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Paragraph: 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. Imperial College COVID-19 Response Team

Table 2: Totalforecasted deaths since the beginning of the epidemic up to 31 March in our model
and in a counterfactual model (assuming no intervention had taken place). Estimated averted deaths
over this time period as a result of the interventions. Numbers in brackets are 95% credible intervals. 2.3 Estimated impact of interventions on deaths

Table 2 shows total forecasted deaths since the beginning of the epidemic up to and including 31
March under ourfitted model and under the counterfactual model, which predicts what would have
happened if no interventions were implemented (and R, = R0 i.e. the initial reproduction number
estimated before interventions). Again, the assumption in these predictions is that intervention
impact is the same across countries and time. The model without interventions was unable to capture
recent trends in deaths in several countries, where the rate of increase had clearly slowed (Figure 3). Trends were confirmed statistically by Bayesian leave-one-out cross-validation and the widely
applicable information criterion assessments —WA|C). By comparing the deaths predicted under the model with no interventions to the deaths predicted in
our intervention model, we calculated the total deaths averted up to the end of March. We find that,
across 11 countries, since the beginning of the epidemic, 59,000 [21,000-120,000] deaths have been
averted due to interventions. In Italy and Spain, where the epidemic is advanced, 38,000 [13,000-
84,000] and 16,000 [5,400-35,000] deaths have been averted, respectively. Even in the UK, which is
much earlier in its epidemic, we predict 370 [73-1,000] deaths have been averted. These numbers give only the deaths averted that would have occurred up to 31 March. lfwe were to
include the deaths of currently infected individuals in both models, which might happen after 31
March, then the deaths averted would be substantially higher. Figure 3: Daily number of confirmed deaths, predictions (up to 28 March) and forecasts (after) for (a)
Italy and (b) Spain from our model with interventions (blue) and from the no interventions
counterfactual model (pink); credible intervals are shown one week into the future. Other countries
are shown in Appendix 8.6. 03/0 25% 50% 753% 100%
(no effect on transmissibility) (ends transmissibility
Relative % reduction in R.

Figure 4: Our model includes five covariates for governmental interventions, adjusting for whether
the intervention was the first one undertaken by the government in response to COVID-19 (red) or
was subsequent to other interventions (green). Mean relative percentage reduction in Rt is shown
with 95% posterior credible intervals. If 100% reduction is achieved, Rt = 0 and there is no more
transmission of COVID-19. No effects are significantly different from any others, probably due to the
fact that many interventions occurred on the same day or within days of each other as shown in
Figure l.

3 Discussion

During this early phase of control measures against the novel coronavirus in Europe, we analyze trends
in numbers of deaths to assess the extent to which transmission is being reduced. Representing the
COVlD-19 infection process using a semi-mechanistic, joint, Bayesian hierarchical model, we can
reproduce trends observed in the data on deaths and can forecast accurately over short time horizons. We estimate that there have been many more infections than are currently reported. The high level
of under-ascertainment of infections that we estimate here is likely due to the focus on testing in
hospital settings rather than in the community. Despite this, only a small minority of individuals in
each country have been infected, with an attack rate on average of 4.9% [l.9%-ll%] with considerable
variation between countries (Table 1). Our estimates imply that the populations in Europe are not
close to herd immunity ("50-75% if R0 is 2-4). Further, with Rt values dropping substantially, the rate
of acquisition of herd immunity will slow down rapidly. This implies that the virus will be able to spread
rapidly should interventions be lifted. Such estimates of the attack rate to date urgently need to be
validated by newly developed antibody tests in representative population surveys, once these become
available. We estimate that major non-pharmaceutical interventions have had a substantial impact on the time-
varying reproduction numbers in countries where there has been time to observe intervention effects
on trends in deaths (Italy, Spain). lfadherence in those countries has changed since that initial period,
then our forecast of future deaths will be affected accordingly: increasing adherence over time will
have resulted in fewer deaths and decreasing adherence in more deaths. Similarly, our estimates of
the impact ofinterventions in other countries should be viewed with caution if the same interventions
have achieved different levels of adherence than was initially the case in Italy and Spain. Due to the implementation of interventions in rapid succession in many countries, there are not
enough data to estimate the individual effect size of each intervention, and we discourage attributing

associations to individual intervention. In some cases, such as Norway, where all interventions were
implemented at once, these individual effects are by definition unidentifiable. Despite this, while
individual impacts cannot be determined, their estimated joint impact is strongly empirically justified
(see Appendix 8.4 for sensitivity analysis). While the growth in daily deaths has decreased, due to the
lag between infections and deaths, continued rises in daily deaths are to be expected for some time. To understand the impact of interventions, we fit a counterfactual model without the interventions
and compare this to the actual model. Consider Italy and the UK - two countries at very different stages
in their epidemics. For the UK, where interventions are very recent, much of the intervention strength
is borrowed from countries with older epidemics. The results suggest that interventions will have a
large impact on infections and deaths despite counts of both rising. For Italy, where far more time has
passed since the interventions have been implemented, it is clear that the model without
interventions does not fit well to the data, and cannot explain the sub-linear (on the logarithmic scale)
reduction in deaths (see Figure 10). The counterfactual model for Italy suggests that despite mounting pressure on health systems,
interventions have averted a health care catastrophe where the number of new deaths would have
been 3.7 times higher (38,000 deaths averted) than currently observed. Even in the UK, much earlier
in its epidemic, the recent interventions are forecasted to avert 370 total deaths up to 31 of March. 4 Conclusion and Limitations

Modern understanding of infectious disease with a global publicized response has meant that
nationwide interventions could be implemented with widespread adherence and support. Given
observed infection fatality ratios and the epidemiology of COVlD-19, major non-pharmaceutical
interventions have had a substantial impact in reducing transmission in countries with more advanced
epidemics. It is too early to be sure whether similar reductions will be seen in countries at earlier
stages of their epidemic. While we cannot determine which set of interventions have been most
successful, taken together, we can already see changes in the trends of new deaths. When forecasting
3 days and looking over the whole epidemic the number of deaths averted is substantial. We note that
substantial innovation is taking place, and new more effective interventions or refinements of current
interventions, alongside behavioral changes will further contribute to reductions in infections. We
cannot say for certain that the current measures have controlled the epidemic in Europe; however, if
current trends continue, there is reason for optimism. Our approach is semi-mechanistic. We propose a plausible structure for the infection process and then
estimate parameters empirically. However, many parameters had to be given strong prior
distributions or had to be fixed. For these assumptions, we have provided relevant citations to
previous studies. As more data become available and better estimates arise, we will update these in
weekly reports. Our choice of serial interval distribution strongly influences the prior distribution for
starting R0. Our infection fatality ratio, and infection-to-onset-to-death distributions strongly
influence the rate of death and hence the estimated number of true underlying cases. We also assume that the effect of interventions is the same in all countries, which may not be fully
realistic. This assumption implies that countries with early interventions and more deaths since these
interventions (e.g. Italy, Spain) strongly influence estimates of intervention impact in countries at
earlier stages of their epidemic with fewer deaths (e.g. Germany, UK). We have tried to create consistent definitions of all interventions and document details of this in
Appendix 8.6. However, invariably there will be differences from country to country in the strength of
their intervention — for example, most countries have banned gatherings of more than 2 people when
implementing a lockdown, whereas in Sweden the government only banned gatherings of more than
10 people. These differences can skew impacts in countries with very little data. We believe that our
uncertainty to some degree can cover these differences, and as more data become available,
coefficients should become more reliable. However, despite these strong assumptions, there is sufficient signal in the data to estimate changes
in R, (see the sensitivity analysis reported in Appendix 8.4.3) and this signal will stand to increase with
time. In our Bayesian hierarchical framework, we robustly quantify the uncertainty in our parameter
estimates and posterior predictions. This can be seen in the very wide credible intervals in more recent
days, where little or no death data are available to inform the estimates. Furthermore, we predict
intervention impact at country-level, but different trends may be in place in different parts of each
country. For example, the epidemic in northern Italy was subject to controls earlier than the rest of
the country.

Question: What is Germany's estimated mean percentage [95% credible interval] of total population infected as of 28th March?
0.72% [0.28%-1.8%]