key: cord-0716370-4dew472b
authors: Baister, M. J.; McTaggart, E.; McMenemy, P.; Megiddo, I.; Kleczkowski, A.
title: COVID-19 in Scottish care homes: A metapopulation model of spread among residents and staff
date: 2021-08-27
journal: nan
DOI: 10.1101/2021.08.24.21262524
sha: fe9f45fbda84d9e860504de93369e4790ad89e8f
doc_id: 716370
cord_uid: 4dew472b

Care homes in the UK were disproportionately affected by the first wave of the COVID-19 pandemic, accounting for almost half of COVID-19 deaths over the course of the period from 6th March - 15th June 2020. Understanding how infectious diseases establish themselves throughout vulnerable communities is crucial for minimising deaths and lowering the total stress on the National Health Service (NHS Scotland). We model the spread of COVID-19 in the health-of NHS Lothian, Scotland over the course of the first wave of the pandemic with a compartmental Susceptible - Exposed - Infected reported - Infected unreported - Recovered - Dead (SEIARD), metapopulation model. Care home residents, care home workers and the rest of the population are modelled as subpopulations, interacting on a network describing their mixing habits. We explicitly model the outbreak's reproduction rate and care home visitation level over time for each subpopulation, and execute a data fit and sensitivity analysis, focusing on parameters responsible for intra-subpopulation mixing: staff sharing, staff shift patterns and visitation. The results suggest that hospital discharges were not predominantly responsible for the early outbreak in care homes, and that only a few such cases led to infection seeding in care homes by the 6th of March Sensitivity analysis show the main mode of entry into care homes are infections by staff interacting with the general population. Visitation (before cancellation) and staff sharing were less significant in affecting outbreak size. Focusing on the protection and monitoring of staff, followed by reductions in staff sharing and quick cancellations of visitation can significantly reduce future infection attack rates of COVID-19 in care homes.

the general population and staff sharing induces a network, connecting care homes in a 22 given community via their workers. This creates the potential for COVID-19 to spread 23 from one home to another; hence, investigation of this pathway is important. We find 24 it natural to describe this using a heterogeneous patch size metapopulation model 25 framework. 26 Very few models explore COVID-19 transmission at a community level and 27 explicitly include the unique dynamics in care homes. For example, in [5, 6] 28 agent-based models (ABMs) of single homes are used to investigate the impact of 29 testing strategies on the disease burden. A report by Nyguen et al. [7] uses an ABM to 30 investigate the impact on care home residents of various vaccine coverage, and staff interaction with the community and visitors. These models [5] [6] [7] do not assess 34 the relative impact of the different COVID-19 pathways into care homes. Nguyen et 35 al. [8] extend [6, 7] , using a hybrid ABM-System Dynamics model, to explore the 36 conditions under which visitation, heterogeneous care homes sizes, and the cohorting 37 of residents impacts COVID-19 outbreak severity. 38 Rosello et al. [9] model an individual care home with a stochastic compartmental 39 model, using multiple FOI's to capture COVID-19 pathways, including visitors, 40 hospital discharges, staff working at other homes, and staff infections from the 41 community. They find that importations of infections by staff from the community are 42 the main driver of outbreaks, and importation by visitors or from hospitals is rare, but 43 do not explicitly model disease spread throughout a network of care homes. In [10] 44 individual care homes and the general public are independent, deterministic SEIR 45 models, with a stochastic external FOI connecting the general public to each home. 46 This FOI depends on the prevalence of COVID-19 in the general public, and the size 47 of each home. Transmission rates in homes and in the general public do not vary over 48 time. In [11] , two weakly-coupled SEIR sub-models with time-dependent transmission 49 rates define the dynamics; one sub-model describes the general public and one 50 describes all care home residents in Stockholm as a single homogeneous group. Again, 51 a single FOI acts on the residents to capture infections from staff and visitors. The 52 models [10, 11] do not differentiate between, and therefore allow comparison of, the 53 COVID-19 pathways into care homes. Bunnik et al. [12] use a compartmental 54 metapopulation model to explore the trade-offs between increasing protection for a 55 "vulnerable" population and relaxing restrictions for the "non-vulnerable" after the 56 first lockdown in Scotland. They use time-dependent transmission rates with three 57 metapopulation groups; vulnerable, shielders and general public. We extend and apply 58 the methodology of [12] in our model, investigating protection to a vulnerable group 59 (care home residents) in ways other than shielding. 60 We construct a SEIARD compartmental metapopulation model to describe the 61 first wave of COVID-19 in a health board in Scotland. The population is divided into 62 groups of care home residents, staff, and general public. Our care home resident group 63 are not a single homogeneous unit as in [11, 12] but are separate units, creating a 64 refined spatial/geographic structure. These units are not independent as in [10] but virus (and infected) but not yet infectious; Infectious and reported (I), infectious 80 individuals that have been identified with a positive test; Unreported infectious (A), 81 infectious individuals that have not been identified with a positive test; Recovered (R), 82 those who had COVID-19 and recovered; and Dead (D), those who died from their 83 illness. Symptomatic and asymptomatic individuals are not modelled explicitly; 84 instead, asymptomatic infections contribute towards a reduction in the reporting rates. 85 This model is illustrated in Fig 1 (a) . The metapopulation structure represents the population of the NHS Lothian health 87 board in Scotland. We distinguish between care home residents, care home workers 88 and the general population, modelling the m = 109 care homes for older adults in NHS 89 Lothian [14] . The j th home has a resident subpopulation, C j , with a corresponding 90 care home worker subpopulation, W j . The general population is encapsulated by the 91 subpopulation G. Each care home includes the same number of residents, a simplifying 92 assumption made due to lack of publicly available data on care home sizes in Lothian. 93 We also assume the worker subpopulations are the same size as residents' [15] .

Each node of the network, i ∈ X := {C 1 , C 2 , ..., C m , W 1 , W 2 , ..., W m , G} with 95 |X| = n, is described in terms of the SEIARD compartmental model with equations:

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The copyright holder for this preprint this version posted August 27, 2021. ; https://doi.org/10.1101/2021.08.24.21262524 doi: medRxiv preprint Susceptibles in subpopulation i (S i ), are infected with a FOI Λ i , and moved to the 97 exposed class (E i ). After a non-infectious latent period of λ days, they become 98 infectious, testing positive at a reporting rate of r i . These identified infections move to 99 the class I i . Hence, any unidentified infections, A i , occur at rate 1r i . After τ 100 infectious days, a person either recovers or dies at the rate µ i . For simplicity, and 101 considering the short span of time the model is designed to describe, non-COVID 102 related deaths are not considered. For similar reasons, we do not include a birth rate 103 or admission of new residents to care homes from the general population.

The constant reporting rate r i differs between the C, W and G populations, but is 105 consistent within these subpopulations. The parameters τ and λ describe the 106 infectious period and latency period, respectively, and are assumed to be the same 107 across all subpopulations. Mortality rates, µ i , vary by subpopulation, reflecting the 108 positive association of serious outcomes of COVID-19 with age [16] . As we are 109 modelling over a period of 4 months (approx. first wave), and immunity after 110 COVID-19 infection lasts as long as 5 months [17] [18], we do not consider a transition 111 from Recovered to Susceptible. 112 We model visitation to each care home by multiplying the proportion of the March 2020, each resident has one visitor per day [6] . Then γ(t) drops to 0, reflecting 116 the policy change to essential visitation only [14, 19] . γ(t) is described by the function 117

with the shape of a sigmoidal logistic function. Thus, visitation is described by

. Given that visitation drops to 0 in the first 2 weeks of the 120 simulation, the changes in population size over that time is negligible, hence we can sharing (use of bank or agency staff) [20, 21] . Therefore, a constant proportion of each 131 homes' assigned workers, ε, are exchanged between homes. We refer to this as staff 132 sharing. We have made the simplifying assumption that the staff sharing network has 133 a topology of a circle, whereby the shared staff for home j are split evenly between 134 homes j − 1 and j + 1. We assume care home residents do not leave their homes.

Interaction across subpopulations is heterogeneous and is described in terms of 138 active individuals who can mix with others. The proportion from subpopulation i who 139 travel to, and mix with, subpopulation k is t ik . The effective population size of 140 subpopulation k, given that others have travelled to it and some people from k have homes, and visitors. The general population consists ofN G (t) people; this includes all 146 the staff not at work and the non-visiting general population.

Our specific time-share assumptions are represented visually as a directed, 148 weighted network in Fig 1 (b) . The corresponding weighted adjacency matrix, the 149 travel/time-share matrix, is T ∈ R n×n , whose [i, j] th element is t ij . The rows and 

,

Disease transmission in the model is assumed to be frequency-dependent. The FOI 156 integrates which infections occur to whom, from whom and where the infection takes 157 place, as in [22, 23] . The FOI acting on subpopulation i, Λ i (see Equation 5 ), accounts 158 for the different groups' people from i mix in over a day and who they encounter. It is 159 most easily understood by considering Λ i S i :

The set of effective populations that subpopulation i travels to is L i , consistent with the non-zero elements in the i th row of the travel matrix T . At effective August 24, 2021 6/23 . CC-BY 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 August 27, 2021. ;  population k, there is t ik S i susceptible individuals from i. At k there will also be t jk (I j + A j ) infectious people from j who have travelled to k. The transmission rate between subpopulation j and i is β ji (t). Therefore,

is the number of new daily infections in i caused by people from j at the effective 161 population k. 162 The transmission rates β ji (t) allow us to represent heterogeneous interaction 163 patterns of individuals between and within different subpopulations. They incorporate 164 the transmission dynamics of COVID-19 changing over time and location, for example, 165 through lockdowns or other changes in behaviour [22] . We write β ji (t) =

describing the transmission rate β ji (t) between subpopulations j and i, with the 167 reproduction rate, R(t) ji , divided by the infectious period, τ . The contact rate and 168 infection probability between subpopulations i and j is captured by R(t) ji . We assume 169 only the transmission rates between and within the subpopulation types (residents C, 170 workers W, general public G) differ. Therefore, the transmission rates are arranged in 171 a symmetric partitioned matrix β ∈ R n×n whose [j, i] th element is β ji (t). The rows 172 and columns of β are in the order of

For simplicity, we have assumed that the resident-resident, worker-resident, and τ , the transmission rates are driven by Ω y . The matrix 181 notation above is the same as for the travel matrix T .

Data & parameter calibration 183 We used data from the network of care homes in NHS Lothian [14] complemented by 184 Public Health Scotland Open Data, breaking down COVID-19 cases and deaths per 185 health board [24, 25] , to inform and calibrate our model. Parameters were found using 186 a mixture of methods, as indicated in Table 1 , including literature search, sensitivity 187 of results, and rigorous fit based on minimising the sum of squares of residuals.

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The copyright holder for this preprint this version posted August 27, 2021. ; https://doi.org/10.1101/2021.08.24.21262524 doi: medRxiv preprint certificate (either as the underlying cause or as a contributory factor) [25] . 199 We assume different reporting rates in the community and in care homes. A

Scottish population study between 10 th April to 15 th June [31] estimated a combined 201 adjusted seroprevalence across their study period (first wave = 10 th April to 15 th 202 June) of 4.3% (95% CI 4.2%-4.5%). As of the week beginning 15 th June 2020, there 203 had been 18,077 positive tests [24] , which as a percentage of Scotland's population 204 (2019 census [27] ) is ∼ 0.33%. We use this information to assume a constant reporting 205 rate in the first wave for the general public of r G = 0.33/4.3 ∼ 0.077.

In Scotland, the policy from the start of March to 16 th April 2020 was to test only 207 the first few symptomatic care home residents, and afterwards, was to test all 208 symptomatic residents [14] . Assuming when there is an outbreak in a home, 40% of 209 the residents end up infected (40% incidence) [28, 29] . Given 48 residents per care 210 home, until 16 th of April we assume a reporting rate of (a few tested)/(total infected) Until the 17 th of April, we assume the staff reporting rate was the same as the 220 general public (0.077). From then on, we assume the care home testing policy change 221 (on the 17 th of April) extended to their staff [14] , and the reported percentage of cases 222 was 83% (the symptomatic proportion [30] ). Our weighted average and constant staff There are two constant death rates in our model: a resident death rate (µ C ) and a 225 general population death rate (µ G ). We assume care home staff to have the same 

The ω G end and ω C end parameters were found to control the timing of peak infection 234 for both the care home residents and general population, leading to the assumed 235 values in Table 1 . The value of ω W end was assumed to be equal to ω C end .

The ω G rate and ω C rate parameters have been assumed to be 0. [14, 19] .

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The ω G low value was set to 0.6, the estimated R t after the first wave in Scotland [34] . 244 Due to the uncertainty in the timing of the drop and the value R t peak, we did not 245 use this source for the ω G high and ω G end parameters. We then assumed that the value of 246 ω C low and ω W low were also 0.6. We have made the simplifying assumption of ω γ low = 0, to 247 avoid the complications of modelling end-of-life visitation in care homes. we assume that all homes operate under two 12 hour shifts per day, i.e., δ = 0.5.

Other shifts are explored in the sensitivity analysis. 259 We make a number of assumptions about the population initially infected. Workers 260 were not initially infected in the model. In the general population, we assume an equal 261 amount of exposed and infected individuals (with and without symptoms) i.e.,

were seeded with infections, representing introductions such as hospital discharges. To 264 account for the delay in infections at the start of the pandemic in care homes 265 compared to the general population, as seen in the data Fig 2, we assume for all 266 j ∈ {1, . . . , m}, I Cj (0) = A Cj (0) = 0. We seeded the homes so that initially infected 267 homes lay equally spaced on the circle sharing structure (see Fig 1 (b) ). If a home is 268 seeded then we assume E Cj (0) = 1, and if not, E Cj (0) = 0.

Data fit 270 The model includes many uncertain parameters (see Table 1 ). These parameters were 271 free to vary subject to constraints based on a combination of assumptions and 272 information from the literature. We used the method of least-squares, aggregating the 273 error of model output against the four data sets for NHS Lothian cases and deaths 274 and choosing the parameter set which minimised this error. The data for NHS Lothian 275 population cases and care home cases were in the form of daily and seven day averages 276 respectively. The death data for both the NHS Lothian population and care homes 277 were in weekly counts. To make the fitting consistent, we transformed the daily and 278 seven day average data into weekly data for conformity (Fig 2) . The constraints on 279 the parameters in our model, described in the previous section, left 6 free parameters 280 for formal fitting. Their ranges used for the data fit are shown in Table 2 . 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 August 27, 2021. ; https://doi.org/10.1101/2021.08.24.21262524 doi: medRxiv preprint To investigate the question of how many care homes were exposed at the start of 282 the pandemic, we ran the fitting separately for H seeded fixed at 1 through 10. We 283 simulated the model over 21,060 combinations of the remaining parameters to calculate 284 the least-squares, for each value of H seeded . We investigate the distribution of the 285 parameters in Table 2 in the top ten best fitting scenarios, for each value of H seeded .

After identifying the parameter set that minimises the least-squares, the base case 288 (Table 2) , we performed a sensitivity analysis. We measured the change in each 289 population's deaths when shifting individual parameters in Table 3 Table 3 . Parameters involved in the sensitivity analysis. Sensitivity shift is the unit of change used for each parameter from its base case. These values were chosen to measure the change in each population's deaths to small perturbations of individual parameters from it's base case.

Sensitivity shift

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The model captures the key features of the COVID-19 related cases and deaths in 297 both care home and general populations, Fig 2. The minimum aggregate least-squares 298 error was 33,042, with our model predicting 3,165 total cases and 817 total deaths 299 compared to the total 3,123 cases and 709 deaths in the data. The average difference 300 between data and predictions was 3.5 cases/deaths per week. In care homes we 301 predicted 871 cases and 411 deaths compared to 903 cases and 423 deaths in the data. 302 Our model does not predict the initial jump in deaths in care homes due to our 303 assumption that infection reporting is constant. Further, our model overestimates the 304 number of deaths for all populations despite a good fit for the cases, as the calculation 305 of death rates is tied to the reporting rates. . CC-BY 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 August 27, 2021. ; In order to assess the initial level of care home exposure to virus, we consider the 313 quality of fit as a function of H seeded . The minimum sum of squares of residuals takes 314 the shape of a parabola, with a minimum at H seeded = 4, see Fig 4. This suggests that 315 a relatively small number of homes were initially exposed to COVID-19. The optimal choice (in terms of the least-squares criterion) for the parameters as 317 used in the data fit (Table 2) is relatively stable with respect to changes in H seeded , 318 Fig 5. The pre-lockdown reproduction rate in care homes, ω C high , appears stable in the 319 range of 4.5 to 4.7, changing for 10 homes seeded with the optimal value lowering to . CC-BY 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 August 27, 2021. ; https://doi.org/10.1101/2021.08.24.21262524 doi: medRxiv preprint of the range of 4 to 8. The distribution for ε changes for H seeded = 10 , with the 325 optimal value going back up to 0.5. This coincides with the rise in E G (0) and the 326 substantial fall in ω C high . This points to the correlation between these 3 parameters.

Similarly, there is a lot of uncertainty in the value of pre-lockdown visitation, ω γ high , 328 with an optimal choice for every value considered in our fitting as we vary H seeded .

This uncertainty highlights that the parameters in our model are highly correlated. As 330 seen in Fig 6 and Fig 7, Fig 5 can also be seen to hint at how effective these 331 parameters are at affecting the outcome of the model. For example, the variability in 332 the chosen value of ε and ω γ high can also be attributed to the relatively small affect 333 they have on the model outcome. . CC-BY 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 August 27, 2021. ; https://doi.org/10.1101/2021.08.24.21262524 doi: medRxiv preprint (Table 1) . Each parameter is increased or decreased from its base case value by the corresponding 'sensitivity shift' value in Table 3 .

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The copyright holder for this preprint this version posted August 27, 2021. ; https://doi.org/10.1101/2021.08.24.21262524 doi: medRxiv preprint Changing staff sharing, ε, and staff shift patterns, δ, the final number of resident 346 deaths do not change significantly, apart from when δ ∼ 1 (Fig 7) . When considering 347 δ = 1, we should also restrict ε = 0, as staff living in care homes would not be shared 

To identify and rank the key modes of ingress into care homes, we used a combination 360 of modelling, data fit and simulations. We find that homes are more at risk to 361 outbreaks through staff infections from the general population, relative to visitation or 362 staff sharing. We also find that outbreaks were not significantly driven by hospital 363 discharges. These findings coincide with the results from Rosello et al., who used a 364 stochastic compartmental model on single care homes in England [9] . We additionally 365 find that that the drop in within-home reproduction rate was 3 weeks behind that of 366 the general 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 August 27, 2021. ;  away from both care home residents and the general population whilst they are not at 377 work would be effective, e.g., organisation of accommodation for care home workers [3] . 378 From our model, we see the most effective solution to keeping care homes safe from 379 infection is to focus on the pathway from general population to workers to residents.

Eliminating staff sharing did not eliminate outbreaks in our model simulations, 381 suggesting that this was not the primary route of infection entering homes. Supporting 382 the literature [3, 20, 37] , reducing staff sharing does reduce the outbreak severity; our 383 model does suggest, however, that the impact is low. This conclusion is limited due to 384 our assumption of the circle sharing contact structure, which in turn reflects limited 385 data availability regarding the contact structure of the care home industry in Lothian 386 (due to commercial sensitivity). A different contact structure could result in staff 387 sharing leading to more/less exportation of infection from homes with outbreaks. A 388 more thorough examination on the contact-structure of this system and how that 389 impacts disease spread dynamics would be an important contribution to the literature. 390

A reduction in visitation reduces resident deaths, as speculated in [3] . Our model 391 predictions support findings that visitation to care homes was not the driving cause of 392 infection in care homes [38] . Since visitation was banned, the evidence for visitation 393 causing outbreaks is limited. Investigation with constant visitation would be necessary 394 to see how the outcome would be different if visitation did not change at all; this was 395 not the focus of our investigation. 396 Our predictions suggest that after the nation-wide lock down, R t within care 397 homes dropped three weeks after it did in the wider population. Several possible 398 explanations exist, including differences in testing availability or testing strategies and 399 the difficulty in controlling care home resident interactions to lower disease 400 transmission. Dropping care homes' reproduction rate 1 day earlier, results in a 10% 401 reduction in resident and worker deaths. Therefore a more thorough investigation into 402 the delay between the general populations' and care homes' reproduction rate is 403 necessary to aid closing this gap in future outbreaks.

The data fit suggests that there were a low number of care homes infected at the 405 beginning of the first wave (H seeded = 4). These initial infections could represent 406 hospital discharges or any other pathway. The result supports the claim from a report 407 on English care homes that resident discharges from hospitals were not the primary 408 cause of care home outbreaks [39] . The hospital discharges are only included as initial 409 care home infections, H seeded . In reality, discharges continued during the first 410 wave [14] and more detailed data will be needed to address this problem. 411 We made a number of simplifying assumptions. Our model does not explicitly 412 account for the variation in susceptibility with age [40] . It is only implicitly addressed 413 by considering different values of β within and outwith of care homes, while keeping 414 the staff and general population homogeneous. Due to the unavailability of data 415 regarding care home worker infections, we expressed worker transmission rates in 416 terms of transmission rates for care home residents and the general population. We 417 assumed the resident-resident and resident-worker transmission rates were equal.

However, contacts between care giving staff and residents are likely more frequent and 419 closer than between residents. On the other hand there may be more adherence or 420 better knowledge of how to use PPE among staff. Also, contact between residents 421 could be reduced more easily during the pandemic [3] . . CC-BY 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 data fit was achieved by minimising the aggregated sum of squared error for 423 each of the four time-series. This method requires the errors to be independent, follow 424 a normal distribution and for the variance to be constant. With the data, we could 425 not estimate the variance over time. To mitigate the effect of the differing variance of 426 the data sets, we shifted the four time-series to the same scale, this being weekly 427 cases/deaths.

The size of individual care homes is believed to be the main factor that influences 429 the likelihood of a care home outbreak [14, 20, 41] . Larger homes typically have more 430 staff and therefore a higher chance of experiencing outbreak before the smaller ones.

In our model we assume a uniform home size in order to keep the model generic. As a 432 result (and since the model is deterministic) COVID-19 enters all modelled care homes 433 concurrently, which may result in underestimation of the initial rate of spread. An 434 obvious extension of the paper would be to consider various sources of heterogeneity, 435 including size.

The National Records Scotland death data used were the dates of death 437 registration, not the date of death. This is limiting, as we are an average of 3 days 438 behind in the prediction of deaths [25] . The data for care home resident deaths 439 includes deaths in hospital; including nosocomial infections, which we do not take into 440 account into our model. We expect this not to limit the interpretation of our results, 441 considering hospital deaths of care home residents make up approximately 5% of the 442 total care home resident deaths [25] . 443 We do not distinguish explicitly between symptomatic and asymptomatic 444 individuals, as in (A) there are people with symptoms that would have been missed by 445 testing. However, asymptomatic infections implicitly affect this model's reporting 446 rates. We do not explicitly model self-isolation or any behavioural change after 447 infection, nor changes in reporting. Reporting differed over time, especially in the 448 early weeks of the pandemic when testing was scarce; in care homes, the national 449 policy was to test only the first few symptomatic residents [14] . into "super spreader" events in care homes [35] and their effect on epidemic response. 456 Finally, this work focuses on disease dynamics over the course of the first wave, it 457 would be interesting to model this system for future waves and to incorporate the 458 implementation of vaccinations. Extending this system to the rest of Scotland or even 459 the entirety of the UK would be a clear extension of this work. . CC-BY 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 August 27, 2021. ; https://doi.org/10.1101/2021.08.24.21262524 doi: medRxiv preprint sharing, are our recommendations for an effective reduction in outbreak size. Our 

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The authors thank Public Health Scotland for their support, and Prof. Bruce Guthrie 475 (University of Edinburgh) for sharing the Lothian care home data. EMT has been