key: cord-0845161-0vha3dkc
authors: Knock, E. S.; Whittles, L. K.; Lees, J. A.; Perez-Guzman, P. N.; Verity, R.; FitzJohn, R. G.; Gaythorpe, K. A.; Imai, N.; Hinsley, W.; Okell, L. C.; Rosello, A.; Kantas, N.; Walters, C. E.; Bhatia, S.; Watson, O. J.; Whittaker, C.; Cattarino, L.; Boonyasiri, A.; Djaafara, B. A.; Fraser, K.; Fu, H.; Wang, H.; Xi, X.; Donnelly, C. A.; Jauneikaite, E.; Laydon, D. J.; White, P. J.; Ghani, A. C.; Ferguson, N. M.; Cori, A.; Baguelin, M.
title: The 2020 SARS-CoV-2 epidemic in England: key epidemiological drivers and impact of interventions
date: 2021-01-13
journal: nan
DOI: 10.1101/2021.01.11.21249564
sha: 8045a351f6248a2eba663e566edde997bc003c35
doc_id: 845161
cord_uid: 0vha3dkc

We fitted a model of SARS-CoV-2 transmission in care homes and the community to regional surveillance data for England. Among control measures implemented, only national lockdown brought the reproduction number below 1 consistently; introduced one week earlier it could have reduced first wave deaths from 36,700 to 15,700 (95%CrI: 8,900-26,800). Improved clinical care reduced the infection fatality ratio from 1.25% (95%CrI: 1.18%-1.33%) to 0.77% (95%CrI: 0.71%-0.84%). The infection fatality ratio was higher in the elderly residing in care homes (35.9%, 95%CrI: 29.1%-43.4%) than those residing in the community (10.4%, 95%CrI: 9.1%-11.5%). England is still far from herd immunity, with regional cumulative infection incidence to 1st December 2020 between 4.8% (95%CrI: 4.4%-5.1%) and 15.4% (95%CrI: 14.9%-15.9%) of the population.

We use a mathematical model of SARS-CoV-2 transmission to reproduce the first two 49 waves of the epidemic across England's seven NHS regions and assess the impact of 50 interventions implemented by the UK government. We analyse the epidemic from 51 importation of SARS-CoV-2 into each region to the 2 nd December 2020: encompassing the 52 first national lockdown from March -May, the interventions implemented as COVID-19 53 those who died in ICU, those who later died in stepdown care and those who were 163 discharged following stepdown care ( Figure 3F ). Among patients over 65, we found the 164 probability of admission to ICU decreased with increasing age. Severity of COVID-19 165 increases with age, but for older patients and those with most severe illness, the benefit of 166 ICU admission, ventilation and the corresponding prognosis may not be better than with 167 oxygen therapy in a general ward (12). Thus, older and more severely infected patients may 168 be directed to care on a general ward rather than admitted to ICU. 169 170 We used estimates of clinical progression to parametrise the transmission model, enabling 171 us to infer temporal and regional differences in disease severity, informed by local 172 demography, observed daily hospital admissions, bed occupancy and deaths. We measured 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 January 13, 2021. Shaded bands depict 95% CrI and interquartile ranges, points depict medians.

Regional variation in the population age distribution did not fully account for differences in 206 severity, with London still experiencing lower mortality when stratified by age ( Figure 4A-B) . 207

The oldest age group (80+) in London had an IFR of 6.1% (95% CrI: 5.2%-6.8%) compared 208 to 12.7% (95% CrI: 10.8%-14.3%) in the North West. 209 210 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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We estimated temporal trends in the IFR for England, by weighting regional estimates by 211 incidence and population demographics. At the start of the first wave, the national IFR was 212 1.25% (95% CrI: 1.18%-1.33%) ( Figure 4E ), consistent with earlier reports from serology 213 data alone (13). The national IFR initially appeared to increase, as transmission widened 214 from London to regions with older populations and greater disease severity. Over the first 215 wave, the proportion of hospital admissions resulting in death decreased, due to 216 improvements in clinical management and alleviation of capacity constraints (14), leading to 217 a national IFR of 0.77% (95% CrI: 0.71%-0.84%) by the end of the first wave. The 218 magnitude of the relative reduction in IFR over time varied between regions, from 36.5% 219 (95% CrI: 26.5%-47.5%) in the North West to 64.6% (95% CrI: 58.6%-68.8%) in London. 220

The IFR was greater among care home residents (35.9%, 95% CrI: 29.1%-43.4%) than in 222 the 80+ in the community (10.4%, 95% CrI: 9.1%-11.5%, Figure 4C ). Many care home 223 residents did not transfer into hospital, and instead died in the facilities where they lived, so 224 conversely the IHR was lower in care home residents (19.1%, 95% CrI: 11.5%-26.8%) than 225 in those aged 80+ in the community (51.1%, 95% CrI: 47.6%-54.3%). We present national 226 estimates of severity at the end of the second wave, stratified by age and care home 227 residency in Table S9 . 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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The proportion of care home residents ever infected with SARS-CoV-2 was 13.7% (95% CrI: 256 10.7%-16.7%), much higher than the 4.2% (95% CrI: 4.0%-4.4%) estimated in >80-year 257 olds living in the community. This difference was consistently observed across all regions 258 ( Figure 5H ). Regional differences in care home attack rates mirrored the patterns seen in the 259 general community, with regions with larger community epidemics also experiencing larger 260 care home epidemics ( Figure 5I ,J). 261 262

We explored counterfactual intervention scenarios and examined the potential impact on 264 mortality of initiating the first national lockdown one week earlier or later; ending that 265 lockdown two weeks earlier or later; and 50% more or less restricted care home visits 266 throughout the epidemic ( Figure 6 ). 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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The timing of the initial national lockdown was crucial in determining the eventual epidemic 276 size in England. Locking down a week earlier could have reduced the first wave death toll 277 (up to 1 st July 2020) from 36,700 to 15,700 (95% CrI: 8,900-26,800) while delaying 278 lockdown by a week would have increased the deaths to 102,600 (95% CrI: 66,400-279 154,800) ( Figure 6A , D). The impact varied by region, with regions with less established 280 epidemics at the time of the first lockdown more sensitive to the timing of the intervention 281 ( Figure S10 ). Locking down a week later may have increased deaths, with large variability 282 by region, from 105% in London to 274% in the Midlands but with very large uncertainty 283 ( Figure S9 ). Initiating a lockdown to interrupt the exponential growth phase of an epidemic 284 has a much greater impact on reducing total mortality than extending an existing lockdown. 285

Due to this asymmetry, relaxing the lockdown measures two weeks earlier (respectively 286 later), could have increased deaths by 9,300 (95% CrI: 700-17,000) (respectively prevented 287 9,800 (95% CrI: 7,400-12,100) deaths) prior to 2 nd December ( Figure 6B, D) . 288

We also explored counterfactual scenarios varying the level of visit restriction in care homes 290 and estimated that reducing contact between the general population and care home 291 residents by 50% could have reduced care home deaths by 44% (95% CrI: 17%-64%) 292 ( Figure 6C) 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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We estimate intense transmission in care homes even during the first national lockdown 303 when Rt eff in the community was well below one in all regions ( Figure 2 ) (18-20). Combined 304 with our counterfactual analysis of restricting visits ( Figure 6) Here we provide updated severity estimates based on multiple contemporary data streams. 315

We estimate considerable regional heterogeneity in severity, broadly consistent in the 316 general population and in care homes for IFR and IHR. London experienced the lowest 317 severity even after adjusting for its younger population. The estimated two-fold reduction 318 over time in IFR ( Figure 4 ) cannot be explained solely by the introduction of dexamethasone 319 which reduces mortality amongst ICU patients (28), but rather a combination of factors 320 including improvements in clinical management, greater experience in treating patients in 321 ICU, and alleviation of capacity constraints (14, 29) . 322 323 Our analysis shows large regional variation in burden, especially in the first wave. This is 324 likely due to the pattern of seeding and the timing of lockdown relative to how advanced 325 each region's epidemic was ( Figure 1A ). Our counterfactual scenarios of initiating the first 326 national lockdown one week earlier or later highlight the importance of early interventions to 327 reduce overall mortality ( Figure 6 ). 328 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The extent and duration of infection-induced immunity to SARS-CoV-2 and its relationship to 330 seropositivity remains unclear. Related seasonal coronaviruses induce immunity that wanes 331 in one or two years (30), though antibody titres following SARS-CoV-1 infection appear to 332 decay more slowly (31). Our estimated cumulative incidence over time ( Figure 5 ), strongly 333 supports the hypothesis that the epidemic decline after the first national lockdown was due 334 to NPIs, with immunity playing a minimal role (32). Population-level immunity was insufficient 335 to prevent a second wave of infection in any region (Figure 1) , illustrated by the increase in 336 reported cases and deaths which prompted the second national lockdown (33). 337

With the authorisation of the first SARS-CoV-2 vaccines in December 2020, we are now 339 entering a new phase in the control of the COVID-19 pandemic. However, our estimates of 340 current population immunity are low, with regional cumulative attack rates ranging from 4.8% 341 to 15.4%, therefore any vaccination campaign will need to achieve high coverage and high 342 levels of protection in vaccinated individuals to allow NPIs to be lifted without a resurgence 343 of transmission. While vaccinating the most vulnerable age and risk groups will considerably 344 reduce the burden of COVID-19, a large proportion of younger age groups may also need to 345 be vaccinated to reach the immunity threshold for control. Our high estimates of 346 transmission in care homes imply that vaccine uptake there will need to be especially high, 347 particularly if vaccine efficacy is lower amongst older age groups. 348

We make a number of simplifying assumptions in our analysis. First, due to the 350 compartmental nature of our model, we do not explicitly model individual care homes, rather 351 the regional care home sector as a whole. However, as care home workers may work across 352 multiple facilities leading to within and between care home transmission, we do not expect 353 the simplification to substantially affect our conclusions. Similarly, we do not model individual 354 households or transmission within and between them. When assessing the impact of NPIs 355 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint on transmission we therefore capture population averages, rather than the contribution of 356 household and non-household contacts. Second, hospital-acquired infections may have 357 contributed to overall transmission, especially around the peak of the epidemic, and to 358 persistence of infection in England over the summer months (34, 35). Our model does not 359 explicitly represent nosocomial transmission; therefore such effects will be encompassed 360 within our regional Rt eff estimates. Third, each data stream was subject to competing biases, 361 which we statistically accounted for as far as possible (supplement section 1.1.2). A key 362 strength of our evidence-synthesis approach is that we do not rely on any single data 363 source, combining multiple perspectives to provide a robust overall picture of the epidemic. 364 Finally, we model the epidemics in each NHS region in England independently without 365 accounting for spatial effects across regional boundaries, or spatial heterogeneity within 366 regions. This spatial scale was determined by the data and reflects limited movement 367 between regions due to travel restrictions but does allow for movement within regions. 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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The copyright holder for this this version posted January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint for-retail-to-reopen-in-june). 568

GOV.UK, Pubs, restaurants and hairdressers to reopen from 4 July -GOV.UK, 569 (available at https://www.gov.uk/government/news/pubs-restaurants-and-570 hairdressers-to-reopen-from-4-july). 571 53.

GOV.UK, Eat Out to Help Out launches today -with government paying half on 572 restaurant bills -GOV.UK, (available at https://www.gov.uk/government/news/eat-out-573

to-help-out-launches-today-with-government-paying-half-on-restaurant-bills). 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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The copyright holder for this this version posted January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint We thank all the colleagues at Public Health England (PHE) and frontline health 636 professionals who have driven and continue to drive the daily response to the epidemic, but 637 also for providing the necessary data to inform this study. This work would not have been 638 possible without their dedication and expertise. The use of pillar 2 PCR testing data was 639 made possible thanks to PHE colleagues and we extend our thanks to Dr Nick Gent and Dr 640

André Charlett for facilitation and their insights into these data. The use of serological data 641 was made possible by colleagues at PHE Porton Down, Colindale, and the NHS Blood 642

Transfusion Service. We are particularly grateful to Dr Gayatri Amirthalingam and Prof Nick 643

Andrews for helpful discussions around these data. We also thank the entire Imperial 644

College London Covid-19 Response Team for their support and feedback throughout. This 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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The copyright holder for this this version posted January 13, 2021. Results ......................................................................................... 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 January 13, 2021. reporting, as well as being influenced by capacity and logistical constraints. These factors 49 are further complicated by the nature of SARS-CoV-2 transmission, whereby a substantial 50

proportion of infected individuals develop very mild symptoms, or remain asymptomatic, but 51

are nonetheless able to infect others (1). In this section, we describe the data used in our 52

analyses, give details on the dynamic transmission model, and present the methods used for 53

fitting the model to the various data sources, accounting for the inherent biases in those 54 data. 55 56

Here we detail the datasets used to calibrate the model to the regional epidemics. We fitted 58 our model to time series data spanning 16th March 2020 to 2nd December 2020 (inclusive), 59

using the data available to us on 14th December 2020, by which point the effect of 60 remaining reporting lags would be minimal. 61 62

We use healthcare data for each NHS region from the UK Government Dashboard 64

(supplementary data files: data_rtm.csv, columns: phe_admissions, phe_occupied, 65 phe_patients) (2). 66

For admissions data, we use the daily number of confirmed COVID-19 patients admitted to 67 hospital, which includes people admitted to hospital who tested positive for COVID-19 in the 68 14 days prior to admission and inpatients who tested positive in hospital after admission, 69

with the latter being reported as admitted on the day prior to their diagnosis. 70

For ICU bed occupancy, we use the daily number of (confirmed) COVID-19 patients in beds 71

which are capable of delivering mechanical ventilation. 72

For the occupancy in general (i.e. non-ICU) hospital beds, we use the daily number of 73 confirmed COVID-19 patients in hospital beds with ICU occupancy subtracted. 74

We use the number of deaths by date of death for people who had a positive COVID-19 test 76 result and died within 28 days of their first positive test provided Public Health England. 77

These can be found on (2). We also use the number among these deaths occurring in 78 hospital (as reported by NHS England) and consider the remainder to have occurred in care 79

homes. While non-hospital deaths may include deaths in other settings, such as in private 80 residences, comparison with ONS data suggests that care home deaths from COVID-19 81 may also have been under-reported. As such we consider non-hospital deaths to be an 82 appropriate proxy for care home deaths, and do not expect the margin for under or over-83 ascertainment to affect our conclusions. These data were provided by PHE and the data we 84

have been using is provided as a supplementary file (supplementary data file: data_rtm.csv, 85 columns: death2, death3) to allow reproducibility of our analysis. 86 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 13, 2021. 133 age 65-69, 5% age 70-74, 15% age 75-79 and 75% age 80+ (9)). We then assume a 1:1 134 ratio of care-home residents to care-home workers and assume that the care-home workers 135 population is homogeneously distributed among the 25-65 population in the region. 136

The contact matrix between the 17 age-groups is based on the POLYMOD contact survey. 137

See parameterisation for more details (10). 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 January 13, 2021. 

We developed a stochastic compartmental transmission-dynamic model incorporating 146

hospital care pathways to reconstruct the course of the COVID-19 epidemic in the seven 147 NHS regions of England ( Figure S 2) . All analyses were done by regions, and then 148 aggregated somehow if needed (e.g. for national IFR, or cumulative incidence). In the 149 following description we do not mention any index denoting the region and thus all notations 150 refer to the same NHS region. 151

We divided each regional population into 19 strata, denoted by the superscript !, 17 strata 153

representing age groups within the general population, and two separate risk groups 154 comprising care home workers (CHW) and care home residents (CHR such that 5% were aged 65-69, 5% aged 70-74, 15% aged 75-79 and 75% aged 80+ (9) and 164 similarly removed from the corresponding age groups in the general population. Again, 165 similarly to care-home workers they do constitute a single group in our model. We thus 166

do not capture specific transmission dynamics within each care home, but rather an average 167 mixing between residents and workers in the regional care home sector as a whole. 168 169 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 January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint and then ultimately into the PCR negativity compartment (/ -!. '$( ). Meanwhile, individuals 192 move into the seropositivity flow upon becoming infectious, entering first into a pre-193 seropositivity compartment (/ /+*0 "#$ ). A proportion of individuals ($ /+*0 "%& ) then seroconvert 194 and move into the seropositivity compartment (/ /+*0 "%& ), while the remainder move into the 195 seronegativity compartment (/ /+*0 '$( ). 196

We calibrated the duration distributions for each hospital compartment, and the age-stratified 197 probabilities of moving between compartments, using the analysis of individual-level patient 198 data (presented below in Section 1.9.2). The required Erlang distributional form was 199 achieved within the constraints of the modelling framework by splitting each model 200 compartment into 0 sequential sub-compartments (Table S 2 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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The copyright holder for this this version posted January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint 1 $ (() = > ? $,P (()Π P (() P (1) 220 where ? $,P (() is the (symmetric) time-varying person-to-person transmission rate from group 221 j to group i, and Π P (() is the number of infectious individuals in group j, given by: 222

Broadly, to parameterise ? $,P ((), we informed mixing in the general population, and between 224 the general population and care home workers using POLYMOD (10) via the R package 225 socialmixr using age-structured regional demography (18). Here C $,P is the (symmetric) person-to-person contact rate between age group i and j, derived 229 from pre-pandemic data (10). B(() is the time-varying transmission rate Dhich encompasses 230 both changes over time in transmission efficiency (e.g. due to temperature) and temporal 231 changes in the overall level of contacts in the population (due to changes in policy and 232 behaviours). 233

We assumed B(() to be piecewise linear: 234 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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Various probabilities of clinical progression within the model are assumed to vary across age 264 groups to account for severity of infection varying with age, and some are assumed to vary 265 in time in order to model improvements in clinical outcomes, such as those achieved through 266 the use of dexamethasone (31). 267

Two probabilities are age-varying but not time-varying, the probability of admission to 268 hospital for symptomatic cases, and the probability of death for severe symptomatic cases in 269 care homes. These were modelled as follows: 270 95% range 0.6-13.9 days broadly consistent with durations in (15) and with duration about 287 half the length observed in hospital streams (see Figure S 5 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 January 13, 2021. population size and potential immunity in the population. 303

To compute the next generation matrix, we calculated the mean duration of infectiousness 304 Δ ' , as 305

306 where parameter and model compartment notations are defined in Table S 2 -Table S 8.  307 For this calculation, the expected durations of stay in compartments were adjusted to 308 account for the discrete-time nature of the model, via calculating the expected number of 309 time-steps (of length _() spent in a given compartment. Note that if in continuous-time a 310 compartment duration is `~Erlang (0, U), then the corresponding discrete-time mean 311 duration is: 312 

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Note that for simplicity the notation we use do refer explicitly to the NHS region of interest. 326 We calculated age-aggregated estimates for each region by weighting the age-specific 327 severity estimates by the cumulative incidence in that age group. Aggregate estimates for 328

England were then calculated by weighting the region-specific estimates by the regional 329 attack rates. 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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We used the tau-leap method (33) to create a stochastic, time-discretised version of the 340 model described in equations (58-162), taking four update steps per day. The process was 341 initialised with ten asymptomatic infectious individuals aged 15-19 on the epidemic start date 342

( [ , a parameter we estimate. For each time step, the model iterated through the procedure 343 described below. In the following, we introduce a small abuse of notation: for transitions 344 involving multiple onward compartments (e.g transition from compartment # to 345 compartments % " or % ! ), for conciseness, we write 346 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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If { ∼ NegBinom(?, Å), then { follows a negative binomial distribution with mean ? and 363

shape Å, such that 364

where Γ(Ü) is the gamma function. The variance of { is ? +`k . 367

If á ∼ BetaBinom(à, â, ä), then á follows a beta-binomial distribution with size à, mean 368 probability â and overdispersion parameter ä, such that 369 

We allow for overdispersion in the observation process to account for noise in the underlying 384 data streams, for example due to day-of-week effects on data collection. We adopt Å = 2 for 385 all NHSE data streams, so that they contribute equal weight to the overall likelihood. 386 387

The model predicted general hospital bed occupancy by confirmed COVID-19 cases, 389 é q0/) (() as: 390 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 13, 2021. Where: 420

421 1.7.6 PCR testing 422

As described in the data section (1.1), we fitted the model to PCR testing data from two 423 separate sources: 424

• pillar 2: the government testing programme, which recommends that individuals with 425

COVID-19 symptoms are tested (34), 426

• the REACT-1 study, which aims to quantify the prevalence of SARS-CoV-2 in a 427 random sample of the England population on an ongoing basis (35). 428

We only use Pillar 2 PCR test results for individuals aged 25 and over (we assume this 430 includes all care home workers and residents). We assume that individuals who get tested 431 through Pillar 2 PCR testing are either newly symptomatic SARS-CoV-2 cases (who will test 432 positive): 433

434 or non-SARS-CoV-2 cases who have symptoms consistent with COVID-19 (who will test 435 negative): 436

where $ {! is the probability of non SARS-CoV-2 cases having symptoms consistent with 438 COVID-19 leading them to seek a PCR test. 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 January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint â -Q "%& (() ∶= vé -Q "%& (()y / vé -Q "%& (() + é -Q '$( (()y (180) 445 People may seek PCR tests for many reasons and thus the pillar 2 data are subject to 446 competing biases. We therefore allowed for an over-dispersion parameter ä -Q A$&A , which we 447 fitted separately for each region in the modelling framework: 448

We incorporated the REACT-1 PCR testing data into the likelihood analogously to the 

The overall likelihood function was then calculated as the product of the likelihoods of the 462 individual observations. 463 464

A closed-form expression of the likelihood of the observed data given the model and its 466 parameters was not analytically tractable, so we used particle filtering methods to obtain an 467 unbiased estimate of the likelihood which can be efficiently sampled from (36). Where 468 appropriate, we used estimates from the literature to set model parameters at fixed values. 469 We limited the parameters being inferred to just those with particular epidemiological 470 interest, or with large uncertainty in existing literature. 471

The model was fitted independently to each NHS region. For each NHS region, we aimed to 473

infer the values of 26 model parameters: 474

• the local epidemic start-date, ( [ ; 475

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The copyright holder for this this version posted January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint • thirteen transmission rates at different time points B R , … , B RQ ; 476

• three parameters governing transmission to and within care homes 477

? !#, , ? !#. , P; 478

• the probability of symptomatic individuals developing serious disease 479 requiring hospitalisation, $ # ab , for the group with the largest probability; 480

• the probability of a care home resident dying in a care home if they have 481 severe disease requiring hospitalisation, $ % ! !#. ; 482

• the probability, at the start of the pandemic, of a patient being admitted to ICU 483 after hospitalisation, $ '!( ab , for the group with the largest probability; 484

• the probabilities, at the start of the pandemic, of dying in a hospital general 485 ward, $ # ! ab , in the ICU, $ '!( ! ab , and in a stepdown ward following ICU, $ , ! ab , 486

for the groups with the largest probability; 487

• the multiplier for hospital mortality after improvement in care, S # ; 488

• the multiplier for probability of admission to ICU after improvement in care, zero when observed values are non-zero, this results in particles of zero weight, which can 500 lead to the particle filter estimating the marginal likelihood to be 0. Therefore, to get a small 501 but non-zero weight for each particle at every observation, within our particle filter likelihood 502

we add a small amount of noise (exponentially distributed with mean 10 S\ ) to count values 503 from the model. 504 505

Within our particle filter we add small amounts of exponentially-distributed noise (with mean 506

10 S\ ) to model outputs prior to calculating likelihood weights to avoid particles of zero 507 weight, instead resulting in small but non-zero weights. 508 We implemented our model and parameter inference in an R package, sircovid (39), 509 available at https://mrc-ide.github.io/sircovid, which uses two further R packages, dust to run 510 the model in efficient compiled code and mcstate to implement the pMCMC sampler using 511

Metropolis-Hastings sampling (40). 512

At each iteration, the sampler proposes an update to the joint distribution of parameters. 513

These proposals are generated from multivariate Gaussian densities centred on the current 514 parameter values, and with a covariance structure chosen to facilitate efficient mixing of the 515

Markov chain. We specified reflecting boundaries for the proposal kernel to ensure that the 516

proposed parameters are both epidemiologically and mathematically plausible and retain 517 symmetry in the proposals. 518 For each regional fit, eight parallel chains of the pMCMC were run for 11,000 iterations, with 519 the first 1,000 discarded as burn-in, and a 1/80 thinning. We assessed convergence visually. 520 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 13, 2021. Dashboard data ( Figure S3 ). We thus undertook a two-step approach to infer the 538 demographic composition of COVID-19 hospitalisations across England. 539

Firstly, we derived an initial approximation of Q # $ by dividing the total number of hospital 540

admissions for age group ! in CHESS over the total number of positive PCR tests (Pillar 2) 541

for !. Both data sources were censored to include patients admitted to hospital or with a 542 specimen data (i.e. the date the test was taken), respectively, between March 1 and 543

December 2, 2020. We ran our full inference framework using this initial approximation 544

for Q # $ and observed its fit to the demographic composition of admissions from the data. 545

As a second step, we refined our initial approximations of Q # $ over a series of iterations of 546 our inference framework, by drawing the modelled ($ # $ }0i+~) and observed ($ # $ a/qÄ0a*i ) 547

proportion of admissions for each age group (i.e. admissions in age group ! divided by all 548 admissions) and using it to derive a re-scaling factor for a new proposal for Q # $ as follows: 549

This process was repeated to obtain a close approximation to the observed proportion of 552 admissions by age and region ( Figure S3) . A key strength of our approach is that we did not 553 overfitted demography by individual regions. Rather, by assuming Q # $ to be independent of 554 geographic region, we allowed our inference framework to derive the number of admissions 555 for each five-year age band ! solely based on Q # $ , the demographic composition of the NHS 556 region and inferred epidemic parameters, such as & f . 557 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 13, 2021. 

The fitted spline (red) was used as input parameters for the probability of hospitalisation by age. 562 563

We also performed extensive preliminary analysis to inform the age-structure of progression 565 parameters within hospital. Data from the COVID-19 Hospitalisation in England Surveillance 566

System (CHESS) were used to fit a simple model of patient clinical progression in hospital. 567

The model structure was designed to mirror the within-hospital component of the wider 568 mechanistic transmission model, but without the complexities arising from unknown 569 admission dates and with greater detail on trends with age ( Figure S 4) . 570 571 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 13, 2021. This gave >5 months for outcomes to complete, and hence justified filtering to patients with 580 resolved outcomes only. The length of stay in each state was taken as the difference 581 between the registered dates of entering and leaving each hospital ward. Lengths of stay 582

were assumed to follow Erlang distributions, as in the wider model, with a distinct mean and 583

shape parameter for each state. Specifically, the probability of being in state é ∈ 584

{$ñi, . , . . , %+, , %+, , B , %+, , ! , -. , -} for à ∈ ℕ [ days was taken as the integral over day 585

à of the Erlang distribution with mean ? _ and shape ò _ : 586 587 Pr(in state é for à days) = ù probabilities were modelled as functions of age using logistic-transformed cubic splines. 592

Knots were defined at coordinates [Ü $ , É Ç $ ], where Ü $ values were fixed at 593

{0, 20, 40, 60, 80, 100, 120} and É Ç $ were free parameters to be estimated. The complete 594 spline, É Ç (å) for å ∈ 0: 120, was obtained from these knots using standard expressions for 595 cubic spline interpolation. Finally, transition probabilities were obtained from the raw É Ç (å) 596 values using the logistic transformation: $ Ç (å) = 1 (1 + i Sl D (a) ) ⁄ . 597

. CC-BY-ND 4.0 International license It is made available under a perpetuity.

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 January 13, 2021. All parameters of the hospital progression model were given priors (Table S 5) and  605 estimated within a Bayesian framework. All length of stay parameters were given uniform 606 priors over a plausible range of values. For transition probabilities, the first spline node É Ç R 607 was given a prior that corresponded to a uniform distribution after logistic transformation, 608

and subsequent spline nodes were given a multivariate normal prior to apply a smoothing 609 constraint to the spline. Parameters were estimated jointly via MCMC using the custom 610 package markovid v1.5.0 (41), which uses the random-walk Metropolis-Hastings algorithm to 611 draw from the joint posterior distribution. MCMC was run for 1000 burn-in iterations and 612 100,000 sampling iterations replicated over 10 independent chains. Convergence was 613 assessed via the Gelman-Rubin diagnostic (all parameters had potential scale reduction 614 factor <1.1) and sampling sufficiency was assessed by visualising posterior distributions and 615 by effective sample size (ESS) calculations (all parameters had ESS >100,000). 616 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 January 13, 2021. 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 January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint To keep serology parameters consistent between all regions we used estimates from the 647 literature to fix the parameters of the seroconversion process. An alternative would have 648

been to use these estimates as priors within a hierarchical model where some parameters 649 would be shared between regions, but this would be much more involved computationally. 650 651

As described in section 1.3.2, the time to seroconversion from leaving the # $ compartment is 652 modelled by an exponential distribution time spent in / /+*0 "#$ $ with a proportion $ /+*0 "%& 653 ultimately seroconverting and moving to / /+*0 "%& $ and the remaining staying negative and 654 moving to / /+*0 '$( $ . 655 656 We fixed $ /+*0 "%& to 0.85 based on the estimate of 85% of infections becoming detectably 657 seropositive with the EUROIMMUN assay used in the NHSBT serological surveys (42). The 658 specificity of the serology test $ /+*0 &"$@ is fixed to 0.99 also from (42). Finally, the sensitivity of 659 serology test $ /+*0 &$'& is assumed to be 1 as it is non-distinguishable from the time varying 660 seroconversion process (Table S7) . 661 662

As for other compartments, we modelled the duration of SARS-CoV-2 PCR-positivity after 664 symptom onset using an Erlang distribution `~Erlang(0, U), with k successive compartments 665 and a total mean time spent of è h and variance è h -. 666

We estimated the parameters of this distribution from Omar et al. (16) , which reported the 667 cumulative distribution of duration of PCR positivity in 523 individuals with mild COVID-19 668 disease in home quarantine in a German region. We performed a survival analysis using a 669 gamma-accelerated failure time model fitted to their data, from which we estimated the 670 mean and variance of the time from symptom onset to PCR negativity. This was used to 671 derive values of k and U shown in Table S 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 January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint Table S 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 January 13, 2021. 

. CC-BY-ND 4.0 International license It is made available under a perpetuity.

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 January 13, 2021. 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 January 13, 2021. ; https://doi.org/10.1101/2021.01.11.21249564 doi: medRxiv preprint

We set priors for the transmission rates B R , … , B RQ to reflect a Gamma distribution for the 678 reproduction number & f with a reasonable 95% confidence interval a priori

The 95% ranges for & [ we used 681 are (i) (2.5, 3.5) at the onset of the epidemic (corresponding to B R ); and then & f (ii) (0.4, 3.5) 682 at announcement of the first lockdown

we used a prior distributions reflecting that these are 688 person-to-person infectious contact rates and thus should be scaled according to regional 689 care home demography. We then used a Gamma distribution with shape 5 and mean [.R { +JB 690 for both of these parameters (recall that we assume there is a 1-to-1 ratio of care home 691 workers to residents in each region

For the parameter governing the reduction in contacts between the general population and 693 care home residents, P, we used an uninformative

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Statistics » COVID-19 Hospital Activity 870

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