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Effects of non-pharmaceutical interventions on COVID-19: A Tale of Two Models

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Effects of non-pharmaceutical interventions on COVID-19: A Tale of Two Models

Abstract

Objective To compare the inference regarding the effectiveness of the various non-pharmaceutical interventions (NPIs) for COVID-19 obtained from different SIR models. Study design and setting We explored two models developed by Imperial College that considered only NPIs without accounting for mobility (model 1) or only mobility (model 2), and a model accounting for the combination of mobility and NPIs (model 3). Imperial College applied models 1 and 2 to 11 European countries and to the USA, respectively. We applied these models to 14 European countries (original 11 plus another 3), over two different time horizons. Results While model 1 found that lockdown was the most effective measure in the original 11 countries, model 2 showed that lockdown had little or no benefit as it was typically introduced at a point when the time-varying reproductive number was already very low. Model 3 found that the simple banning of public events was beneficial, while lockdown had no consistent impact. Based on Bayesian metrics, model 2 was better supported by the data than either model 1 or model 3 for both time horizons. Conclusions Inferences on effects of NPIs are non-robust and highly sensitive to model specification. Claimed benefits of lockdown appear grossly exaggerated.
Effects of non-pharmaceutical interventions on COVID-19:
A Tale of Two Models
Vincent Chin1,2, John P.A. Ioannidis4,5,6,7,8, Martin A. Tanner3, and Sally
Cripps1,2,*
1ARC Centre for Data Analytics for Resources and Environments, Australia
2School of Mathematics and Statistics, The University of Sydney, Australia
3Department of Statistics, Northwestern University, USA
4Stanford Prevention Research Center, Department of Medicine, Stanford
University, USA
5Department of Epidemiology and Population Health, Stanford University, USA
6Department of Biomedical Data Sciences, Stanford University, USA
7Department of Statistics, Stanford University, USA
8Meta-Research Innovation Center at Stanford (METRICS), Stanford University,
USA
*Corresponding author: sally.cripps@sydney.edu.au +61 425-276-967
July 23, 2020
Abstract
In this paper, we compare the inference regarding the effectiveness of the various non-
pharmaceutical interventions (NPIs) for COVID-19 obtained from two SIR models, both
produced by the Imperial College COVID-19 Response Team. One model was applied to
European countries and published in Nature 1, concluding that complete lockdown was by
far the most effective measure and 3 million deaths were avoided in the examined countries.
The Imperial College team applied a different model to the USA states 2. Here, we show
that inference is not robust to model specification and indeed changes substantially with
the model used for the evolution of the time-varying reproduction number, denoted by Rt.
Applying to European countries the model that the Imperial College team used for the USA
states shows that complete lockdown has no or little effect, since it was introduced typically
at a point when Rtwas already very low. We also show that results are not robust to the
inclusion of additional follow-up data.
Keywords: COVID-19; Non-pharmaceutical Interventions; Bayesian SIR Models
1
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1 A Tale of Two Models
The two models (Flaxman et al.1and Unwin et al. 2) produced by the Imperial College COVID-19
Response Team aim to explain the evolution of Rt. We will refer to these models as model 1
(the model applied to European countries in the Nature publication 1) and model 2 (the model
applied to the USA states2), respectively. The two models for the Rtare fundamentally different.
In model 1, the proportional variation of Rtfrom the initial R0is modelled as a step function and
only allowed to change in response to an intervention. Therefore, any decrease in Rt(even if this
decrease is a result of the increasing proportion of the population who are infected, to changes
in human behaviour, clustered contact structures and/or pre-existing immunity3) must, by the
model construction, be attributed to interventions and the impact is immediate with no time lag
or gradual change, when a new intervention is adopted. In model 2, the proportional variation
of Rtfrom R0has a different functional form and is allowed to vary with mobility indicators for
various activities. These mobility indicators are proxies for changes in human behaviour, whether
that change is due to one or more centrally imposed interventions or whether it is the product of
individuals responding to the epidemic on their own initiative independently of centrally imposed
interventions. Model 2 also does not presume step functions and is therefore capable of capturing
more gradual changes over time. Model 1 is deliberately simple and designed to test the impact
of interventions without the confounders of mobility data, which themselves could be the product
of the interventions. Model 2 leaves out interventions and uses mobility data as predictors in the
evolution of Rt. The advantage of model 2 is that it gives a more flexible estimate of Rt, by
allowing it to change with mobility trends. Although there is no explicit causal structure in model
2, the time sequence of the data and events makes inference around the impact of interventions
possible by observing if the change in Rtprecedes a given intervention or interventions or not.
Here, we apply both models 1 and 2 to the European data to compare the results and inferences
they obtain. See supplementary methods for details on methods and data.
2 Results
There are two main observations when comparing the modeling results in Figure 1a, as well as the
corresponding Extended Data Figures 1a1e. First, and most notable, is that while the models give
very different trajectories of Rt, both models produce similar and accurate fit to the observed daily
death counts. That is, very different processes of Rtgive rise to the same daily death
count data. The second observation is that inference regarding the impact of interventions varies
significantly between the two models. The inference from model 1 indicates that lockdown had
the biggest impact of all the interventions in all countries. Indeed, Flaxman et al.1states that
Lockdown has an identifiable large impact on transmission (81% [75%- 87%] reduction).
In contrast, model 2 shows clearly that Rtwas falling well before lockdown, which occurred
after the sharp decline in Rt. With the exception of Belgium (and to a lesser degree France), this
is consistently seen across the European countries (see Extended Data Figures 1a1e) and is in
line with the mobility data, see Figure 2. At the time lockdown was adopted in the UK, Rthad
already decreased to 1.46 (95% CI, 0.89 to 2.20) from an initial R0of 4.46 (95% CI, 2.62 to 7.20)
according to model 2, and the largest drop in Rtoccurred after the implementation of self-isolation
measures and encouraging social distancing, see Table 1.
We also evaluated the effect of extending the time horizon of analysis until July 12th where
2
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(a) Daily infections, daily deaths and Rtuntil May 5th.
(b) Daily infections, daily deaths and Rtuntil July 12th in columns 1–3. Column 4 is a magnification of
column 3 around the period of the NPIs.
Figure 1: United Kingdom. The start time for the plots is 30 and 10 days before 10 deaths are
recorded, in the two models, respectively. Observed counts of daily infections and daily deaths are
shown in red, and their corresponding 50% and 95% CIs are shown in dark blue and light blue
respectively.
3
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Switzerland
United Kingdom
Norway
Portugal
Spain
Sweden
Germany
Greece
Italy
Netherlands
Austria
Belgium
Denmark
France
MarAprMayJun Jul MarAprMayJun Jul
MarAprMayJun Jul MarAprMayJun Jul
−100
−50
0
50
−100
−50
0
50
−100
−50
0
50
−100
−50
0
50
Date
Percentage change from baseline
Location
Retail &
recreation
Grocery &
pharmacy
Transit
stations
Workplaces
Residential
Average (retail,
grocery, transit,
work)
Figure 2: Percentage change in mobility from baseline level from February 15th to July 12th, by
locations in each of the European countries examined in Flaxman et al. 1, as well as an additional
three countries consisting of Greece, the Netherlands and Portugal. Average mobility is computed
based on the trends in retailers and recreation venues, grocery markets and pharmacy, transit
stations and workplaces. Black dashed lines in each plot indicate the lockdown start and end
dates.
restrictions had been lifted in some of these countries. We include an additional three countries,
i.e. Greece, the Netherlands and Portugal, in the analysis. Extended Data Table 1shows the end
dates of school closures, ban on public events and lockdown used in the analysis. Figure 1b shows
a comparison of the results obtained from both models for the UK for the extended data while
Extended Data Figures 2a2g show similar results for the remaining 13 countries. Table 2tabulates
4
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Country R0
Rtimmediately at NPIs introduction
SI SD SC EB LD
UK 3.74 3.72 3.70 3.64 0.66 0.66
(3.33, 4.22) (3.29, 4.19) (3.24, 4.18) (3.03, 4.18) (0.53, 0.80) (0.53, 0.80)
Austria 3.91 0.68 0.68 3.81 3.87 0.68
(2.96, 5.22) (0.56, 0.79) (0.56, 0.79) (2.84, 5.12) (2.90, 5.13) (0.56, 0.79)
Belgium 5.06 5.03 4.89 4.89 4.99 0.90
(4.10, 6.42) (4.07, 6.41) (3.83, 6.31) (3.83, 6.31) (4.02, 6.39) (0.78, 1.01)
Denmark 3.50 3.45 3.38 3.38 3.45 0.73
(2.60, 4.66) (2.56, 4.60) (2.54, 4.57) (2.54, 4.57) (2.56, 4.60) (0.61, 0.85)
France 4.48 4.33 4.33 4.37 4.44 0.71
(3.96, 5.09) (3.62, 5.07) (3.62, 5.07) (3.68, 5.07) (3.80, 5.08) (0.62, 0.82)
Germany 4.01 3.99 3.96 3.90 0.73 0.73
(3.40, 4.86) (3.39, 4.71) (3.36, 4.68) (3.33, 4.68) (0.61, 0.84) (0.61, 0.84)
Italy 3.41 3.29 3.29 3.34 3.29 0.69
(3.06, 3.79) (2.90, 3.70) (2.90, 3.70) (3.02, 3.72) (2.90, 3.70) (0.62, 0.75)
Norway 3.10 3.00 2.98 3.01 3.07 0.44
(2.25, 4.02) (2.19, 3.90) (2.17, 3.89) (2.20, 3.91) (2.23, 3.91) (0.28, 0.61)
Spain 4.66 0.67 4.62 4.55 0.67 0.67
(3.91, 5.51) (0.58, 0.75) (3.90, 5.46) (3.49, 5.45) (0.58, 0.75) (0.58, 0.75)
Sweden 2.69 2.68 2.66 0.72
(2.28, 3.09) (2.27, 3.07) (2.27, 3.05) (0.54, 0.93)
Switzerland 3.26 3.24 3.15 3.17 3.22 0.54
(2.69, 3.93) (2.68, 3.85) (2.64, 3.78) (2.66, 3.82) (2.66, 3.86) (0.43, 0.66)
(a) Model 1.
Country R0
Rtimmediately at NPIs introduction
SI SD SC EB LD
UK 4.46 4.33 4.20 2.41 1.46 1.46
(2.64, 7.20) (3.23, 5.58) (3.13, 5.41) (1.69, 3.25) (0.89, 2.20) (0.89, 2.20)
Austria* 2.69 0.87 0.87 1.43 0.87
(1.06, 5.71) (0.34, 1.78) (0.34, 1.78) (0.56, 2.91) (0.34, 1.78)
Belgium 4.36 4.19 4.29 4.29 4.49 4.46
(2.38, 7.17) (2.27, 6.72) (2.33, 6.89) (2.33, 6.89) (2.47, 7.18) (3.09, 6.09)
Denmark 2.39 1.29 0.89 0.89 1.29 0.69
(1.08, 5.13) (0.56, 2.51) (0.38, 1.75) (0.38, 1.75) (0.56, 2.51) (0.28, 1.40)
France 4.05 3.62 3.62 4.02 4.53 2.15
(2.46, 6.49) (2.68, 4.62) (2.68, 4.62) (3.01, 5.14) (3.38, 5.88) (1.35, 3.10)
Germany 4.49 4.18 4.15 4.04 1.24 1.24
(2.42, 7.22) (2.25, 6.78) (2.24, 6.74) (2.84, 5.55) (0.74, 1.84) (0.74, 1.84)
Italy 4.62 1.74 1.74 2.87 1.74 1.22
(2.71, 7.29) (1.05, 2.50) (1.05, 2.50) (2.02, 3.75) (1.05, 2.50) (0.74, 1.80)
Norway* 2.22 0.65 0.82 0.60
(1.04, 4.95) (0.24, 1.37) (0.32, 1.67) (0.31, 1.02)
Spain 5.25 1.64 5.31 4.30 1.64 1.64
(3.28, 7.83) (1.00, 2.39) (4.12, 6.71) (3.25, 5.52) (1.00, 2.39) (1.00, 2.39)
Sweden 3.79 3.24 2.77 1.59
(1.85, 6.81) (1.64, 5.62) (1.84, 3.97) (1.03, 2.23)
Switzerland* 3.45 2.46 2.43 2.80 0.99
(1.54, 6.40) (1.58, 3.56) (1.56, 3.52) (1.77, 4.13) (0.60, 1.45)
(b) Model 2.
Table 1: Basic reproduction number R0and time-varying reproduction number Rtimmediately at
time of introduction of NPIs given by both models using data up to May 5th for all eleven countries
analysed in Flaxman et al.1. These NPIs are self-isolation (SI), social distancing (SD), school
closure (SC), event ban (EB) and lockdown (LD). 95% credible intervals are given in parentheses
below the corresponding point estimates. Countries where the seeding of new infections occur
after the introduction of NPIs are denoted with an asterisk.
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the original R0and Rtat the time of adoption of each NPI in each country for both models for the
period March 4th to July 12th. The change in inference from model 1 as a result of the additional
data is astonishing. Table 2, Figure 1b, and Extended Data Figures 2a2g show that with the
inclusion of the data until July 12th, Rtbefore lockdown was already below 1 for ten of the fourteen
countries. The 95% credible intervals for the UK, Austria, Germany and Spain exceeded 1 before
lockdown. Indeed, in contrast to the results reported in the Nature paper1, results from model 1
suggest that the banning of public events and social distancing are more proximally related to the
reduction in Rtthan lockdown. For example, while the results from model 1 in Figure 1a, which
corresponds to the data until May 5th, suggests that lockdown led to the largest decrease in Rt, it
now indicates that the largest decrease in Rthappened after social distancing is practised from a
mean value of 5.27 (95% CI, 4.50 to 6.04) to 2.10 (95% CI, 1.61 to 2.64)! Note that the inference
from model 1 regarding the relative effectiveness of lockdown is now more consistent with the
inference from model 2 across most countries. Finally, we should point out that Figure 1b show
that the gradual increase in Rtfollowing the minimum value commenced well before the lifting of
lockdown. This suggests that as people become less frightened by the prospect of a catastrophe,
mobility (see Figure 2), and hence the time-varying reproduction number increases.
3 Conclusion
These findings clearly present policy makers with a conundrum. Which results should be used to
guide policy making in lifting restrictions? Flaxman et al.1make the statement We find that,
across 11 countries, since the beginning of the epidemic, 3,100,000 [2,800,000 - 3,500,000] deaths
have been averted due to interventions. However, we have shown that two different models,
both of which give plausible fits to the actual death count data, yield vastly different inferences
concerning the effectiveness of intervention strategies for the period March 4th to May 5th in the
UK. Results are also different when the observation period is extended and easing of restrictions
is included in the model. Although it is tempting to congratulate ourselves on our decision to
implement lockdown, citing the number of lives that were saved, we should resist this temptation,
and examine other possible explanations. Failure to do this and therefore mis-attribute causation
could mean we fail to find the optimal solution to this very challenging and complex problem, given
that complete lockdown can also have many adverse consequences4.
We do not want to reach the opposite extreme of claiming with certainty that lockdown defi-
nitely had no impact. Other investigators using a different analytical approach have suggested also
benefits from lockdown, but of much smaller magnitude (13% relative risk reduction5) that might
not necessarily match complete lockdown-induced harms in a careful decision analysis. Another
modeling approach has found that benefits can be reaped by simple self-imposed interventions
such as washing hands, wearing masks, and some social distancing6. Observational data need to
be dissected very carefully and substantial uncertainty may remain even with the best modelling7.
Regardless, causal interpretations from models that are not robust should be avoided. Given the
analyses that we have performed using the two models that the Imperial College team has de-
veloped, one cannot exclude that the attribution of benefit to complete lockdown is a modelling
artefact.
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Country R0
Rtimmediately at NPIs introduction
SI SD SC EB LD
UK 5.26 5.27 2.10 1.96 0.84 0.84
(4.53, 6.00) (4.50,6.04) (1.61,2.64) (1.45,2.50) (0.79,0.89) (0.79,0.89)
Austria 4.66 0.70 0.70 1.94 2.08 0.70
(3.94, 5.49) (0.63,0.75) (0.63,0.75) (1.42,2.62) (1.53,2.81) (0.63,0.75)
Belgium 4.89 4.90 0.80 0.80 2.18 0.72
(4.00, 6.04) (3.99,6.06) (0.69,0.97) (0.69,0.97) (1.55,3.06) (0.69,0.74)
Denmark 4.41 1.98 0.72 0.72 1.98 0.76
(3.76, 5.07) (1.42,2.78) (0.65,0.78) (0.65,0.78) (1.42,2.78) (0.69,0.86)
France 4.73 0.77 0.77 1.97 2.12 0.72
(4.07, 5.43) (0.71,0.85) (0.71,0.85) (1.46,2.61) (1.54,2.90) (0.67,0.76)
Germany 4.63 4.64 1.85 1.73 0.75 0.75
(3.95, 5.31) (3.95,5.35) (1.41,2.36) (1.27,2.22) (0.69,0.80) (0.69,0.80)
Greece 3.88 3.89 1.44 3.63 0.63 0.73
(2.82, 4.81) (2.83,4.85) (1.01,1.89) (2.61,4.68) (0.47,0.75) (0.67,0.79)
Italy 4.38 0.72 0.72 4.11 0.72 0.76
(3.85, 4.94) (0.65,0.77) (0.65,0.77) (3.33,4.76) (0.65,0.77) (0.72,0.80)
Netherlands 4.36 0.77 0.77 0.71 0.77 0.72
(3.73, 5.00) (0.65,0.94) (0.65,0.94) (0.64,0.78) (0.65,0.94) (0.67,0.77)
Norway 3.92 1.64 0.64 1.64 1.76 0.67
(3.29, 4.57) (1.12,2.32) (0.56,0.71) (1.13,2.31) (1.20,2.51) (0.59,0.79)
Portugal 5.30 0.87 0.93 0.87 0.93 0.87
(4.31, 6.43) (0.73,1.02) (0.75,1.19) (0.73,1.03) (0.75,1.19) (0.84,0.90)
Spain 4.58 0.76 1.83 1.71 0.76 0.76
(3.86, 5.33) (0.74,0.79) (1.38,2.33) (1.24,2.20) (0.74,0.79) (0.74,0.79)
Sweden 4.82 4.83 1.91 0.88
(3.80, 5.89) (3.80,5.89) (1.53,2.34) (0.85,0.92)
Switzerland 4.26 4.27 0.70 1.77 1.90 0.64
(3.52, 5.33) (3.49,5.33) (0.60,0.85) (1.29,2.43) (1.37,2.65) (0.61,0.68)
(a) Model 1.
Country R0
Rtimmediately at NPIs introduction
SI SD SC EB LD
UK 4.43 4.35 4.22 2.35 1.43 1.43
(2.55,7.08) (3.11,5.92) (3.02,5.73) (1.59,3.18) (0.84,2.17) (0.84,2.17)
Austria* 2.38 0.78 0.78 1.21 0.78
(1.05,5.37) (0.34,1.54) (0.34,1.54) (0.52,2.36) (0.34,1.54)
Belgium 4.29 3.91 2.45 2.45 4.26 1.48
(2.15,7.07) (2.13,6.31) (1.61,3.48) (1.61,3.48) (2.69,6.17) (0.92,2.13)
Denmark 2.02 1.12 0.83 0.83 1.12 0.67
(1.03,5.03) (0.50,2.11) (0.37,1.60) (0.37,1.60) (0.50,2.11) (0.28,1.30)
France 4.17 3.39 3.39 3.76 4.25 2.04
(2.47,6.76) (2.48,4.48) (2.48,4.48) (2.78,4.96) (3.13,5.65) (1.28,2.97)
Germany 4.11 3.52 3.50 3.50 1.29 1.29
(2.12,7.09) (1.85,5.94) (1.83,5.90) (2.31,5.08) (0.78,1.94) (0.78,1.94)
Greece* 1.92 0.69 0.50 0.41
(1.03,4.41) (0.29,1.29) (0.24,0.81) (0.19,0.68)
Italy 4.22 1.90 1.90 2.91 1.90 1.39
(2.41,6.86) (1.21,2.70) (1.21,2.70) (2.06,3.88) (1.21,2.70) (0.88,2.01)
Netherlands 3.38 2.77 2.77 2.45 2.77 1.09
(1.53,6.43) (1.75,4.21) (1.75,4.21) (1.58,3.62) (1.75,4.21) (0.67,1.59)
Norway* 1.99 0.61 0.74 0.59
(1.01,4.73) (0.25,1.20) (0.32,1.42) (0.31,0.99)
Portugal 2.87 0.94 2.40 1.64 2.40 0.79
(1.15,6.00) (0.54,1.45) (0.97,4.71) (0.71,3.09) (0.97,4.71) (0.45,1.24)
Spain 5.25 1.74 5.09 4.16 1.74 1.74
(3.25,8.05) (1.05,2.50) (3.76,6.81) (3.04,5.58) (1.05,2.50) (1.05,2.50)
Sweden 3.02 2.51 2.27 1.58
(1.36,6.00) (1.32,4.44) (1.47,3.42) (1.07,2.20)
Switzerland* 2.83 2.05 2.03 2.29 1.03
(1.27,5.59) (1.26,3.09) (1.25,3.05) (1.37,3.53) (0.64,1.52)
(b) Model 2.
Table 2: Basic reproduction number R0and time-varying reproduction number Rtimmediately
at time of introduction of NPIs given by both models using data up to July 12th for all eleven
countries analysed in Flaxman et al.1plus Greece, the Netherlands and Portugal. These NPIs
are self-isolation (SI), social distancing (SD), school closure (SC), event ban (EB) and lockdown
(LD). 95% credible intervals are given in parentheses below the corresponding point estimates.
Countries where the seeding of new infections occur after the introduction of NPIs are denoted
with an asterisk.
7
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Acknowledgement
We congratulate the Imperial College Response Team for sharing openly the code for their models
and for the overall transparency of their work that has allowed performing these analyses. We also
thank Jack Wood for his help in the construction of Extended Data Table 1.
Author Contributions
All authors contributed equally to this work. VC performed all the computations and produced all
the graphics. SC wrote the initial draft. JI and MT wrote subsequent drafts. All authors discussed
the results and implications and commented on the manuscript at all stages.
Conflicts of Interest
None.
Code Availability
All source code for the replication of our results is available from the Imperial College COVID-19 Re-
sponse Team’s Github repository: https://github.com/ImperialCollegeLondon/covid19model.
Daily confirmed cases and deaths data are publicly available from the European Centre of Disease
Control’s website.
References
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[2] Unwin, H. J. T. et al. State-level tracking of COVID-19 in the United States. medRxiv
(2020). Doi: https://doi.org/10.1101/2020.07.13.20152355.
[3] Grifoni, A. et al. Targets of T cell responses to SARS-CoV-2 coronavirus in humans with
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[5] Islam, N. et al. Physical distancing interventions and incidence of coronavirus disease 2019:
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[7] Ioannidis, J. P. A., Cripps, S. & Tanner, M. A. Forecasting for COVID-19 has failed. Inter-
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[13] The Local. AFTER LOCKDOWN: Are Denmark’s and Norway’s restrictions
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Supplementary Methods
Model 2 assumes that Rtis a function of mobility and allows this impact to vary regionally by the
use of regional specific random effects terms. The data used by Unwin et al.2to estimate Rtis
the Google’s COVID-19 Community Mobility Report. We adapt this methodology to the European
context by modelling potential idiosyncrasies in mobility trends across countries using country-
specific random effects. To complete the specification of model 2 for the European data, we use
Google’s COVID-19 Community Mobility Report8which provides data measuring the percentage
change in mobility compared to a baseline level for visits to a number of location categories; retailers
and recreation venues, grocery markets and pharmacies, parks, transit stations, workplaces and
residential places. We use the average change in mobility across all location categories, excluding
residential places and parks, as a measure of the reduction in mobility.
The seeding of new infections in model 2 is chosen to be 10 days before the day a country has
cumulatively observed 10 deaths so that mobility data are available for all the countries examined.
In the UK, this corresponds to March 4th, which is later than the infection start date of February
13th used by Flaxman et al.1.
For posterior inference of model 2, we use the same prior distributions as in Unwin et al.2
except for R0, where a weakly informative prior of a normal distribution truncated below at 1 with
mean 3.28 and standard deviation 2 is used. This prior is chosen so that approximately 95% of the
prior density is between 1 and 79, and that R0is above the critical value of 1 at the start of the
epidemic. For model 1, we use the same priors as in Flaxman et al.1for the analysis up to May
5th and July 12th.
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Extended Data Figure 1a: Austria and Belgium. Plots of daily infections, daily deaths and time-
varying reproduction number Rtuntil May 5th. The start time for the plots is 30 and 10 days
before 10 deaths are recorded, in the two models, respectively. Observed counts of daily infections
and daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark
blue and light blue respectively.
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Extended Data Figure 1b: Denmark and France. Plots of daily infections, daily deaths and time-
varying reproduction number Rtuntil May 5th. The start time for the plots is 30 and 10 days
before 10 deaths are recorded, in the two models, respectively. Observed counts of daily infections
and daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark
blue and light blue respectively.
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 1c: Germany and Italy. Plots of daily infections, daily deaths and time-
varying reproduction number Rtuntil May 5th. The start time for the plots is 30 and 10 days
before 10 deaths are recorded, in the two models, respectively. Observed counts of daily infections
and daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark
blue and light blue respectively.
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 1d: Norway and Spain. Plots of daily infections, daily deaths and time-
varying reproduction number Rtuntil May 5th. The start time for the plots is 30 and 10 days
before 10 deaths are recorded, in the two models, respectively. Observed counts of daily infections
and daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark
blue and light blue respectively.
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Extended Data Figure 1e: Sweden and Switzerland. Plots of daily infections, daily deaths and
time-varying reproduction number Rtuntil May 5th. The start time for the plots is 30 and 10 days
before 10 deaths are recorded, in the two models, respectively. Observed counts of daily infections
and daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark
blue and light blue respectively.
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Country School closures Public events ban Lockdown
UK X X May 13th
Austria May 18th XMay 1st
Belgium July 1st XJune 7th
Denmark X X April 20th
France June 22th XMay 11th
Germany July 7th XMay 6th
Greece June 1st June 15th May 30th
Italy X X May 4th
Netherlands June 15th July 1st May 11th
Norway May 11th June 2nd April 21st
Portugal X X July 5th
Spain X X May 26th
Sweden 7X7
Switzerland June 6th XJune 21st
Extended Data Table 1: End dates for school closures10 , public events ban10 and lockdown in each
country11;12;13. NPIs that are still in place are shown in X, while NPIs that were not implemented
are shown in 7.
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Extended Data Figure 2a: Austria and Belgium. Plots of daily infections, daily deaths and time-
varying reproduction number Rtin columns 1–3 until July 12th. The start time for the plots is
30 and 10 days before 10 deaths are recorded, in the two models, respectively. Column 4 is a
magnification of column 3 around the period of the NPIs. Observed counts of daily infections and
daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark blue
and light blue respectively.
17
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 2b: Denmark and France. Plots of daily infections, daily deaths and time-
varying reproduction number Rtin columns 1–3 until July 12th. The start time for the plots is
30 and 10 days before 10 deaths are recorded, in the two models, respectively. Column 4 is a
magnification of column 3 around the period of the NPIs. Observed counts of daily infections and
daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark blue
and light blue respectively.
18
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 2c: Germany and Greece. Plots of daily infections, daily deaths and time-
varying reproduction number Rtin columns 1–3 until July 12th. The start time for the plots is
30 and 10 days before 10 deaths are recorded, in the two models, respectively. Column 4 is a
magnification of column 3 around the period of the NPIs. Observed counts of daily infections and
daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark blue
and light blue respectively.
19
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 2d: Italy and the Netherlands. Plots of daily infections, daily deaths and
time-varying reproduction number Rtin columns 1–3 until July 12th. The start time for the plots
is 30 and 10 days before 10 deaths are recorded, in the two models, respectively. Column 4 is a
magnification of column 3 around the period of the NPIs. Observed counts of daily infections and
daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark blue
and light blue respectively.
20
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 2e: Norway and Portugal. Plots of daily infections, daily deaths and time-
varying reproduction number Rtin columns 1–3 until July 12th. The start time for the plots is
30 and 10 days before 10 deaths are recorded, in the two models, respectively. Column 4 is a
magnification of column 3 around the period of the NPIs. Observed counts of daily infections and
daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark blue
and light blue respectively.
21
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 2f: Spain and Sweden. Plots of daily infections, daily deaths and time-
varying reproduction number Rtin columns 1–3 until July 12th. The start time for the plots is
30 and 10 days before 10 deaths are recorded, in the two models, respectively. Column 4 is a
magnification of column 3 around the period of the NPIs. Observed counts of daily infections and
daily deaths are shown in red, and their corresponding 50% and 95% CIs are shown in dark blue
and light blue respectively.
22
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
Extended Data Figure 2g: Switzerland. Plots of daily infections, daily deaths and time-varying
reproduction number Rtin columns 1–3 until July 12th. The start time for the plots is 30 and 10
days before 10 deaths are recorded, in the two models, respectively. Column 4 is a magnification
of column 3 around the period of the NPIs. Observed counts of daily infections and daily deaths
are shown in red, and their corresponding 50% and 95% CIs are shown in dark blue and light blue
respectively.
23
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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 July 27, 2020. .https://doi.org/10.1101/2020.07.22.20160341doi: medRxiv preprint
... However, in the case of a finite population, the effective reproduction number falls automatically and necessarily over time since the number of infections would otherwise diverge 55 . A recent preprint report from Chin et al. 56 explored the two models proposed by the Imperial College 44 by expanding the scope to 14 European countries from the 11 countries studied in the Table 2. Comparisons using the 4-point criteria. Comparability was considered if at least 3 out of 4 of the following conditions were similar: a) population density, b) percentage of the urban population, c) Human Development Index and d) total area of the region. ...
... They added a third model that considered banning public events as the only covariate. The authors concluded that the claimed benefits of lockdown appear grossly exaggerated since inferences drawn from effects of NPIs are non-robust and highly sensitive to model specification 56 . The same explanation for the discrepancy can be applied to other publications where mathematical models were created to predict outcomes [14][15][16][17][18] . ...
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A recent mathematical model has suggested that staying at home did not play a dominant role in reducing COVID-19 transmission. The second wave of cases in Europe, in regions that were considered as COVID-19 controlled, may raise some concerns. Our objective was to assess the association between staying at home (%) and the reduction/increase in the number of deaths due to COVID-19 in several regions in the world. In this ecological study, data from www.googl e.com/covid 19/ mobil ity/, ourworldindata.org and covid.saude.gov.br were combined. Countries with > 100 deaths and with a Healthcare Access and Quality Index of ≥ 67 were included. Data were preprocessed and analyzed using the difference between number of deaths/million between 2 regions and the difference between the percentage of staying at home. The analysis was performed using linear regression with special attention to residual analysis. After preprocessing the data, 87 regions around the world were included, yielding 3741 pairwise comparisons for linear regression analysis. Only 63 (1.6%) comparisons were significant. With our results, we were not able to explain if COVID-19 mortality is reduced by staying at home in ~ 98% of the comparisons after epidemiological weeks 9 to 34.
... Epidemiological models can be desirable because they directly model the underlying mechanisms, but they are prone to overfitting in the presence of scant or low-quality, noisy data. This leads to nonrobustness (see [13,14]) since they require estimates of key parameters that are highly uncertain, and whose impact may reverberate significantly in highly nonlinear exponential growth models. No single approach dominates the rest, especially at the current stage of our understanding of the pandemic. ...
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... Moreover, Global Epidemic and Mobility Model (GLEAM) was applied to study the impact of applied travel limitations on the spread of the virus internally and outside the country [7]. The analysis of three different models for NPI effectiveness estimation [6] showed that the estimated effect highly depends on the model selected for this purpose. ...
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... Zudem besteht, wie das Autorenteam selbst anmerkte, ein großes methodisches Problem darin, dass die verschiedenen Interventionen relativ rasch nacheinander implementiert wurden, so dass die zeitlichen Effekte der unterschiedlichen Restriktionen nicht wirklich zu trennen waren. Gerade dieser Aspekt ist anschließend aus methodischer Sicht erheblich kritisiert worden, da aufgrund von zahlreichen Daten aus Europa und den Vereinigten Staaten deutlich wurde, dass Indikatoren wie die Reproduktionszahl bereits vor der rechtlichen Einführung des Lockdowns drastisch gesunken war [409]. ...
... A more realistic number is at least 2X lower, well fewer than 5.2 million deaths "saved." It is also worth mentioning that the efficacy of lockdown has been questioned in several studies, reducing the benefit of lockdown potentially markedly further (Supplementary Table 4) (149)(150)(151)(152)(153)(154)(155). Second, consider the costs of lockdown (144,(156)(157)(158). ...
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... Zudem besteht, wie das Autorenteam selbst anmerkte, ein großes methodisches Problem darin, dass die verschiedenen Interventionen relativ rasch nacheinander implementiert wurden, so dass die zeitlichen Effekte der unterschiedlichen Restriktionen nicht wirklich zu trennen waren. Gerade dieser Aspekt ist anschließend aus methodischer Sicht erheblich kritisiert worden, da aufgrund von zahlreichen Daten aus Europa und den Vereinigten Staaten deutlich wurde, dass Indikatoren wie die Reproduktionszahl bereits vor der rechtlichen Einführung des Lockdowns drastisch gesunken war [409]. ...
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In the coronavirus disease 2019 (COVID-19) pandemic, a large number of non-pharmaceutical measures that pertain to the wider group of social distancing interventions (e.g. public gathering bans, closures of schools, workplaces and all but essential business, mandatory stay-at-home policies, travel restrictions, border closures and others) have been deployed. Their urgent deployment was defended with modelling and observational data of spurious credibility. There is major debate on whether these measures are effective and there is also uncertainty about the magnitude of the harms that these measures might induce. Given that there is equipoise for how, when and if specific social distancing interventions for COVID-19 should be applied and removed/modified during reopening, we argue that informative randomised-controlled trials are needed. Only a few such randomised trials have already been conducted, but the ones done to-date demonstrate that a randomised trials agenda is feasible. We discuss here issues of study design choice, selection of comparators (intervention and controls), choice of outcomes and additional considerations for the conduct of such trials. We also discuss and refute common counter-arguments against the conduct of such trials.
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Objective To evaluate the association between physical distancing interventions and incidence of coronavirus disease 2019 (covid-19) globally. Design Natural experiment using interrupted time series analysis, with results synthesised using meta-analysis. Setting 149 countries or regions, with data on daily reported cases of covid-19 from the European Centre for Disease Prevention and Control and data on the physical distancing policies from the Oxford covid-19 Government Response Tracker. Participants Individual countries or regions that implemented one of the five physical distancing interventions (closures of schools, workplaces, and public transport, restrictions on mass gatherings and public events, and restrictions on movement (lockdowns)) between 1 January and 30 May 2020. Main outcome measure Incidence rate ratios (IRRs) of covid-19 before and after implementation of physical distancing interventions, estimated using data to 30 May 2020 or 30 days post-intervention, whichever occurred first. IRRs were synthesised across countries using random effects meta-analysis. Results On average, implementation of any physical distancing intervention was associated with an overall reduction in covid-19 incidence of 13% (IRR 0.87, 95% confidence interval 0.85 to 0.89; n=149 countries). Closure of public transport was not associated with any additional reduction in covid-19 incidence when the other four physical distancing interventions were in place (pooled IRR with and without public transport closure was 0.85, 0.82 to 0.88; n=72, and 0.87, 0.84 to 0.91; n=32, respectively). Data from 11 countries also suggested similar overall effectiveness (pooled IRR 0.85, 0.81 to 0.89) when school closures, workplace closures, and restrictions on mass gatherings were in place. In terms of sequence of interventions, earlier implementation of lockdown was associated with a larger reduction in covid-19 incidence (pooled IRR 0.86, 0.84 to 0.89; n=105) compared with a delayed implementation of lockdown after other physical distancing interventions were in place (pooled IRR 0.90, 0.87 to 0.94; n=41). Conclusions Physical distancing interventions were associated with reductions in the incidence of covid-19 globally. No evidence was found of an additional effect of public transport closure when the other four physical distancing measures were in place. Earlier implementation of lockdown was associated with a larger reduction in the incidence of covid-19. These findings might support policy decisions as countries prepare to impose or lift physical distancing measures in current or future epidemic waves.
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Understanding adaptive immunity to SARS-CoV-2 is important for vaccine development, interpreting coronavirus disease 2019 (COVID-19) pathogenesis, and calibration of pandemic control measures. Using HLA class I and II predicted peptide ‘megapools’, circulating SARS-CoV-2−specific CD8⁺ and CD4⁺ T cells were identified in ∼70% and 100% of COVID-19 convalescent patients, respectively. CD4⁺ T cell responses to spike, the main target of most vaccine efforts, were robust and correlated with the magnitude of the anti-SARS-CoV-2 IgG and IgA titers. The M, spike and N proteins each accounted for 11-27% of the total CD4⁺ response, with additional responses commonly targeting nsp3, nsp4, ORF3a and ORF8, among others. For CD8⁺ T cells, spike and M were recognized, with at least eight SARS-CoV-2 ORFs targeted. Importantly, we detected SARS-CoV-2−reactive CD4⁺ T cells in ∼40-60% of unexposed individuals, suggesting cross-reactive T cell recognition between circulating ‘common cold’ coronaviruses and SARS-CoV-2.
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Epidemic forecasting has a dubious track-record, and its failures became more prominent with COVID-19. Poor data input, wrong modeling assumptions, high sensitivity of estimates, lack of incorporation of epidemiological features, poor past evidence on effects of available interventions, lack of transparency, errors, lack of determinacy, looking at only one or a few dimensions of the problem at hand, lack of expertise in crucial disciplines, groupthink and bandwagon effects and selective reporting are some of the causes of these failures. Nevertheless, epidemic forecasting is unlikely to be abandoned. Some (but not all) of these problems can be fixed. Careful modeling of predictive distributions rather than focusing on point estimates, considering multiple dimensions of impact, and continuously reappraising models based on their validated performance may help. If extreme values are considered, extremes should be considered for the consequences of multiple dimensions of impact so as to continuously calibrate predictive insights and decision-making. When major decisions (e.g. draconian lockdowns) are based on forecasts, the harms (in terms of health, economy, and society at large) and the asymmetry of risks need to be approached in a holistic fashion, considering the totality of the evidence.
Oxford COVID-19 Government Response Tracker
  • T Hale
  • S Webster
  • A Petherick
  • T Phillips
  • B Kira
Hale, T., Webster, S., Petherick, A., Phillips, T. & Kira, B. Oxford COVID-19 Government Response Tracker. Retrieved from: https://github.com/OxCGRT/covid-policy-tracker (2020). Last accessed: July 15, 2020.