medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

A spatial model of CoVID-19 transmission in England and Wales: early
spread and peak timing
Leon Danon (1), Ellen Brooks-Pollock (2), Mick Bailey (3), Matt Keeling (4)
1.
2.
3.
4.

L.Danon@exeter.ac.uk, University of Exeter
Ellen.Brooks-Pollock@bristol.ac.uk, University of Bristol
Mick.Bailey@bristol.ac.uk, University of Bristol
M.J.Keeling@warwick.ac.uk University of Warwick

Abstract
BackgroundAn outbreak of a novel coronavirus, named CoVID-19, was first reported in China on 31
December 2019. As of 9 February 2020, cases have been reported in 25 countries, including
probable cases of human-to-human transmission in England.
Methods
We adapted an existing national-scale metapopulation model to capture the spread of CoVID-19
in England and Wales. We used 2011 census data to capture population sizes and population
movement, together with parameter estimates from the current outbreak in China.
Results
We predict that a CoVID-19 outbreak will peak 126 to 147 days (~4 months) after the start ofperson-to-person transmission in England and Wales in the absence of controls, assuming
biological parameters remain unchanged. Therefore, if person-to-person transmission persistsfrom February, we predict the epidemic peak would occur in June. The starting location has
minimal impact on peak timing, and model stochasticity varies peak timing by 10 days.
Incorporating realistic parameter uncertainty leads to estimates of peak time ranging from 78
days to 241 days after person-to-person transmission has been established. Seasonal changes
in transmission rate substantially impact the timing and size of the epidemic peak, as well as thetotal attack rate.
Discussion
We provide initial estimates of the potential course of CoVID-19 in England and Wales in theabsence of control measures. These results can be refined with improved estimates of
epidemiological parameters, and permit investigation of control measures and costeffectiveness analyses. Seasonal changes in transmission rate could shift the timing of the peakinto winter months, which will have important implications for health-care capacity planning.

NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.

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medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

Introduction
An outbreak of a novel coronavirus, recently renamed CoVID-19, was first reported from
Wuhan, China on 31 December 2019. During January 2020, the outbreak spread to multiple
cities in China, and the first cases started appearing outside China. By the end of January 2020,
9,720 cases had been confirmed in China, with 106 confirmed cases outside China across 19
different countries(1).
Epidemiological analysis of the outbreak was quickly used to start estimating epidemiologicallyrelevant parameters, such as the basic reproduction number, the serial interval, the incubation
period and the case fatality rate(2–7). Initial estimates suggested that the reproduction number
was between 2 and 3 and the case fatality rate was less than 4%(8). Control of spread bycontact tracing and isolation appears to be challenging, given what is currently known about thevirus (9).
Mathematical models are useful tools for understanding and predicting the possible course of an
outbreak, given a set of underlying assumptions. Here, we adapt a metapopulation model of
disease transmission in England and Wales to capture the spread of CoVID-19(10). The aim is
to provide predictions about the likely timing of the peak of the epidemic in England and Walesand spatial features of spread.
Methods
Model description
We use an existing national-scale stochastic metapopulation model of disease transmission in
England and Wales. The model structure is based on the metapopulation model described indetail in Danon et al (2009)(10). In this model, the population is divided into electoral wards.
Because of the changes in data availability, we restricted the model to England and Wales,
whereas the original model covered Great Britain.
Movement between wards
Transmission between wards occurs via the daily movement of individuals. For each ward, we
assume that individuals contribute to the force of infection in their “home” ward during the night
and their “work” ward during the day. See Danon et al 2009 for further details(10).
Population and movement data
Data for population and movement of individuals come from the 2011 census of the United
Kingdom. The population size of each of the 8,570 electoral wards is available directly from the
Office of National Statistics (ONS) website. The number of individuals moving between locations
is also available from the ONS website, but at the level of census output areas (OAs). We
aggregated the data from OA level to electoral wards level. Spatial location of electoral ward
centres are extracted from maps available from the ONS websites.
CoVID-19 specific parameters
We use a Susceptible-Exposed-Infectious-Infectious-Recovered (SEIIR) model within eachward to capture the progression of disease within an individual (figure 1). Initial analyses used
SARS-like parameters for the incubation period and infectious period, which now appear todiffer from CoVID-19(4). Li et al (2020) analysed data on 425 cases reported in Wuhan in China
and fitted a log-normal distribution to the incubation period, and a gamma distribution for theserial interval(2). The infectious period for SARS was estimated as the serial interval minus the2medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

incubation period, but as Li et al did not report the correlation between incubation period andserial interval, we were not able to estimate the infectious period distribution from the data, but
used a uniform distribution between 2 and 3 days, to give a mean serial interval of
approximately 7-8, in line with current estimates. We used two infectious states to represent a
mildly symptomatic or prodromal period and a period with more pronounced symptoms. In theabsence of data on the relative magnitude of these two infections states, we assumed the sameelength of time in each infectious state and assumed that each state was equally infectious. We
sampled from each of the distributions 100 times independently (Table 1).

Figure 1: Model structure within each ward, together with associated parameters estimated from the literature.

Parameter
Incubation
periodReproduction
numberInfectious
periodValues and distribution
Referencelognorm(meanlog=log(5.2),sdlog=0.35) Li et al(2)gamma(scale=2.2/100,shape=100)

Li et al(2)uniform(2, 3)

Estimated from the mean
serial interval (7.5 days)
minus the mean incubation
period (5.2 days) from Li etal(2)Table 1: Biological parameters and distributions used in the model.

Initialisation and baseline model
The census data are used to initialise the population sizes within each of the 8,570 wards. At
the start of the model, all individuals are assumed to be susceptible to infection with no3

medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

underlying immunity in the population. We investigated a range of starting scenarios by seeding
the infection in example wards London, Birmingham, Brighton, Sheffield and Cardiff. To seed
infection in a ward, we move five individuals (non-commuters) from the susceptible
compartment to the first infectious state.
Impact of seasonality
We investigated the impact of a seasonally affected transmission rate, to capture potential
decreased transmission during the summer months. We captured seasonal transmission byreplacing the constant transmission rate with a time-varying transmission rate given by: 

1 


2
1  cos

2
365

0

Where is the magnitude of the seasonal difference in transmission, ranging from(noseasonality) to(maximum seasonality with no transmission at the peak of the summer).

1

Epidemic characteristics
From the model, we extracted the total number of infections per day, as the number ofindividuals in both of the Infectious states, and the number of infected wards per day as the total
number of wards with at least one individual in one of the two Infectious states. The spatial
growth of the epidemic in England and Wales was visualised using interactive maps. We
estimated the timing of the epidemic peak from the aggregated epidemic curve and calculated
95% prediction intervals from the model simulations.
Implementation and data availability
The model is coded in C and is available on github (http://github.com/ldanon/MetaWards). The
data are freely available from the Office for National Statistics website, or can be downloadedwith the code at the github repository.
Results
We predict that, in the absence of any interventions, a disease with “best-guess” CoVID-19-likeparameters will peak a median of 133 days (range 126 - 147 days) following the start of personto-person transmission in England and Wales. Intrinsic model stochasticity is responsible forvariation between model runs. Using exactly the same parameters and seeding the infection in
the same initial wards resulted in a difference in peak timing of +/- 10 days (figure 2). The attack
rate for best-guess parameters had a median of 45799874 (81.67% range 81.64-81.69), with apeak incidence median 1,116,692.

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medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

Figure 2: The number of cases of CoVID-19 in England and Wales in the absence of any control measures, 100
realisations of the spatial model, seeded in Brighton, using best-guess parameters from Li et. al. (top) Daily infection
dynamics. (middle) The distribution of predicted time to peak incidence. (bottom) The distribution of predicted attack
rate.

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medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

The initial location of cases had some, but limited impact on the timing of the epidemic in
England and Wales. Epidemics seeded in Brighton, London, Birmingham and Sheffield resulted
in synchronised epidemics in England, reaching urban areas first followed by rural areas.
Epidemics started in Cardiff had a slower time to peak but still resulted in a generalised
outbreak.
Spatially, some disaggregation between England and Wales regions is observed. An outbreakstarting in Brighton, (South East England) peaks in London and the South East first, and North
East England, Yorkshire and Humber and Wales last, with a ten-day lag between regions(Figure 3).

Figure 3: Predicted epidemic curves for a CoVID-19 outbreak broken down by region for England and Wales.

Model predictions are highly sensitive to parameter values and incorporating parameter
uncertainty increases the variability of model predictions. In the absence of any control
measures, all predictions resulted in epidemics that peaked within a year from the start ofperson-to-person transmission in England and Wales. Estimates of peak time ranged from 78
days to 241 days (Figure 4).

6medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

Figure 4: The variability in predicted epidemic curves for a Covid-19 outbreak in England and Wales, seeded in
Brighton, in the absence of any control measures incorporating measured parameter uncertainty. (top) Daily infection
dynamics. (middle) The distribution of predicted time to peak incidence. (bottom) The distribution of predicted attack
rate.

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medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

However, seasonality in transmission has a large impact on epidemic timing, peak incidence,and final attack rates. Assuming no difference in transmission rate during the year leads to asingle large epidemic after approximately 4 months (June time if transmission starts in
February), as above. With a 25% reduction in transmission the epidemic is smaller and peaks
later, reducing the overall attack rate by 20%. A 50% reduction in transmission results in asmaller epidemic before the summer, followed by a resurgence in cases in the following winter.
The attack rate is 10% less than a non-seasonal epidemic. A 75% reduction in transmission
over the summer resulted in a delayed large outbreak, but with a similar attack rate. If
transmission decreases to zero over the summer then the resulting outbreak is much reduced,
with an attack rate of less than 1% (Figure 5, Table 2).

Figure 5: Effect of seasonal changes in transmission rate, assuming a reduction in transmission over the summer.
(main panel) Incidence over time, for different values of seasonal scaling. (inset) Variation of scaling term for thecourse of one year, with transmission being at its lowest in July.

Seasonal Term

Timing of Peak Incidence at Peak Attack Rate

01391172819

81.9

0.25

159

615599

65.0

0.50

343

330311

69.4

0.75

375

1227280

80.3

1.0

100

6547

0.53

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medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

Table 2: Effect of seasonal variation on the timing (shown in days following initial seeding), the height of the peak,
and the final attack rate.

Discussion
We predict that, in the absence of control measures and with no seasonality in transmission, theintroduction of CoVID-19 in England and Wales has the potential to result in a synchronised
outbreak that peaks at around 4 months following the start of person-to-person transmission.
Our findings suggest that the height of the epidemic and the attack rate is highly dependent on
seasonality of transmission and that even small changes in transmission risk can lead to largechanges in attack rate due to the spatial disaggregation of the population at risk.
A combination of control measures and seasonal changes in transmission rate could shift thepeak of the outbreak to the winter of 2020/21, with little effect on the final attack rate. If contact
tracing and isolation efforts succeed in reducing transmission, but are unable to control theepidemic (9), an additional influx of severe CoVID-19 cases may exacerbate existing challenges
with winter healthcare demand. A careful analysis of the impact of control measures on thetiming of incidence of severe cases is warranted.
The strength of this model lies in the spatial heterogeneity which tempers transmission. As acomparison, an equivalent non-spatial model results in the epidemic peaking after 34 days,
nearly four times faster than this spatial model, and would be unable to capture the interaction
between spatial transmission and seasonality. The estimated total number of people infected in
the spatial model is marginally smaller than for a non-spatial model, as the infection has theopportunity to die-out in local parts of the country. As the model framework was developed andpublished in 2009, it was possible to re-deploy the model for these new circumstances;developing such a model from scratch during an outbreak would be a significant challenge.
A key element missing from our model is morbidity, mortality and the treatment of cases. The
model in its current form predicts the total number of infections in the community rather than
diagnosed cases. Observations from China suggest that many cases have mild symptoms andthat only around 5% of cases have been reported and diagnosed (3). The parameter estimates
we used from China appear to be substantially different to previous coronaviruses (6). Should
CoVID-19 continue spreading the UK it will become possible to get UK-specific parameter
estimates and improve prediction accuracy.
As with all modelling, it is impossible to capture the full complexity of an epidemic. In this model,
the major assumptions are that we have assumed that there is no change in behaviour during
the course of the epidemic. In practice, as the epidemic starts spreading in England and Wales
there may well be a systematic change in behaviour as was seen during the H1N1 influenza
pandemic in 2009. We have not included any age-effects, such as differential mixing,
susceptibility or infectiousness. That means that we are not able to investigate the impact ofschool closures or the impact of the summer holidays, which had a large impact on the H1N1
influenza pandemic in 2009.
Acknowledgements
EBP was funded by the National Institute for Health Research Health Protection Research Unit
(NIHR HPRU) in Evaluation of Interventions at University of Bristol in partnership with Public
Health England (PHE). The views expressed are those of the author(s) and not necessarily

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medRxiv preprint doi: https://doi.org/10.1101/2020.02.12.20022566; this version posted February 14, 2020. The copyright holder for this preprint(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
It is made available under a CC-BY-NC-ND 4.0 International license .

those of the NHS, the NIHR, the Department of Health or Public Health England. LD gratefully
acknowledges the financial support of The Alan Turing Institute under the EPSRC grant
EP/N510129/1.

References
1.
World Health Organization (WHO). Novel Coronavirus (COVID19) Situation Report-23.
2020.
2.
Li Q, Guan X, Wu P, Wang X, Zhou L, Tong Y, et al. Early Transmission Dynamics in
Wuhan, China, of Novel Coronavirus–Infected Pneumonia. N Engl J Med. 2020
Jan;NEJMoa2001316.
3.
Read JM, Bridgen JR, Cummings DA, Ho A, Jewell CP. Novel coronavirus 2019-nCoV:
early estimation of epidemiological parameters and epidemic predictions. medRxiv.
2020;2020.01.23.20018549.
4.
Wu JT, Leung K, Leung GM. Nowcasting and forecasting the potential domestic andinternational spread of the 2019-nCoV outbreak originating in Wuhan, China: a modellingstudy. Lancet (London, England). 2020 Jan;0(0).
5.
Imai N, Cori A, Dorigatti I, Baguelin M, Donnelly CA, Riley S, et al. Report 3:
Transmissibility of 2019-nCoV. 2020.
6.
Liu T, Hu J, Kang M, Lin L, Zhong H, Xiao J, et al. Transmission dynamics of 2019 novel
coronavirus (2019-nCoV). bioRxiv [Internet]. 2020 Jan 26 [cited 2020 Feb
13];2020.01.25.919787. Available from:https://www.biorxiv.org/content/10.1101/2020.01.25.919787v1
7.
Abbott S, Hellewell J, Munday J, Funk S, Funk S. The transmissibility of novel
Coronavirus in the early stages of the 2019-20 outbreak in Wuhan: Exploring initial pointsource exposure sizes and durations using scenario analysis. Wellcome Open Res[Internet]. 2020 Feb 3 [cited 2020 Feb 13];5:17. Available from:https://wellcomeopenresearch.org/articles/5-17/v1
8.
Dorigatti I, Okell L, Cori A, Imai N, Baguelin M, Bhatia S, et al. Report 4: Severity of 2019novel coronavirus (nCoV). 2020.
9.
Hellewell J, Abbott S, Gimma A, Bosse NI, Jarvis CI, Russell TW, et al. Feasibility ofcontrolling 2019-nCoV outbreaks by isolation of cases and contacts. medRxiv [Internet].
2020 Feb 11 [cited 2020 Feb 13];2020.02.08.20021162. Available from:https://www.medrxiv.org/content/10.1101/2020.02.08.20021162v1
10.
Danon L, House T, Keeling M. The role of routine versus random movements on the
spread of disease in Great Britain. Epidemics [Internet]. 2009; Available from:http://linkinghub.elsevier.com/retrieve/pii/S1755436509000553

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