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Paragraph: Our methods assume that changes in the reproductive number — a measure of transmission - are an immediate response to these interventions
being implemented rather than broader gradual changes in behaviour. Our model estimates these
changes by calculating backwards from the deaths observed over time to estimate transmission that
occurred several weeks prior, allowing for the time lag between infection and death. One of the key assumptions of the model is that each intervention has the same effect on the
reproduction number across countries and over time. This allows us to leverage a greater amount of
data across Europe to estimate these effects. It also means that our results are driven strongly by the
data from countries with more advanced epidemics, and earlier interventions, such as Italy and Spain. We find that the slowing growth in daily reported deaths in Italy is consistent with a significant impact
of interventions implemented several weeks earlier. In Italy, we estimate that the effective
reproduction number, Rt, dropped to close to 1 around the time of Iockdown (11th March), although
with a high level of uncertainty. Overall, we estimate that countries have managed to reduce their reproduction number. Our
estimates have wide credible intervals and contain 1 for countries that have implemented a||
interventions considered in our analysis. This means that the reproduction number may be above or
below this value. With current interventions remaining in place to at least the end of March, we
estimate that interventions across all 11 countries will have averted 59,000 deaths up to 31 March
[95% credible interval 21,000-120,000]. Many more deaths will be averted through ensuring that
interventions remain in place until transmission drops to low levels. We estimate that, across all 11
countries between 7 and 43 million individuals have been infected with SARS-CoV-Z up to 28th March,
representing between 1.88% and 11.43% ofthe population. The proportion of the population infected

to date — the attack rate - is estimated to be highest in Spain followed by Italy and lowest in Germany
and Norway, reflecting the relative stages of the epidemics. Given the lag of 2-3 weeks between when transmission changes occur and when their impact can be
observed in trends in mortality, for most of the countries considered here it remains too early to be
certain that recent interventions have been effective. If interventions in countries at earlier stages of
their epidemic, such as Germany or the UK, are more or less effective than they were in the countries
with advanced epidemics, on which our estimates are largely based, or if interventions have improved
or worsened over time, then our estimates of the reproduction number and deaths averted would
change accordingly. It is therefore critical that the current interventions remain in place and trends in
cases and deaths are closely monitored in the coming days and weeks to provide reassurance that
transmission of SARS-Cov-Z is slowing. SUGGESTED CITATION

Seth Flaxman, Swapnil Mishra, Axel Gandy et 0/. Estimating the number of infections and the impact of non—
pharmaceutical interventions on COVID—19 in 11 European countries. Imperial College London (2020), doi:
https://doi.org/10.25561/77731

1 Introduction

Following the emergence of a novel coronavirus (SARS-CoV-Z) in Wuhan, China in December 2019 and
its global spread, large epidemics of the disease, caused by the virus designated COVID-19, have
emerged in Europe. In response to the rising numbers of cases and deaths, and to maintain the
capacity of health systems to treat as many severe cases as possible, European countries, like those in
other continents, have implemented or are in the process of implementing measures to control their
epidemics. These large-scale non-pharmaceutical interventions vary between countries but include
social distancing (such as banning large gatherings and advising individuals not to socialize outside
their households), border closures, school closures, measures to isolate symptomatic individuals and
their contacts, and large-scale lockdowns of populations with all but essential internal travel banned. Understanding firstly, whether these interventions are having the desired impact of controlling the
epidemic and secondly, which interventions are necessary to maintain control, is critical given their
large economic and social costs. The key aim ofthese interventions is to reduce the effective reproduction number, Rt, ofthe infection,
a fundamental epidemiological quantity representing the average number of infections, at time t, per
infected case over the course of their infection. Ith is maintained at less than 1, the incidence of new
infections decreases, ultimately resulting in control of the epidemic. If Rt is greater than 1, then
infections will increase (dependent on how much greater than 1 the reproduction number is) until the
epidemic peaks and eventually declines due to acquisition of herd immunity. In China, strict movement restrictions and other measures including case isolation and quarantine
began to be introduced from 23rd January, which achieved a downward trend in the number of
confirmed new cases during February, resulting in zero new confirmed indigenous cases in Wuhan by
March 19th. Studies have estimated how Rt changed during this time in different areas ofChina from
around 2-4 during the uncontrolled epidemic down to below 1, with an estimated 7-9 fold decrease
in the number of daily contacts per person.1'2 Control measures such as social distancing, intensive
testing, and contact tracing in other countries such as Singapore and South Korea have successfully
reduced case incidence in recent weeks, although there is a riskthe virus will spread again once control
measures are relaxed.3'4

The epidemic began slightly laterin Europe, from January or later in different regions.5 Countries have
implemented different combinations of control measures and the level of adherence to government
recommendations on social distancing is likely to vary between countries, in part due to different
levels of enforcement. Estimating reproduction numbers for SARS-CoV-Z presents challenges due to the high proportion of
infections not detected by health systems”7 and regular changes in testing policies, resulting in
different proportions of infections being detected over time and between countries. Most countries
so far only have the capacity to test a small proportion of suspected cases and tests are reserved for
severely ill patients or for high-risk groups (e.g. contacts of cases). Looking at case data, therefore,
gives a systematically biased view of trends. An alternative way to estimate the course of the epidemic is to back-calculate infections from
observed deaths. Reported deaths are likely to be more reliable, although the early focus of most
surveillance systems on cases with reported travel histories to China may mean that some early deaths
will have been missed. Whilst the recent trends in deaths will therefore be informative, there is a time
lag in observing the effect of interventions on deaths since there is a 2-3-week period between
infection, onset of symptoms and outcome. In this report, we fit a novel Bayesian mechanistic model of the infection cycle to observed deaths in
11 European countries, inferring plausible upper and lower bounds (Bayesian credible intervals) of the
total populations infected (attack rates), case detection probabilities, and the reproduction number
over time (Rt). We fit the model jointly to COVID-19 data from all these countries to assess whether
there is evidence that interventions have so far been successful at reducing Rt below 1, with the strong
assumption that particular interventions are achieving a similar impact in different countries and that
the efficacy of those interventions remains constant over time. The model is informed more strongly
by countries with larger numbers of deaths and which implemented interventions earlier, therefore
estimates of recent Rt in countries with more recent interventions are contingent on similar
intervention impacts. Data in the coming weeks will enable estimation of country-specific Rt with
greater precision. Model and data details are presented in the appendix, validation and sensitivity are also presented in
the appendix, and general limitations presented below in the conclusions. 2 Results

The timing of interventions should be taken in the context of when an individual country’s epidemic
started to grow along with the speed with which control measures were implemented. Italy was the
first to begin intervention measures, and other countries followed soon afterwards (Figure 1). Most
interventions began around 12th-14th March. We analyzed data on deaths up to 28th March, giving a
2-3-week window over which to estimate the effect of interventions. Currently, most countries in our
study have implemented all major non-pharmaceutical interventions. For each country, we model the number of infections, the number of deaths, and Rt, the effective
reproduction number over time, with Rt changing only when an intervention is introduced (Figure 2-
12). Rt is the average number of secondary infections per infected individual, assuming that the
interventions that are in place at time t stay in place throughout their entire infectious period. Every
country has its own individual starting reproduction number Rt before interventions take place. Specific interventions are assumed to have the same relative impact on Rt in each country when they
were introduced there and are informed by mortality data across all countries. Figure l: Intervention timings for the 11 European countries included in the analysis. For further
details see Appendix 8.6. 2.1 Estimated true numbers of infections and current attack rates

In all countries, we estimate there are orders of magnitude fewer infections detected (Figure 2) than
true infections, mostly likely due to mild and asymptomatic infections as well as limited testing
capacity. In Italy, our results suggest that, cumulatively, 5.9 [1.9-15.2] million people have been
infected as of March 28th, giving an attack rate of 9.8% [3.2%-25%] of the population (Table 1). Spain
has recently seen a large increase in the number of deaths, and given its smaller population, our model
estimates that a higher proportion of the population, 15.0% (7.0 [18-19] million people) have been
infected to date. Germany is estimated to have one of the lowest attack rates at 0.7% with 600,000
[240,000-1,500,000] people infected. Imperial College COVID-19 Response Team

Table l: Posterior model estimates of percentage of total population infected as of 28th March 2020. Country % of total population infected (mean [95% credible intervall)
Austria 1.1% [0.36%-3.1%]
Belgium 3.7% [1.3%-9.7%]
Denmark 1.1% [0.40%-3.1%]
France 3.0% [1.1%-7.4%]
Germany 0.72% [0.28%-1.8%]
Italy 9.8% [3.2%-26%]
Norway 0.41% [0.09%-1.2%]
Spain 15% [3.7%-41%]
Sweden 3.1% [0.85%-8.4%]
Switzerland 3.2% [1.3%-7.6%]
United Kingdom 2.7% [1.2%-5.4%]

2.2 Reproduction numbers and impact of interventions

Averaged across all countries, we estimate initial reproduction numbers of around 3.87 [3.01-4.66],
which is in line with other estimates.1'8 These estimates are informed by our choice of serial interval
distribution and the initial growth rate of observed deaths. A shorter assumed serial interval results in
lower starting reproduction numbers (Appendix 8.4.2, Appendix 8.4.6). The initial reproduction
numbers are also uncertain due to (a) importation being the dominant source of new infections early
in the epidemic, rather than local transmission (b) possible under-ascertainment in deaths particularly
before testing became widespread. We estimate large changes in Rt in response to the combined non-pharmaceutical interventions. Our
results, which are driven largely by countries with advanced epidemics and larger numbers of deaths
(e.g. Italy, Spain), suggest that these interventions have together had a substantial impact on
transmission, as measured by changes in the estimated reproduction number Rt. Across all countries
we find current estimates of Rt to range from a posterior mean of 0.97 [0.14-2.14] for Norway to a
posterior mean of2.64 [1.40-4.18] for Sweden, with an average of 1.43 across the 11 country posterior
means, a 64% reduction compared to the pre-intervention values. We note that these estimates are
contingent on intervention impact being the same in different countries and at different times. In all
countries but Sweden, under the same assumptions, we estimate that the current reproduction
number includes 1 in the uncertainty range. The estimated reproduction number for Sweden is higher,
not because the mortality trends are significantly different from any other country, but as an artefact
of our model, which assumes a smaller reduction in Rt because no full lockdown has been ordered so
far. Overall, we cannot yet conclude whether current interventions are sufficient to drive Rt below 1
(posterior probability of being less than 1.0 is 44% on average across the countries). We are also
unable to conclude whether interventions may be different between countries or over time. There remains a high level of uncertainty in these estimates. It is too early to detect substantial
intervention impact in many countries at earlier stages of their epidemic (e.g. Germany, UK, Norway). Many interventions have occurred only recently, and their effects have not yet been fully observed
due to the time lag between infection and death. This uncertainty will reduce as more data become
available. For all countries, our model fits observed deaths data well (Bayesian goodness of fit tests). We also found that our model can reliably forecast daily deaths 3 days into the future, by withholding
the latest 3 days of data and comparing model predictions to observed deaths (Appendix 8.3). The close spacing of interventions in time made it statistically impossible to determine which had the
greatest effect (Figure 1, Figure 4). However, when doing a sensitivity analysis (Appendix 8.4.3) with
uninformative prior distributions (where interventions can increase deaths) we find similar impact of

Imperial College COVID-19 Response Team

interventions, which shows that our choice of prior distribution is not driving the effects we see in the

main analysis. Figure 2: Country-level estimates of infections, deaths and Rt. Left: daily number of infections, brown
bars are reported infections, blue bands are predicted infections, dark blue 50% credible interval (CI),
light blue 95% CI. The number of daily infections estimated by our model drops immediately after an
intervention, as we assume that all infected people become immediately less infectious through the
intervention. Afterwards, if the Rt is above 1, the number of infections will starts growing again. Middle: daily number of deaths, brown bars are reported deaths, blue bands are predicted deaths, CI
as in left plot. Right: time-varying reproduction number Rt, dark green 50% CI, light green 95% CI. Icons are interventions shown at the time they occurred.

Question: What is a way to measure virus transmission?
reproductive number