key: cord-0846213-dpvbsu5o
authors: Booton, R. D.; MacGregor, L.; Vass, L.; Looker, K. J.; Hyams, C.; Bright, P. D.; Harding, I.; Lazarus, R.; Hamilton, F.; Lawson, D.; Danon, L.; Pratt, A.; Wood, R.; Brooks-Pollock, E.; Turner, K. M. E.
title: Estimating the COVID-19 epidemic trajectory and hospital capacity requirements in South West England: a mathematical modelling framework
date: 2020-06-12
journal: nan
DOI: 10.1101/2020.06.10.20084715
sha: 9944329e1910d80d7132f65b21afff4fdd311444
doc_id: 846213
cord_uid: dpvbsu5o

Objectives: To develop a regional model of COVID-19 dynamics, for use in estimating the number of infections, deaths and required acute and intensive care (IC) beds using the South West of England (SW) as an example case. Design: Open-source age-structured variant of a susceptible-exposed-infectious-recovered (SEIR) deterministic compartmental mathematical model. Latin hypercube sampling and maximum likelihood estimation were used to calibrate to cumulative cases and cumulative deaths. Setting: SW at a time considered early in the pandemic, where National Health Service (NHS) authorities required evidence to guide localised planning and support decision-making. Participants: Publicly-available data on COVID-19 patients. Primary and secondary outcome measures: The expected numbers of infected cases, deaths due to COVID-19 infection, patient occupancy of acute and IC beds and the reproduction ("R") number over time. Results: SW model projections indicate that, as of the 11th May 2020 (when 'lockdown' measures were eased), 5,793 (95% credible interval, CrI, 2,003 - 12,051) individuals were still infectious (0.10% of the total SW England population, 95%CrI 0.04 - 0.22%), and a total of 189,048 (95%CrI 141,580 - 277,955) had been infected with the virus (either asymptomatically or symptomatically), but recovered, which is 3.4% (95%CrI 2.5 - 5.0%) of the SW population. The total number of patients in acute and IC beds in the SW on the 11th May 2020 was predicted to be 701 (95%CrI 169 - 1,543) and 110 (95%CrI 8 - 464) respectively. The R value in SW England was predicted to be 2.6 (95%CrI 2.0 - 3.2) prior to any interventions, with social distancing reducing this to 2.3 (95%CrI 1.8 - 2.9) and lockdown/ school closures further reducing the R value to 0.6 (95CrI% 0.5 - 0.7). Conclusions: The developed model has proved a valuable asset for local and regional healthcare services. The model will be used further in the SW as the pandemic evolves, and - as open source software - is portable to healthcare systems in other geographies.

Each compartment is stratified by age-group (0-4, 5-17, 18-29, 30-39, 40-142 49, 50-59, 60-69, ≥70) where denotes the stage of COVID-19 (S,E,I,A,H,C,R,D) and 143 denotes the age group class of individuals. Age groups were chosen to capture key 144 social contact patterns (primary, secondary and tertiary education and employment) 145

and variability in hospitalisation rates and outcomes from COVID-19 especially in older 146 age groups. The total in each age group is informed by recent Office for National 147

Statistics (ONS) estimates [21] . 148

Susceptible individuals become exposed to the virus at a rate governed by the 149 force of infection , and individuals are non-infectious in the exposed category. A 150 proportion move from exposed to symptomatic infection and the remaining to 151 asymptomatic infection, both at the latent rate . Individuals leave both the 152 asymptomatic and symptomatic compartments at rate . All asymptomatic individuals 153 eventually recover and there are no further stages of disease: the rate of leaving the 154 asymptomatic compartment is therefore equivalent to the infectious period, . A 155 proportion of symptomatic individuals go on to develop severe symptoms which 156 require hospitalisation, but not intensive care. Once requiring hospitalisation, we 157 assume individuals are no longer infectious to the general population due to self-158 isolation guidelines restricting further mixing with anyone aside from household 159 members (if unable to be admitted to hospital) or frontline NHS staff (if admitted to 160 hospital). Individuals move out of the acute hospitalised compartment at rate , either 161 through death, being moved to intensive care at rate , or through recovery (all 162 remaining individuals). A proportion of patients requiring IC will die at rate , while 163 the rest will recover. 164 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.10.20084715 doi: medRxiv preprint equations: 166

(1 )

Hospitalised in acute bed " = " " − " (1 )

Recovered #' ! #% = " + (1 − " ) " + (1 − )(1 − ) " + S1 − " U " (1 )

. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. 

. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. 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 June 12, 2020. (2) 205

The basic reproduction number R0

The basic reproduction numberof COVID-19 is estimated to be 2.79 ± 1.16 [24] . 207

We include this estimate within our model by calculating the maximum eigenvalue of 208 the contact matrix , and allowing the transmission parameter to vary such thatis 209 equal to the maximum eigenvalue of multiplied by the infectious period and the 210 transmission parameter . This gives the value for the initial basic reproduction Table 1 . We used available published literature to 216 inform parameter estimates. We used the following publicly-available metrics for 217 model fitting: regional cumulative cases in SW England (tested and confirmed case in 218 hospital), and deaths (daily/cumulative counts) from the Public Health England 219 COVID-19 dashboard [14] , and ONS weekly provisional data on COVID-19 related 220 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. Figure S1 for the best 100 fits.

. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.10.20084715 doi: medRxiv preprint output the cumulative cases and deaths in the SW. We output the predicted proportion 250 of the population who are infectious and who have ever been infected over time. 251

Finally, we estimate the daily and cumulative patterns of admission to and discharge 252 from hospital (intensive care and acute) and cumulative mortality from COVID-19. fitting values are shown in Figure S1a (and the priors in Figure S1b ). All results are 259

shown with median and 95% credible intervals (95%CrI). Figure 2 shows the projected numbers of exposed, recovered and infectious 269 (asymptomatic and symptomatic infections) until lockdown measures were lessened 270 on the 11 th May 2020. On this date, the model predicts that a total of 5,793 (95%CrI 271 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. 

. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.10.20084715 doi: medRxiv preprint intensive care beds 283 The total number of patients in acute (non-intensive care) hospital beds across SW 284

England was projected to be 701 (95%CrI 169 -1,543) and the total number of 285 patients in intensive care hospital beds was projected to be 110 (95%CrI 8 -464) on 286 the 11 th May 2020 ( Figure 3 ). Note that these ranges are quite large due to the 287 uncertainty in the data and as more data becomes available these predictions will 288 change. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.10.20084715 doi: medRxiv preprint number for COVID-19 in the South West of England. We predict that prior to any 302 interventions R was 2.6 (95%CrI 2.0 -3.2), and the introduction of social distancing 303 reduced this number to 2.3 (95%CrI 1.8 -2.9). At the minimum, R was 0.6 (95%CrI 304 0.5 -0.7) after all prior interventions were enacted and adhered to (social distancing, 305 school closures and lockdown). 

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The copyright holder for this preprint this version posted June 12, 2020. .

We have developed a deterministic ordinary differential equation model of the 311 epidemic trajectory of COVID-19 focussing on acute and IC hospital bed capacity 312 planning to support local NHS authorities, calibrating to SW-specific data. The model 313 is age-structured and includes time-specific implementation of current interventions 314 (following advice and enforcement of social distancing, school closures and lockdown) 315

to predict the potential range of COVID-19 epidemic trajectories. 316

Using the publicly-available data on cases and deaths, combined with the early 317 estimates of parameters from early epidemics in other settings, we predict that on the 318 11 th May 2020 a total of 5,793 (95%CrI 2,003 -12,051) were infectious, which equates 319 to 0.10% (95%CrI 0.04 -0.22%) of the total SW population. In addition, we find that 320 the model predicts a total of 189,048 (95%CrI 141,580 -277,955) have had the virus 321 but recovered, which is 3.4% (95%CrI 2.5 -5.0%) of the SW population. 322

We also estimate that the total number of patients in acute hospital beds in SW 323

England on 11 th May 2020 was 701 (95%CrI 169 -1,543) and in IC were 110 (95%CrI 324 8 -464), while the R number has decreased from 2.6 (95%CrI 2.0 -3.2) to 0.6 325 (95%CrI 0.5 -0.7) after all interventions were enacted and fully adhered to. 326

The fits generally agree well with both the daily case data, and the cumulative 327 count of deaths in the SW, although the model overestimates the case data at early 328 stages, and underestimates later on (which can see seen in Figure S2a , and a scatter 329 plot of expected versus observed outputs in Figure S2b ). This could be because we 330 are using formal fitting methods, or from the under-reporting of cases in the early 331 epidemic. 332 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. [8]. In addition, the information which informs our parameter selection is rapidly 356 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.10.20084715 doi: medRxiv preprint analysis, we identified the following parameters as critical in determining the epidemic 358 trajectory within our model -the percentage of infections which become symptomatic, 359 the recovery time for cases which do not require hospital, the period between acute 360 and IC occupancy, the length of stay in IC, the probability of transmission per contact 361 and the gradual implementation of lockdown rather than immediate effect. Other 362 parameters (such as the percentage reduction in school-age contacts from school 363 closures) did not seem to influence the dynamic trajectory as strongly -and thus we 364 assume point estimates for these parameters. However, for example assuming that 365 95% of school-age contacts are reduced as a direct result of school closures is 366 perhaps an overestimate, and future modelling work should address these 367 uncertainties and their impacts on the epidemic trajectory of COVID-19 (but in this 368 case, this value was somewhat arbitrary, and the assumption was used in the absence 369 of school-age contact survey data). More research is urgently needed to refine these 370 parameter ranges and to validate these biological parameters experimentally. 371

We have also assumed that there is no nosocomial transmission of infection 372 between hospitalised cases and healthcare workers, as we do not have good data for 373 within-hospital transmission. However frontline healthcare staff were likely to have 374 been infected early on in the epidemic [34], which could have implications for our 375 predicted epidemic trajectory. Our model also assumes a closed system, which may 376 not strictly be true due to continuing essential travel. But given that up until 11 th May, 377 travel restrictions are very severe due to lockdown measures [5], any remaining inter-378 regional travel is likely to have minimal effects on our model outputs. 379 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.10.20084715 doi: medRxiv preprint spatially structure the population as in other UK modelling [9,10], but we do include 382 age-specific mixing based on POLYMOD data [22] , and the post-lockdown CoMix 383 study [11] . We also explicitly measure the total asymptomatic infection, and the total 384 in each of the clinically relevant hospital classes (acute or IC), which is a strength of 385 our approach. Future models could also take into account local bed capacity within 386 hospitals (including Nightingale centres) and accommodate the effect of demand 387 outstripping supply leading to excess deaths, inclusive of non-hospital-based death 388 such as is occurring within care homes. As with all modelling, we have not taken into 389 account all possible sources of modelling misspecification. Some of these 390 misspecifications will tend to increase the predicted epidemic period, and others will 391 decrease it. One factor that could significantly change our predicted epidemic period 392 is the underlying structure within the population leading to heterogeneity in the average 393 number of contacts under lockdown e.g. key workers have high levels of contact but 394 others are able to minimise contacts effectively, this might lead to an underestimate of 395 ongoing transmission, but potentially an overestimate of the effect of releasing 396 lockdown. We also know that there are important socio-economic considerations in 397 determining people's ability to stay at home and particularly to work from home [37] . 398

Early UK modelling predicted the infection peak to be reached roughly 3 weeks 399 from the initiation of severe lockdown measures, as taken by the UK government in 400 mid-March [8]. A more recent study factoring spatial distribution of the population 401 indicated the peak to follow in early April due toreducing to below 1 in many settings 402 in weeks following lockdown [9]. Other modelling indicated that deaths in the UK would 403 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. State, also highlights the peak of excess bed demand varies geographically, with this 418 peak ranging between the 2 nd week of April, through to May dependent on the State 419 under consideration. The modelling based in France also cautioned that due to only 420 5.7% of the population having been infected by 11 th May when the restrictions would 421 be eased, the population would be vulnerable to a second epidemic peak thereafter 422

The ONS in England estimated that an average of 0.25% of the population had 424 COVID-19 between the 4 th and 17 th May 2020 (95% confidence interval: 0.16 -0.38%) 425

[40], which is greater than the 0.10% (95%CrI 0.04 -0.22%) we found with our model 426 (on 11 th May 2020), but with some overlap. In addition, the ONS estimated that 6.78% 427 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. May 2020 (2 weeks later) , demonstrating that our model estimates may be 432 within sensible bounds, and further highlighting the need for more regional estimates 433 of crucial epidemiological parameters and seroprevalence. We have assumed that 434 individuals are not susceptible to reinfection within the model timeframe, however in 435 future work it will be important to explore this assumption. It is not known what the long 436 term pattern of immunity to COVID-19 will be [43] , and this will be key to understanding 437 the future epidemiology in the absence of a vaccine or effective treatment options. 438

With this in mind, our findings demonstrate that there are still significant data 439 gaps -and in the absence of such data, mathematical models can provide a valuable 440 asset for local and regional healthcare services. This regional model will be used 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 June 12, 2020. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. Increasing m does slightly increase the estimate of the infectious population (total 698 infectious). This is explained by including models with slightly higher R value, i.e. R is 699 biased upwards as we move further away from the best answer. The bias is small 700 compared to the modelling uncertainty. 

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