward contact tracing 214 Identified contacts of a confirmed case that would adhere to self-isolation guidance, spent up to 14 215 days in self-isolation [33] ; we set the time required to be spent in self-isolation to elapse 14 days from 216 the day the index case became symptomatic.

The modelled tracing scheme looked up contacts for an index case up to two days before onset of 218 symptoms. We assumed that the probability of an individual being able to recall their 'dynamic' 219 contacts diminishes with time, from 0.5 one day previously, reducing in increments of 0.1, such that the 220 probability of successfully tracing a contact five days prior to the tracing occurring is 0.1. Once again, 221 other assumptions could be explored and a wider range of assumptions, collectively, would generate 222 more variation in the results. We give an overview of isolation, test and trace related parameters in 223 Table 4 . is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 20, 2020. ; https://doi.org/10.1101/2020.11.18.20230649 doi: medRxiv preprint Simulation outline 225 We used the described model framework to evaluate the transmission dynamics of SARS-CoV-2 226 amongst the workforce under different workplace-targeted NPIs. We also assessed the role of ad-227 herence to the underlying social distancing guidance and engagement with test-and-trace. 228 We ran all simulations with a population of 10,000 workers and a simulation time corresponding to 229 365 days. For the default working pattern, we applied a simplifying assumption that all workers had 230 the same working pattern of five days at the workplace (that can be considered to be Monday to 231 Friday) and two days off (Saturday and Sunday). All individuals began the simulation susceptible, 232 with the exception of ten individuals seeded in an infectious state; of whom we set between five to eight 233 individuals as being asymptomatically infected (randomly sampled), with the remaining individuals 234 (between two to five) symptomatic.

Our assessment comprised four strands. First, we studied how alterations to the proportion of workers 236 who were working from home may alter the course of an outbreak. Second, we inspected the role 237 of different working patterns upon the spread of infection. Third, we considered an introduction of 238 COVID-secure workplace measures by capping work contacts and imposing a potential reduction on 239 transmission risk in work settings. Finally, we analysed the impact of the level of adherence to isolation 240 measures and test and trace interventions. 241 We outline each of the four assessments in further detail below. Across all sections of analysis, we were 242 interested in measures associated with outbreak severity (size and peak in cases), extent of isolation 243 (cumulative isolation time and daily peak) and outbreak duration. For each parameter configuration 244 we ran 1,000 simulations, amalgamating 50 batches of 20 replicates. Each batch of 20 replicates was 245 obtained using a distinct network realisation. Unless stated otherwise, we assumed the measures being 246 studied in each piece of analysis began from day 15 (i.e. the outbreak had been ongoing for two weeks). 247 We performed the model simulations in Julia v1.5.

Proportion of the workforce working from home 249 We first investigated the impact of specified fractions of the workforce working from home full time 250 (i.e. five days a week). Throughout, we assumed a 70% adherence to testing, tracing and isolation 251 measures. We initially tested the proportion of the workforce working from home (consistent across all 252 sectors) from none (value 0) to all (value 1) in increments of 0.1. We also looked at a situation where 253 subjectively chosen proportions of workers within each work sector work from home. We set this highest 254 in office based roles (70% working from home), at a moderate level in primary and manufacturing trade 255 occupations (for example, repair with 50% working from home and construction with 30% working 256 from home), lower again in sales and customer service roles such as retail (20% working from home) 257 and assumed those in the education, health, care home and social work sectors continued duties at the 258 workplace (0% working from home). Overall, approximately 35% of the workforce was working from 259 home.

Role of worker patterns 261 We explored two alternative choices related to the scheduling of workers being present at their usual 262 workplace: (i) synchronous work pattern -workers returned to work for a given number of days, but 263 all workers were scheduled to work on the same days; or (ii) asynchronous working pattern -workers 264 all returned to work for a given number of days per week, with the days of return randomly assigned 265 to each worker. We assumed a 70% adherence to testing, tracing and isolation measures. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 20, 2020. ; https://doi.org/10.1101/2020.11.18.20230649 doi: medRxiv preprint COVID-secure workplaces 267 We define a workplace to be 'COVID-secure' if measures have been taken to reduce the number of 268 contacts workers have and decrease the risk of transmission for those contacts that remain. We assessed 269 all workplaces undergoing changes to their contact structures, combined with a possible reduction in 270 transmission risk across work based contacts. We simulated all combinations of work team sizes of 2, 271 5 or 10, in conjunction with the scaling of the baseline work sector transmission risks (for both static 272 and dynamic work contacts) by a factor of either 0.25, 0.5, 0.75 or 1. We assumed that everyone within 273 a team was connected with each other, but with no one else at the workplace. We did not amend the 274 distributions of dynamic contacts occurring at the workplace. 275 We assumed all individuals were at the workplace five days a week (Monday to Friday). As well as the 276 baseline assumption of 70% adherence to testing, tracing and isolation measures, to inform the effects 277 brought about solely by COVID-secure measures (in the absence of other NPIs), we also considered 278 runs with 0% adherence (i.e. in the absence of) to test, trace and isolate measures.

Adherence to isolation, test and trace 280 Finally, we analysed the sensitivity of our model to the underlying adherence parameter, which defines 281 whether or not an individual will both adhere to isolation guidelines and engage with test-and-trace. 282 We sampled adherence between 0 and 1 in increments of 0.1. We assumed an identical adherence to 283 isolation restrictions independent of the cause (presence of symptoms, household member displaying 284 symptoms, identified as a close contact of an infected by contact tracing). For this analysis, we assumed 285 all individuals were at the workplace five days a week (Monday to Friday). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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Working from home 288 One potential control option, where implementable and appropriate, is to ask a proportion of the 289 workforce to work from home.

Assuming a 70% adherence to testing, tracing and isolation measures, we found that a greater pro-291 portion of the workforce working from home led to a lower R t value during the early stages of the 292 epidemic, flattening both the epidemic and proportion in isolation curves (Fig. 2, left column) . Work-293 ing from home is also effective in reducing the final size of the outbreak and total-isolation days, but 294 ineffective for reducing outbreak duration (Fig. 3) . 295 While one approach to implementing work from home measures is to have a standardised approach 296 across all work sectors, we demonstrated the flexibility of the model construction by also simulating 297 one example of a scenario with a differing proportion of workers within each work sector reverting to 298 working from home (labelled N-U in Fig. 3) . While our example configuration had about 35% of the 299 overall population of workers working from home, the uneven distribution across sectors meant the 300 returned summary statistic distributions and threshold event probabilities were actually comparable to 301 roughly 20% of workers in all work sectors switching to working from home from day 15. In addition, 302 the estimated outbreak duration distribution was similar to the scenario of all workers carrying on 303 working at the workplace.

Asynchronous work schedules 305 Rather than stipulating a proportion of the population to work from home full-time (five days a 306 week), we can instead consider the case where workers only work from home on specified days, and 307 are physically present at their workplace otherwise.

Workers present at the workplace for five days per work week (the default assumption) resulted in a 309 sustained rapid growth of the outbreak and a large epidemic peak. As one would expect, reducing the 310 number of days workers are present at the workplace results in a significantly smaller outbreak (Fig. 2 , 311 central and right columns). For asynchronous work patterns, we see fewer infections and a lower 312 infection peak when compared with scenarios where all workers work on the same days, particularly 313 for working weeks with the majority of days spent at the workplace (Figs. 4(a) and 4(b)). In contrast, 314 with four or five days of the working week being undertaken at the workplace, asynchronous work 315 patterns gave higher median and upper bound estimates for total isolation-days than synchronous 316 worker patterns (Fig. 4(c) ). We would also expect asynchronous worker patterns to deliver an extended 317 outbreak duration (Fig. 4(d) ).

When workers return to work on different working days, we see a reduced likelihood of a large outbreak 319 compared with when individuals all work on the same days, especially when workers spend a larger 320 number of days at their workplace. Specifically, for a scenario of spending five days at the workplace, 321 over half of the population were infected in 52% of our model simulations using a synchronised working 322 schedule, versus 41% of model simulations using asynchronous working schedules. We also observe 323 that the chance of each individual, on average, being required to isolate in excess of 1% of the year 324 was marginally reduced for one to three asynchronous working days at the workplace (Fig. 4(e) , 325 Table S7 ). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 20, 2020. ; Fig. 2 : Infectious case prevalence, isolation and R t temporal profiles under alternative worker practices and scheduling. We considered three work practice and scheduling assumptions: (left column) percentage of workers that work from home; (central column) synchronous work pattern; (right column) asynchronous work pattern. From day 15, test, trace and isolate guidance was introduced, with an adherence of 70%. For the statistics (row one) infectious case prevalence, (row two) proportion in isolation, and (row three) the effective reproduction number R t (the number of people, on average, each person that became infected at time t passed the virus onto), we present median temporal traces (solid lines), with the shaded regions in rows one and two representing the 50% prediction intervals. Lighter intensities correspond to: a higher fraction of workers working from home (ranging from 0 to 1; left column); a greater number of days per week being spent working from home rather than spent at the workplace (ranging from 0 to 5 days; central and right column).

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The copyright holder for this this version posted November 20, 2020. ; https://doi.org/10.1101/2020.11.18.20230649 doi: medRxiv preprint Table S5 for percentile summary statistics). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint and asynchronous (cyan) worker patterns. In all panels, we summarise outputs from 1,000 simulations (with 20 runs per network, for 50 network realisations). The white markers denote medians and solid black lines span the 25th to 75th percentiles. We give central and 95% prediction intervals in Table S6 . Table S7 for percentile summary statistics). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 20, 2020. ; https://doi.org/10.1101/2020. 11.18.20230649 doi: medRxiv preprint We assessed the impact of all workplaces undergoing changes to their contact structures, combined 328 with a possible reduction in transmission risk across workplace contacts. Inspecting runs with 70% 329 adherence to isolation and contact tracing based NPIs, for the tested combinations of work team size 330 and adjustments to transmission risk across workplace setting contacts, we found that smaller teams 331 and a greater reduction in transmission risk per contact led to a flattening of the temporal profile 332 of infectious prevalence Fig. 5 . The effect of team size was relatively small compared to that from 333 scaling the transmission risk, and was most pronounced when the latter did not occur. For very low 334 transmission risk settings, the team size appeared to have almost no effect. The relationship with the 335 proportion of people isolating over time was comparable (Fig. 6 ).

If we allow for larger work team sizes and lower magnitudes of reduction in transmission risk, there 337 was an increased probability of large outbreaks occurring (Fig. 7(a) ). In particular, reducing the 338 transmission risk by 75% led to no simulation runs with more than half the population of workers 339 becoming infectious. On the other hand, with work teams sizes of up to 10 people and no reduction in 340 work setting contact transmission risk, nearly half of all runs (48%) resulted in a cumulative infectious 341 case proportion in excess of 0.5.

We found there was less relative change in the estimated probability of an outbreak lasting longer 343 than 150 days ( Fig. 7(b) ), when considering the maximum work team size for unmodified transmission 344 risk (0.98 for work team sizes up to 2, 0.97 for work team sizes of up to 10) than when reducing the 345 transmission risk by 75% (0.87 for work team sizes up to 2, 0.93 for work team sizes of up to 10). 346 Furthermore, the smaller, shorter epidemics brought about by capping work team sizes to a maximum 347 of two people and a 75% reduction in transmission risk was reflected in reductions in the amount of 348 isolation required (Figs. 7(c) and 7(d), Table S8 ).

However, solely implementing COVID-secure guidance (i.e. capped work team size and potential re-350 duction in transmission risk across workplace contacts, but no use of isolation or contact tracing), had 351 a more severe effect on the projected outbreak size. With work teams sizes of up to 10 people and 352 no reduction in work setting contact transmission risk, all runs resulted in over half of the individuals 353 in the network becoming infected (Fig S9, Table S9 ). For the measure of outbreak duration, across 354 transmission risk scalings there were shorter epidemic tails when the permitted work team size was up 355 to 10 people, with probabilities ranging from 0.10 to 0.63, compared to a maximum work team size of 356 two (probability range 0.31-0.70) or five (probability range 0.22-0.68). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 20, 2020. ; Fig. 5 : Temporal profiles of the proportion of the population in an infectious state for twelve value combinations of COVID-secure workplace parameters. We display outputs for combinations of, from day 15, work team sizes being capped at 2, 5 or 10 people, paired with scaling the transmission risk in COVID-secure workplaces by 0.25, 0.50, 0.75 or 1.00, respectively. Also from day 15, trace, trace and isolate measures were introduced and had an adherence percentage of 70%. We assumed all individuals were at the workplace five days a week (Monday to Friday). Traces and regions in grey correspond to the period where no interventions were in place (up to day 15). The solid line gives the median trace. Filled regions depict the 50%, 90% and 99% prediction intervals (with dark, moderate and light shading, respectively).

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The copyright holder for this this version posted November 20, 2020. ; Fig. 6 : Temporal profiles of the proportion of the population in isolation under twelve value combinations of COVID-secure workplace parameters. We display outputs for combinations of, from day 15, work team sizes being capped at 2, 5 or 10 people, paired with scaling the transmission risk in COVIDsecure workplaces by 0.25, 0.50, 0.75 or 1.00, respectively. Also from day 15, trace, trace and isolate measures were introduced and had an adherence percentage of 70%. We assumed all individuals were at the workplace five days a week (Monday to Friday). Traces and regions in grey correspond to the period where no interventions were in place (up to day 15). The solid line gives the median trace. Filled regions depict the 50%, 90% and 99% prediction intervals (with dark, moderate and light shading, respectively).

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The copyright holder for this this version posted November 20, 2020. ; https://doi.org/10.1101/2020.11.18.20230649 doi: medRxiv preprint Table S8. 18 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted November 20, 2020. ; https://doi.org /10.1101 /10. /2020 Adherence to isolation guidelines and engagement with test-and-trace 358 Finally, we assessed the sensitivity of our model set-up to different levels of adherence. This applied 359 to both the adherence to isolation measures and engagement with test-and-trace. 360 With sufficiently high adherence, the introduction of test, trace and isolate measures alone was enough 361 to significantly decrease the size of the epidemic, with a swift decline in the effective reproduction 362 number R t to below 1 (Fig. 8) . However, this came at the cost of significantly more people being 363 in isolation at any one time, and the total number of isolation days. Both these effects were less 364 pronounced at lower adherence levels. 365 Unsurprisingly, when adherence to the NPIs was high we found that a lower proportion of the network 366 became infected, with a correspondingly lower epidemic peak (Figs. 9(a) and 9(b)). For even higher 367 levels of adherence, the smaller size of the outbreak offset the increase in isolation directly due to greater 368 adherence ( Fig. 9(c) ). When adherence was low, we observed a large, rapidly spreading outbreak. For 369 increased adherence, there was a relative decrease in the epidemic size and a slight slow down in spread 370 across the network, resulting in the expected duration of the outbreak becoming longer (Figs. 9(d) 371 and 9(e)). 372 Fig. 8 : Infectious case prevalence, isolation and R t temporal profiles under self-isolation and contact tracing NPIs. For the statistics (column one) infectious case prevalence, (column two) proportion in isolation, and (column three) the effective reproduction number R t (the number of people, on average, each person that became infected at time t passed the virus onto), we present median temporal traces (solid lines), with lighter intensity corresponding to a higher adherence to the interventions (ranging from 0 to 1). In columns one and two, shaded regions represent 50% prediction intervals.

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The copyright holder for this this version posted November 20, 2020. ; https://doi.org/10.1101/2020.11.18.20230649 doi: medRxiv preprint Table S5 for percentile summary statistics). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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In this study, we have developed a model to analyse the spread of SARS-CoV-2 in the working 374 population, considering the risk of spread in workplaces, households, social and other settings. We 375 have investigated the impact of working from home, temporally asynchronous working patterns and 376 COVID-secure measures upon disease spread and illustrated how strong adherence to NPIs is predicted 377 to interrupt transmission.

Under our selected model assumptions, 'switching off' network connections by having a significant 379 portion of the population of workers working from home was effective in reducing the final size of the 380 outbreak and total-isolation days; we also recognise that flattening the epidemic curve would typically 381 result in a prolonged outbreak duration with lower prevalence. It can be seen from UK data that 382 an instruction to work from home where possible to do so formed part of a collection of measures 383 that were effective in sending the initial wave of SARS-CoV-2 infection into decline [34] . Further, we 384 have demonstrated that a non-uniform adoption (of working from home) across work sectors will not 385 necessarily translate to outcomes equivalent to the overall fraction of the labour market who revert to 386 working from home. A sector-specific approach may be explored to determine optimal combinations 387 of work from home percentage across applicable sectors (where working from home is possible), whilst 388 maximising the overall proportion of workers able to attend the workplace.

Another approach to modifying work-associated mixing patterns is to alter the scheduling of when 390 workers attend the workplace. For asynchronous work patterns we observed fewer infections and a 391 lower infection peak. We postulate similar outcomes for flexible start and finish times that suits 392 an employee's needs. There are also indications some businesses envisage to retain flexible working 393 habits longer-term [35] , incorporating flexible work times and working from home [36] , which would 394 result in the percentage of the UK workforce reporting a flexible working pattern increasing above a 395 October-December 2019 estimate of 28.5% [37] . 396 It is clear that not all work sectors would be able to implement a work from home policy or allow 397 flexible, asynchronous work patterns. In April, during the first wave of infection in the UK, 46.6% 398 of respondents to a UK-based survey reported having done any work from home in the reference 399 week [38] . However, we have shown that the introduction of COVID-secure measures in the workplace 400 that reduce the number and transmission risk of contacts between workers can help to stem the spread 401 of the virus in the population, especially if other NPIs are not possible.

The use of these workplace-targeted interventions should be carefully considered, and the effect and 403 fallout from each weighed against each other. Every decision has an impact on people's lives and 404 livelihoods. In the event of enforced alterations to working practices, it is vital to consider harms to 405 businesses and to personal well-being and mental health, with those affected being fully supported. 406 We believe that a sector-specific combination of workplace-targeted policies could help to both slow 407 the spread of SARS-CoV-2 and reduce the negative impact to workers, as well as the people and 408 businesses that depend on them.

Prior modelling studies have indicated that nationally applied NPIs (such as social distancing, self-410 isolation upon symptom onset and household quarantine) may reduce the spread of SARS-CoV-2 [39-411 41] . Our analysis corroborates these findings, implying that high adherence to isolation and tracing 412 measures can break chains of transmission by reducing the quantity and riskiness of contacts. The 413 ultimate success of contact tracing operations is dependent on the rapid detection of cases and isolation 414 of contacts (for simplicity we applied a consistent two day turnaround time for this process, though 415 there is observed non-uniformity and temporal variation in these distributions [42] ). Given the burden 416 when tracing large numbers of contacts, there is the potential the system could be overwhelmed when 417 the incidence of new cases occurs at a rapid rate [43] . is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 20, 2020. ; https://doi.org/10.1101/2020. 11.18.20230649 doi: medRxiv preprint Nonetheless, multiple studies have demonstrated, through applying stochastic branching-process mod-419 els, that the use of backward contact tracing (as a complement to forward contact tracing) to identify 420 infector individuals and their other infectees can robustly improve outbreak control [44, 45] . Nat-421 urally, identification of infectors, and subsequent forward tracing of their contacts were they to be 422 identified, adds to operational pressures. These considerations need to be balanced against finite 423 resources, suggesting the use of a coupled health economic analysis to determine under what circum-424 stances backward contact tracing would be most efficient. Other operational considerations include 425 the adoption of digital approaches to enable the application of tracing at scale [46] .

Our data-driven approach to parameterise the work sector populations and contact structures high-427 lights the heterogeneities that are present in the system. However, there are characteristics of the 428 underlying contact structure that our model formulation does not presently capture, whose inclusions 429 may yield a better understanding of the impact of an infectious disease outbreak. We have not con-430 sidered clustering of individuals within an individual workplace to capture the fact that, for example, 431 individuals who share an office will be exposed to higher risk. We would expect this to have a stronger 432 effect upon transmission within larger workplaces. In addition, the risk of contracting COVID-19 at 433 work, and the risk of developing serious or fatal COVID-19 should infection occur, will also depend on 434 personal vulnerability [47] . Strong determinants of individual risk are the presence of comorbidities 435 and age, which could be correlated with job type. Furthermore, our system contained active workers 436 only, with children and the elderly not present. The susceptibility to infection and severity of clinical 437 outcomes generally differs in the youngest and eldest ages compared to those of adults. Thus, the in-438 corporation of age and risk stratification in an expanded network model and the consequential impact 439 of the disease dynamics amongst the population merits further investigation.

Another aspect we have not included here is the presence of other respiratory infections. Such an 441 extension would permit the study of test capacity requirements when levels of cough and fever are 442 high due to non-COVID-19 causes. This is especially of concern during the winter period, with 443 expectations of the national test and trace system being put under extra strain [48] . 444 Lastly, while we have informed our model based on UK data, the model may be applied to other coun-445 tries given the availability of the necessary data to parameterise the model. Modifying the framework 446 to other contexts that have contacts occurring across several reasonably well-defined settings (such as 447 school communities) we perceive as another viable extension.

Models of infectious disease transmission are one tool that can assess the impact of options seeking 449 to control a disease outbreak. Here, we have presented a network model to study epidemic spread 450 of SARS-CoV-2 amongst a population with layered contacts capturing multiple encounter settings, 451 including distinct work sectors. Our work demonstrates the potential uses of this choice of model 452 framework in generating a range of epidemiological measures, which may be analysed to assess the 453 impact of interventions targeting the workforce. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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Supporting Text S1

The process for generating the work and social contact layers of the network.

A description of the data underpinning the contact distribution assumptions.

Summary of the use of contact survey data to estimate the relative transmission risk across contacts between individuals occurring in household versus non-household settings.

Overview of simulation outputs in the absence of any interventions.

Supplementary results.

Summary statistics to support the figures.

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COVID-19 transmission in a university setting: a rapid review of modelling studies

High COVID-19 transmission potential associated with re-opening universities can be mitigated with layered interventions

Modelling SARS-CoV-2 transmission in a UK university setting

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