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SARS-CoV-2 phylodynamics differentiates the effectiveness of non-pharmaceutical interventions

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Quantifying the effectiveness of large-scale non-pharmaceutical interventions against COVID-19 is critical to adapting responses against future waves of the pandemic. By combining phylogenetic data of 5,198 SARS-CoV-2 genomes with the chronology of non-pharmaceutical interventions in 57 countries, we examine how interventions and combinations thereof alter the divergence rate of viral lineages, which is directly related to the epidemic reproduction number. Home containment and education lockdown had the largest independent impacts and were predicted to reduce the reproduction number by 35% and 26%, respectively. However, we find that in contexts with a reproduction number >2, no individual intervention is sufficient to stop the epidemic and increasingly stringent intervention combinations may be required. Our phylodynamic approach can complement epidemiological models to inform public health strategies against COVID-19.
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SARS-CoV-2 phylodynamics differentiates
the effectiveness of non-pharmaceutical interventions
Jean-Philippe Rasigade1,2*, Anaïs Barray1, Julie Teresa Shapiro1, Charlène Coquisart3,4, Yoann
Vigouroux3,4, Antonin Bal1,2,5, Grégory Destras1,2,5, Philippe Vanhems1,6, Bruno Lina1,2,5,
Laurence Josset1,2,5, Thierry Wirth3,4*.
1CIRI, Centre International de Recherche en Infectiologie, Université de Lyon, Inserm U1111,
Université Claude Bernard Lyon 1, CNRS UMR5308, Ecole Normale Supérieure de Lyon, Lyon
69007, France.
2Institut des Agents Infectieux, Hospices Civils de Lyon, Lyon 69004, France.
3Institut de Systématique, Evolution, Biodiversité (ISYEB), Muséum national d’Histoire
naturelle, CNRS, Sorbonne Université, Université des Antilles, EPHE, Paris 75005, France.
4PSL University, EPHE, Paris 75014, France.
5Centre National de Référence des Virus Respiratoires, Hospices Civils de Lyon, Lyon 69004,
France.
6Service d’Hygiène, Epidémiologie, Infectiovigilance et Prévention, Hospices Civils de Lyon
(HCL), Lyon 69008, France.
*Correspondence to: jean-philippe.rasigade@univ-lyon1.fr and wirth@mnhn.fr
Abstract:
Quantifying the effectiveness of large-scale non-pharmaceutical interventions against COVID-19
is critical to adapting responses against future waves of the pandemic. By combining phylogenetic
data of 5,198 SARS-CoV-2 genomes with the chronology of non-pharmaceutical interventions in
57 countries, we examine how interventions and combinations thereof alter the divergence rate of
viral lineages, which is directly related to the epidemic reproduction number. Home containment
and education lockdown had the largest independent impacts and were predicted to reduce the
reproduction number by 35% and 26%, respectively. However, we find that in contexts with a
reproduction number >2, no individual intervention is sufficient to stop the epidemic and
increasingly stringent intervention combinations may be required. Our phylodynamic approach
can complement epidemiological models to inform public health strategies against COVID-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 August 26, 2020. .https://doi.org/10.1101/2020.08.24.20180927doi: medRxiv preprint
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Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome
coronavirus 2 (SARS-CoV-2), emerged in China in late 2019 (13). Facing or anticipating the
pandemic, the governments of most countries implemented a wide range of large-scale non-
pharmaceutical interventions in order to reduce COVID-19 transmission (4). These included
closing schools, universities, or workplaces, cancelling public events, or restricting personal
movements. Concerns have been raised regarding the impact of such interventions on the
economy, education, and, indirectly, the healthcare system (5).
Understanding the effectiveness of each non-pharmaceutical intervention against COVID-
19 is critical to implementing appropriate responses against current or future waves of the
pandemic. Comparative studies of interventions published so far yielded conflicting results (69).
Epidemiological studies of interventions against an epidemic face several challenges.
Mathematical models informed by counts of confirmed cases or deaths ignore the relationships
and transmission patterns between cases. Counts themselves can vary in accuracy and timeliness
depending on countries’ health facilities, surveillance systems, and the changing definitions of
cases. Even when an intervention immediately reduces the transmission rate, a detectable reduction
of disease incidence can be much delayed, especially when testing and diagnoses are restricted to
specific patient populations. This delay from intervention to incidence reduction, combined with
the variety and simultaneous implementation of interventions (4, 9), complicates the identification
of their individual effects.
Unlike epidemiological case counts, viral genomes bear phylogenetic information relevant
to disease transmission. Extracting this information is the goal of phylodynamics, which relies on
evolutionary theory and bioinformatics to model the dynamics of an epidemic (10). The dates of
viral transmission events can also be inferred from genome sequences to alleviate, at least in part,
the problems of delayed detection of an intervention’s effect. Here, we conducted a phylodynamic
analysis of 5,198 SARS-CoV-2 genomes from 57 countries to estimate the independent effects of
9 large-scale non-pharmaceutical interventions on the transmission rate of COVID-19 during the
early dissemination phase of the pandemic. We adapted an established phylogenetic method (11,
12) to model variations of the divergence rate of SARS-CoV-2 in response to interventions and
combinations thereof. Building on known relationships between the viral divergence rate and the
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effective reproduction number 𝑅 (13), we quantify the reduction of 𝑅 independently attributable
to each intervention, exploiting heterogeneities in their nature and timing across countries in
multivariate models. In turn, these results allow us to estimate the probability of stopping the
epidemic (𝑅< 1) when implementing selected combinations of interventions.
Survival modelling of viral transmission
The dissemination and detection of a virus in a population can be described as a transmission tree
(Fig. 1A) whose shape reflects that of the dated phylogeny of the sampled pathogens (Fig. 1B). In
a phylodynamic context, it is assumed that each lineage, represented by a branch in the
phylogenetic tree, belongs to a single patient and that lineage divergence events, represented by
tree nodes, coincide with transmission events (10). Thus, branches in a dated phylogeny represent
intervals of time between divergence events interpreted as transmission events. This situation can
be translated in terms of survival analysis, which models rates of event occurrence, by considering
divergence as the event of interest and by treating branch lengths as time-to-event intervals (Fig.
1C-D). Phylogenetic survival analysis was devised by E. Paradis and applied to detecting temporal
variations in the divergence rate of tanagers (11) or fishes (14), but it has not been applied to
pathogens so far (12, 15, 16).
To quantify the effect of non-pharmaceutical interventions on the transmission rate of
COVID-19, we adapted the original model in (11) to account for the specific setting of viral
phylodynamics (see Methods). Hereafter, we refer to the modified model as phylodynamic
survival analysis. In survival analysis terms, we interpret internal branches of the phylogeny (those
that end with a transmission event) as time-to-event intervals and terminal branches (those that
end with a sampling event) as censored intervals (Fig. 1C; see Methods). The time-to-event
intervals are loosely related to the so-called clinical onset serial interval, which is the delay
between the onset of symptoms in the source and infected patients in a transmission pair (but see
(17)).
The predictors of interest in our setting, namely, the non-pharmaceutical interventions,
vary both through time and across lineages depending on their geographic location. To model this,
we assigned each divergence event (and subsequent branch) to a country using maximum-
likelihood ancestral state reconstruction (18). Each assigned branch was then associated with the
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set of non-pharmaceutical interventions that were active or not in the country during the interval
spanned by the branch. Intervals containing a change of intervention were split into subintervals
(19). These (sub)intervals were the final observations (statistical units) used in the survival models.
Models were adjusted for the hierarchical dependency structure introduced by interval splits and
country assignations (18).
Fig. 1. Conceptual overview of phylodynamic survival analysis. Under the assumption that each
viral lineage in a phylogeny belongs to an infected patient, the dates of viral transmission and
sampling events in a transmission tree (A) coincide with the dates of divergence events (nodes)
and tips, respectively, of the dated phylogeny reconstructed from the viral genomes (B). Treating
viral transmission as the event of interest for survival modelling, internal branches connecting two
divergence events are interpreted as time-to-event intervals while terminal branches, that do not
end with a transmission event, are interpreted as censored intervals (C). Translating the dated
phylogeny in terms of survival events enables visualizing the probability of transmission through
time as a Kaplan-Meier curve (D) and modelling the transmission rate using Cox proportional
hazards regression.
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Phylodynamic survival models estimate variations of the reproduction number
The evolution of lineages in a dated viral phylogeny can be described as a birth-death process with
a divergence (or birth) rate 𝜆 and an extinction (or death) rate 𝜇 (20). In a phylodynamic context,
the effective reproduction number 𝑅 equals the ratio of the divergence and extinction rates (20).
Coefficients of phylodynamic survival models (the so-called hazard ratios; see Methods) act as
multiplicative factors of the divergence rate 𝜆, independent of the true value of 𝜆 which needs not
be specified nor evaluated. As 𝑅= 𝜆 𝜇
, multiplying 𝜆 by a coefficient also multiplies 𝑅,
independent of the true value of 𝜇. Thus, coefficients of phylodynamic survival models estimate
variations of 𝑅 in response to predictor variables without requiring external knowledge of, or
making assumptions about 𝜆 and 𝜇.
Variations in COVID-19 transmission rates across countries
We assembled a composite dataset by combining a dated phylogeny of SARS-CoV-2 (Fig. 2A),
publicly available from Nextstrain (21) and built from the GISAID initiative data (22), with a
detailed timeline of non-pharmaceutical interventions available from the Oxford COVID-19
Government Response Tracker (OxCGRT) (18, 23). Figure S1 shows a flowchart outlining the
data sources, sample sizes and selection steps of the study. Phylogenetic and intervention data
covered the early phase of the epidemic up to May 4, 2020.
The 5,198 SARS-CoV-2 genomes used to reconstruct the dated phylogeny were collected
from 74 countries. Detailed per-country data including sample sizes are shown in Data S1. Among
the 10,394 branches in the phylogeny, 2,162 branches (20.8%) could not be assigned to a country
with >95% confidence and were excluded, also reducing the number of represented countries from
74 to 59 (Fig. S1; a comparison of included and excluded branches is shown in Fig. S2). The
remaining 4,025 internal branches had a mean time-to-event (delay between transmission events)
of 4.4 days (Fig. 2B). These data were congruent with previous estimates of the mean serial interval
of COVID-19 ranging from 3.1 days to 7.5 days (24). The 4,207 terminal branches had a mean
time-to-censoring (delay from infection to detection) of 10.6 days (Figure 2A-B). This pattern of
longer terminal vs. internal branches is typical of a viral population in fast expansion (10).
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We compared the timing and dynamics of COVID-19 spread in countries represented in
our dataset (Figure 2C-D), pooling countries with <10 assigned transmission events into an
‘others’ category. The estimated date of the first local transmission event in each country showed
good concordance with the reported dates of the epidemic onset (Pearson correlation = 0.84; Fig.
S3). The relative effective reproduction number 𝑅 per country, taking China as reference, ranged
from -55.6% (95%CI, -71.4% to -29.9%) in Luxembourg to +11.7% (95% CI, -6.7% to +33.8%)
in Spain (Fig. 2C). Notice that these estimates are averages over variations of 𝑅 through time in
each country, up to May 4, 2020. Exemplary survival curves of transmission events are shown in
Fig. 2E-F. Relative 𝑅’s are not expected to necessarily correlate with the reported counts of
COVID-19 cases across all countries due to the confounding effects of population sizes, case
detection policies and the number of genomes included. Nevertheless, the relative 𝑅’s across
countries substantially correlated with the reported cumulative counts up to May 12 (Fig. 2G-H),
including COVID-19 cases (Pearson correlation with log-transformed counts, 0.46, 95% CI, 0.07
to 0.73), deaths (correlation 0.59, 95% CI, 0.24 to 0.80), cases per million inhabitants (correlation
0.39, 95% CI, -0.01 to 0.69) and deaths per million inhabitants (correlation 0.56, 95% CI, 0.21 to
0.79).
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Figure 2. Comparison of the timing and reproduction numbers of the COVID-19 epidemic
in 74 countries based on a dated phylogeny. A: dated phylogeny of 5,198 SARS-CoV-2
genomes where internal (time-to-event) and terminal (time-to-censoring) branches are colored red
and blue, respectively. B: histogram of internal and terminal branch lengths. C: box-and-whisker
plots of the distribution over time of the inferred transmission events in each country, where boxes
denote interquartile range (IQR) and median, whiskers extend to dates at most 1.5x the IQR away
from the median date, and circle marks denote dates farther than 1.5 IQR from the median date.
D: point estimates and 95% confidence intervals of the relative effective reproduction number,
expressed as percent changes relative to China, in 27 countries with ≥10 assigned transmission
events. Countries with <10 assigned transmission events (n=32) were pooled into the ‘Others’
category. E, F: representative Kaplan-Meier survival curves of the probability of transmission
through time in countries with comparable (E) or highly different (F) transmission rates. ‘+’ marks
denote censoring events. Numbers denote counts of internal branches and, in brackets, terminal
branches. G, H: scatter plots of the reported numbers of COVID-19 cases and deaths per country,
in absolute values (G) and per million inhabitants (H).
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Disentangling the individual effectiveness of non-pharmaceutical interventions
The implementation and release dates of large-scale non-pharmaceutical interventions against
COVID-19 were available for 57 countries out of the 59 represented in the dated phylogeny.
Definitions of the selected interventions are shown in Table 1 (18). Branches assigned to countries
with missing intervention data, namely, Latvia and Senegal, were excluded from further analysis
(n=22/8,262 (0.3%); see Fig. S1). Up to May 4, 2020, the interventions most universally
implemented were information campaigns, restrictions on international travel and education
lockdown (>95% of countries) (Fig. S4). The least frequent were the closure of public
transportation (35%) and home containment (72%). Public information campaigns came first and
home containment came last (median delay across countries, 5 days before and 24 days after the
first local transmission event, respectively; Fig. 3A). Survival curves for each intervention are
shown in Fig. S5. Most interventions were implemented in combination and accumulated over
time rather than replacing each other (Fig. S4; median delays between interventions are shown in
Fig. S6; correlations in Fig. S7; and a detailed timeline of interventions in Data S2). However, we
observed a substantial heterogeneity of intervention timing across the 57 countries (Fig. 3A),
suggesting that individual intervention effects can be discriminated by multivariate analysis given
the large sample size (n=8,210 subintervals).
A multivariate phylogenetic survival model, including the 9 interventions and controlling
for between-country 𝑅 variations (see Methods), showed a strong fit to the data (likelihood-ratio
test compared to the null model, P < 10-196). In this model, the interventions most strongly and
independently associated with a reduction of the effective reproduction number 𝑅 of SARS-CoV-
2 were home containment (𝑅 percent change, -34.6%, 95%CI, -43.2 to -24.7%), education
lockdown (-25.6%, 95%CI, -33.4 to -16.9%), restricting gatherings (-22.3%, 95%CI, -33.4 to -
9.4%) and international travel (-16.9%, 95%CI, -27.5 to -4.8%). We failed to detect a substantial
impact of other interventions, namely information campaigns, cancelling public events, closing
workplaces, restricting internal movement, and closing public transportation (Fig. 3B). Based on
coefficient estimates, all interventions were independently predicted to reduce 𝑅 (even by a
negligible amount), in line with the intuition that no intervention should accelerate the epidemic.
Contrasting with previous approaches that constrained coefficients (9), this intuition was not
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enforced a priori in our multivariate model, in which positive coefficients (increasing 𝑅) might
have arisen due to noise or collinearity between interventions. The absence of unexpectedly
positive coefficients suggests that our model correctly captured the epidemic slowdown that
accompanied the accumulation of interventions.
Table 1. Selected large-scale non-pharmaceutical interventions against COVID-19.
Non
-
pharmaceutical intervention
OxCGRT identifier
Definition
Information campaign H1 Coordinated public information
campaign across traditional and social
media
Restrict international travel C8 Ban or quarantine arrivals from high-risk
regions
Education lockdown C1 Require closing for some or all
education levels or categories, e.g., high
schools, public schools, universities
Cancel public events C3 Require cancelling of all public events
Restrict gatherings >100 pers. C4 Prohibit gatherings over 100 persons
Close workplaces C2 Require closing or working from home
for some or all non-essential sectors or
categories of workers
Restrict internal movements C7 Require closing routes or prohibit most
citizens from using them
Close public transport C5 Require closing of public transport or
prohibit most citizens from using it
Home containment C6 Require not leaving house with or
without exceptions for daily exercise,
grocery shopping and essential trips
NOTE. OxCGRT, Oxford COVID-19 Government Response Tracker initiative,
www.bsg.ox.ac.uk/covidtracker
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Estimated intervention effects are robust to time-dependent confounders and collinearity
A reduction of 𝑅 through time, independent of the implementation of interventions, might lead to
overestimate their effect in our model. Several potential confounders might reduce 𝑅 through time
but cannot be precisely estimated and included as control covariates. These included the
progressive acquisition of herd immunity, the so-called artificial diversification slowdown
possibly caused by incomplete sampling, and time-dependent variations of the sampling effort (see
Methods). To quantify this potential time-dependent bias, we constructed an additional model
including the age of each branch as a covariate (Table S1). The coefficients in this time-adjusted
model only differed by small amounts compared to the base model. Moreover, the ranking by
effectiveness of the major interventions remained unchanged, indicating that our estimates were
robust to time-dependent confounders.
We also quantified the sensitivity of the estimated intervention effects to the inclusion of
other interventions (collinearity) by excluding interventions one by one in 9 additional models
(Fig. 3C). This pairwise interaction analysis confirmed that most of the estimated effects were
strongly independent. Residual interferences were found for gathering restrictions, whose full-
model effect of -22.3% was reinforced to -33.5% when ignoring home containment; and for
cancelling public events, whose full-model effect of -0.97% was reinforced to -15.1% when
ignoring gathering restrictions. These residual interferences make epidemiological sense because
home containment prevents gatherings and gathering restrictions also prohibit public events.
Overall, the absence of strong interferences indicated that our multivariate model reasonably
captured the independent, cumulative effect of interventions, enabling ranking their impact on
COVID-19 spread.
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Figure 3. Non-pharmaceutical interventions variably reduce the reproduction number of
COVID-19. Data derive from the phylogenetic survival analysis of 4,191 internal and 4,019
terminal branches of a dated phylogeny of SARS-CoV-2 genomes, combined with a chronology
of interventions in 57 countries. A: box-and-whisker plots of the delay between the 1st SARS-
CoV-2 divergence event and the intervention. Plot interpretation is similar with Fig. 2C. B: point
estimates and 95% confidence intervals of the independent % change of the effective reproduction
number predicted by each intervention in a multivariate, mixed-effect phylogenetic survival model
adjusted for between-country variations. C: matrix of pairwise interactions between the
interventions (in rows) estimated using 9 multivariate models (in columns), where each model
ignores exactly one intervention. Negative (positive) differences in blue (red) denote a stronger
(lesser) predicted effect of the intervention in row when ignoring the intervention in column. D,
E: simulated impact of interventions implemented independently (D) or in sequential combination
(E) on the count of simultaneous cases in an idealized population of 1 million susceptible
individuals using compartmental SIR models with a basic reproduction number 𝑅= 3 (black
lines) and a mean infectious period of 2 weeks. Shaded areas in (D) denote 95% confidence bands.
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Simulating intervention effectiveness in an idealized population
To facilitate the interpretation of our estimates of the effectiveness of interventions against
COVID-19, we simulated each intervention’s impact on the peak number of cases, whose
reduction is critical to prevent overwhelming the healthcare system (Fig. 3D and Fig. S8). We used
compartmental Susceptible-Infected-Recovered (SIR) models with a basic reproduction number
𝑅= 3 and a mean infectious period of 2 weeks based on previous estimates (25, 26), in an
idealized population of 1 million susceptible individuals (see Methods). In each model, we
simulated the implementation of a single intervention at a date chosen to reflect the median delay
across countries (Fig. 3A) relative to the epidemic onset (see Methods). On implementation date,
the effective reproduction number was immediately reduced according to the estimated
intervention’s effect shown in Fig. 3B.
In this idealized setting, home containment, independent of all other restrictions, only
halved the peak number of cases from 3.0x105 to 1.5x105 (95% CI, 1.0x105 to 2.0x105) (Fig. 3D).
However, a realistic implementation of home containment also implies other restrictions including,
at least, restrictions on movements, gatherings, and public events. This combination resulted in a
relative 𝑅 of -50.8% (95% CI, -59.4% to -40.2%) and a 5-fold reduction of the peak number of
cases to 6.0x104 (95% CI, 1.9x104 to 1.2x105). Nevertheless, if 𝑅= 3 then a 50% reduction is
still insufficient to reduce 𝑅 below 1 and stop the epidemic. This suggests that even when
considering the most stringent interventions, combinations may be required. To further examine
this issue, we estimated the effect of accumulating interventions by their average chronological
order shown in Fig. 3A, from information campaigns alone to all interventions combined including
home containment (Fig. 3E). Strikingly, only the combination of all interventions completely
stopped the epidemic under our assumed value of 𝑅. To estimate the effectiveness of combined
interventions in other epidemic settings, we computed the probabilities of reducing 𝑅 below 1 for
values of 𝑅 ranging from 1.5 to 3.5 (Table 2; see Methods). The same probabilities for individual
interventions are presented in Table S2, showing that no single intervention would stop the
epidemic if 𝑅≥ 2. These results may help inform decisions on the appropriate stringency of the
restrictions required to control the epidemic under varying transmission regimes.
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Table 2. Predicted reduction of the COVID-19 effective reproduction number under increasingly stringent
combinations of non
-
pharmaceutical interventions.
Probability of reducing
𝑹
𝒕
below 1
Accumulated interventions Relative Rt
(c
umulative % change)
R0=1.5 R0=2.0
R0=2.5 R0=3.0
R0=3.5
Information campaign -6.0 (-17.0 to +6.5) <0.01 <0.01 <0.01 <0.01 <0.01
Restrict intl. travel -21.9 (-35.0 to -6.1) 0.05 <0.01 <0.01 <0.01 <0.01
Education lockdown -41.9 (-52.5 to -29.0) 0.91 0.07 <0.01 <0.01 <0.01
Cancel public events -42.5 (-54.0 to -28.1) 0.90 0.11 <0.01 <0.01 <0.01
Restrict gatherings >100 pers. -55.3 (-63.4 to -45.5) 1.00 0.86 0.14 <0.01 <0.01
Close workplaces -59.7 (-67.6 to -50.0) 1.00 0.98 0.48 0.04 <0.01
Restrict internal movements -60.6 (-67.9 to -51.6) 1.00 0.99 0.56 0.06 <0.01
Close public transport -65.1 (-72.6 to -55.7) 1.00 1.00 0.87 0.36 0.05
Home containment -77.2 (-81.5 to -71.9) 1.00 1.00 1.00 1.00 0.98
Discussion
We present a phylodynamic analysis of how the divergence rate and reproduction number of
SARS-CoV-2 varies in response to large-scale non-pharmaceutical interventions in 57 countries.
Our results suggest that no single intervention, including home containment, is sufficient on its
own to stop the epidemic (𝑅< 1). Increasingly stringent combinations of interventions may be
required depending on the effective reproduction number.
Home containment was repeatedly estimated to be the most effective response in
epidemiological studies from China (27), France (28), the UK (29), and Europe (9). Other studies
modelled the additional (or residual) reduction of 𝑅 by an intervention after taking into account
those previously implemented (4, 8). Possibly because home containment was the last
implemented intervention in many countries, these studies reported a weaker or even negligible
additional effect compared to earlier interventions. In our study, home containment, even when
implemented last, had the strongest independent impact on epidemic spread (𝑅 percent change, -
34.6%), which was further amplified (-50.8%) when taking into account implicit restrictions on
movements, gatherings and public events.
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We found that education lockdown substantially decreased COVID-19 spread (𝑅 percent
change, -25.6%). Contrasting with home containment, the effectiveness of education lockdown
has been more hotly debated. This intervention ranked among the most effective ones in a study
of 41 countries (4) but had virtually no effect on transmission in other reports from Europe (8, 9).
Children have been estimated to be poor spreaders of COVID-19 and less susceptible than adults
to develop disease after an infectious contact, counteracting the effect of their higher contact rate
(6, 30). However, the relative susceptibility to infection was shown to increase sharply between
15 and 25 years, from 0.40 to 0.79 (30). Importantly, we could not differentiate the effect of closing
schools and universities because both closures coincided in all countries. Thus, our finding that
education lockdowns reduce COVID-19 transmission might be driven by contact rate reductions
in older students rather than in children, as hypothesized elsewhere (4), and, in addition, by parents
staying at home with their children.
Restrictions on gatherings of >100 persons appeared more effective than cancelling public
events (𝑅 percent changes, -22.3% vs. -1.0%, respectively) in our phylodynamic model, in line
with previous results from epidemiological models (4). Notwithstanding that gathering restrictions
prohibit public events, possibly causing interferences between estimates (Fig. 3C), this finding is
intriguing. Indeed, several public events resulted in large case clusters, the so-called
superspreading events, that triggered epidemic bursts in France (31), South Korea (32) or the U.S.
(33). A plausible explanation for not detecting the effectiveness of cancelling public events is that
data-driven models, including ours, better capture the cumulative effect of more frequent events
such as gatherings than the massive effect of much rarer events such as superspreading public
events. This bias towards ignoring the so-called ‘Black Swan’ exceptional events (34) suggests
that our findings (and others’ (4)) regarding restrictions on public events should not be interpreted
as an encouragement to relax these restrictions but as a potential limit of modelling approaches
(but see (35)).
There are other limitations to our study, including its retrospective design. We could not
consider important non-pharmaceutical interventions that are difficult to date and quantify, such
as contact tracing or case isolation policies. Data were analyzed at the national level, although
much virus transmission was often concentrated in specific areas and some non-pharmaceutical
interventions were implemented at the sub-national level (36). From a statistical standpoint, the
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interval lengths in the dated phylogeny were treated as fixed quantities in the survival models.
Ignoring the uncertainty of the estimated lengths might underestimate the width of confidence
intervals, although this is unlikely to have biased the pointwise estimates and the ranking of
interventions’ effects. The number of genomes included by country did not necessarily reflect the
true number of cases, which might have influenced country comparison results in Fig. 2, but not
intervention effectiveness models in Fig. 3 which were adjusted for between-country variations of
𝑅. Finally, our estimates represent averages over many countries with different epidemiological
contexts, healthcare systems, cultural behaviors and nuances in intervention implementation
details and population compliance. This global approach facilitates unifying the interpretation of
intervention effectiveness, but this interpretation still needs to be adjusted to local contexts by
policy makers.
Beyond the insights gained into the impact of interventions against COVID-19, our
findings highlight how phylodynamic survival analysis can help leverage pathogen sequence data
to estimate epidemiological parameters. Contrasting with the Bayesian approaches adopted by
most, if not all, previous assessments of intervention effectiveness (4, 7, 9), phylodynamic survival
analysis does not require any quantitative prior assumption or constraint on model parameters. The
method should also be simple to implement and extend by leveraging the extensive software
arsenal of survival modelling. Phylodynamic survival analysis may complement epidemiological
models as pathogen sequences accumulate, allowing to address increasingly complex questions
relevant to public health strategies.
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Materials and Methods
Definitions and chronology of non-pharmaceutical interventions
The nature, stringency and timing of non-pharmaceutical interventions against COVID-19 have
been collected and aggregated daily since January 1, 2020 by the Oxford COVID-19 Government
Response Tracker initiative of the Blavatnik School of Government, UK (4, 23). As of May 12,
2020, the interventions are grouped into three categories, namely: closures and containment (8
indicators), economic measures (4 indicators) and health measures (5 indicators). Indicators use 2-
to 4-level ordinal scales to represent each intervention’s stringency, and an additional flag
indicating whether the intervention is localized or general. Details of the coding methods for
indicators can be found in (37). We focused on large-scale interventions against transmission that
did not target specific patients (for instance, we did not consider contact tracing) and we excluded
economic and health interventions except for information campaigns. This rationale led to the
selection of the 9 indicators shown in Table 1. To facilitate interpretation while constraining model
complexity, the ordinal-scale indicators in OxCGRT data were recoded as binary variables in
which we only considered government requirements (as opposed to recommendations) where
applicable. We did not distinguish between localized and nation-wide interventions because
localized interventions, especially in larger countries, targeted the identified epidemic hotspots.
As the data did not allow to differentiate closures of schools and universities, we use the term
‘education lockdown’ (as opposed to ‘school closure’ in (23)) to avoid misinterpretation regarding
the education levels concerned.
Phylodynamic survival analysis in measurably evolving populations
The original phylogenetic survival model in (11) and its later extensions (38) considered intervals
backward in time, from the tips to the root of the tree, and were restricted to trees with all tips
sampled at the same date relative to the root (ultrametric trees). Censored intervals (intervals that
do not end with an event) in (11) were used to represent lineages with known sampling date but
unknown age. In contrast, viral samples in ongoing epidemics such as COVID-19 are typically
collected through time. A significant evolution of the viruses during the sampling period violates
the ultrametric assumption. To handle phylogenies of these so-called measurably evolving
populations (39), we propose a different interpretation of censoring compared to (11). Going
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forward in time, the internal branches of a tree connect two divergence events while terminal
branches, those that end with a tip, connect a divergence event and a sampling event (Fig. 1B).
Thus, we considered internal branches as time-to-event intervals and terminal branches as censored
intervals representing the minimal duration during which no divergence occurred (Fig. 1C).
SARS-CoV-2 phylogenetic data
SARS-CoV-2 genome sequences have been continuously submitted to the Global Initiative on
Sharing All Influenza Data (GISAID) by laboratories worldwide (22). To circumvent the
computational limits of phylogeny reconstruction and time calibration techniques, the sequences
of the GISAID database are subsampled before analysis by the Nextstrain initiative, using a
balanced subsampling scheme through time and space (21, 40). Phylogenetic reconstruction uses
maximum-likelihood phylogenetic inference based on IQ-TREE (41) and time-calibration uses
TreeTime (42). See (43) for further details on the Nextstrain bioinformatics pipeline. A dated
phylogeny of 5,211 SARS-CoV-2 genomes, along with sampling dates and locations, was
retrieved from nextstrain.org/ncov on May 12, 2020. Genomes of non-human origin (n = 13) were
discarded from analysis. Polytomies (unresolved divergences represented as a node with >2
descendants) were resolved as branches with an arbitrarily small length of 1 hour, as recommended
for adjustment of zero-length risk intervals in Cox regression (44). Of note, excluding these zero-
length branches would bias the analysis by underestimating the number of divergence events in
specific regions of the phylogeny. Maximum-likelihood ancestral state reconstruction was used to
assign internal nodes of the phylogeny to countries in a probabilistic fashion, taking the tree shape
and sampling locations as input data (45). To prepare data for survival analysis, we decomposed
the branches of the dated phylogeny into a set of time-to-event and time-to-censoring intervals
(Fig. 1C). Intervals were assigned to the most likely country at the origin of the branch when this
country’s likelihood was >0.95. Intervals in which no country reached a likelihood of 0.95 were
excluded from further analysis (Figs. S1-S2). Finally, intervals during which a change of
intervention occurred were split into sub-intervals, such that all covariates, including the country
and interventions, were held constant within each sub-interval and only the last subinterval of an
internal branch was treated as a time-to-event interval. This interval-splitting approach is
consistent with an interpretation of interventions as external time-dependent covariates (19), which
are not dependent on the event under study (the viral divergence).
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Mixed-effect Cox proportional hazard models
Variations of the divergence rate 𝜆 in response to non-pharmaceutical interventions were modelled
using mixed-effect Cox proportional hazard regression (reviewed in (46)). Models treated the
country and phylogenetic branch as random effects to account for non-independence between sub-
intervals of the same branch and between branches assigned to the same country. The predictors
of interest were not heritable traits of SARS-CoV-2, thus, phylogenetic autocorrelation between
intervals was not corrected for. Time-to-event data were visualized using Kaplan-Meier curves
with 95% confidence intervals. The regression models had the form
𝜆(𝑡)= 𝜆(𝑡)exp(𝑋⋅ 𝛽 + 𝛼+𝛾)
where 𝜆(𝑡) is the hazard function (here, the divergence rate) at time 𝑡 for the 𝑖th
observation, 𝜆(𝑡) is the baseline hazard function, which is neither specified or explicitly
evaluated, 𝑋 is the set of predictors of the 𝑖th observation (the binary vector of active non-
pharmaceutical interventions), 𝛽 is the vector of fixed-effect coefficients, 𝛼 is the random
intercept associated with the 𝑗th phylogenetic branch and 𝛾 is the random intercept associated
with the 𝑘th country. Country comparison models (Fig. 2D), in which the country was the only
predictor and branches were not divided into subintervals, did not include random intercepts. Raw
model coefficients (the log-hazard ratios) additively shift the logarithm of the divergence rate 𝜆.
Exponentiated coefficients exp𝛽 (the hazard ratios) are multiplicative factors (fold-changes) of
the divergence rate. To ease interpretation, hazard ratios were reported as percentage changes of
the divergence rate or, equivalently, of the effective reproduction number 𝑅, equal to (exp𝛽
1)×100. Analyses were conducted using R 3.6.1 (the R Foundation for Statistical Computing,
Vienna, Austria) with additional packages ape, survival and coxme.
Estimating the effect of combined interventions
Pointwise estimates and confidence intervals of combined interventions were estimated by adding
individual coefficients and their variance-covariances. Cox regression coefficients have
approximately normal distribution with mean vector 𝑚 and variance-covariance matrix 𝑉,
estimated from the inverse Hessian matrix of the likelihood function evaluated at 𝑚. From well-
known properties of the normal distribution, the distribution of a sum of normal deviates is normal
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with mean equal to the sum of the means and variance equal to the sum of the variance-covariance
matrix of the deviates. Thus, the coefficient corresponding to a sum of coefficients with mean 𝑚
and variance 𝑉 has mean ∑𝑚 and variance ∑𝑉, from which we derive the point estimates and
confidence intervals of a combination of predictors. Importantly, summing over the covariances
captures the correlation between coefficients when estimating the uncertainty of the combined
coefficient.
Probability of stopping an epidemic
A central question regarding the effectiveness of interventions or combinations thereof is whether
their implementation can stop an epidemic by reducing 𝑅 below 1 (Table 2). Suppose that some
intervention has an estimated log-hazard ratio 𝛽
. 𝛽
has approximately normal distribution with
mean 𝛽 and variance 𝜎, written 𝛽
∼ 𝑁(𝛽,𝜎). For some fixed value of 𝑅, the estimated post-
intervention reproduction number 𝑅
= 𝑅exp𝛽
. The probability 𝑝 that 𝑅
< 1 is
𝑑𝑅
 d𝑅
 where 𝑑 denotes the probability density function. To solve the integral, remark that
log𝑅
= log𝑅+𝛽
, hence, log𝑅
∼ 𝑁log𝑅+𝛽
,𝜎. Using a change of variables in the
integral and noting that log1 = 0, we obtain the closed-form solution
𝑝 =  𝑑log𝑅
 d log𝑅
 = Φ0log𝑅+𝛽
,𝜎,
where Φ is the cumulative density function of the normal distribution with mean log𝑅+𝛽
and
variance 𝜎. By integrating over the coefficient distribution, this method explicitly considers the
estimation uncertainty of 𝛽
when estimating 𝑝.
Potential time-dependent confounders
Time-dependent phylodynamic survival analysis assumes that variations of branch lengths though
time directly reflect variations of the divergence rate, which implies that branch lengths are
conditionally independent of time given the divergence rate. When the phylogeny is reconstructed
from a fraction of the individuals, as is the case in virtually all phylodynamic studies including
ours, this conditional independence assumption can be violated. This is because incomplete
sampling increases the length of more recent branches relative to older branches (47), an effect
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called the diversification slowdown (48, 49). Noteworthy, this effect can be counteracted by a high
extinction rate (16, 47), which is expected in our setting and mimicks an acceleration of
diversification. Moreover, whether the diversification slowdown should be interpreted as a pure
artifact has been controversial (49, 50). Notwithstanding, we considered incomplete sampling as a
potential source of bias in our analyses because a diversification slowdown might lead to an
overestimation of the effect of non-pharmaceutical interventions. Additionally, the selection
procedure used by Nextstrain to collect genomes included in the dated phylogeny possibly
amplified the diversification slowdown by using a higher sampling fraction in earlier phases of the
epidemic (40). To verify whether the conclusions of our models were robust to this potential bias,
we built an additional multivariate model including the estimated date of each divergence event
(the origin of the branch) as a covariate. The possible relation between time and the divergence
rate is expectedly non-linear (47) and coefficient variations resulting from controlling for time
were moderate (Table S1), thus, we refrained from including a time covariate in the reported
regression models as this might lead to overcontrol. Further research is warranted to identify an
optimal function of time that might be included as a covariate in phylodynamic survival models to
control for sources of diversification slowdown.
Compartmental epidemiological models
Epidemic dynamics can be described by partitioning a population of size 𝑁 into three
compartments, the susceptible hosts 𝑆, the infected hosts 𝐼, and the recovered hosts 𝑅. The
infection rate 𝑏 governs the transitions from 𝑆 to 𝐼 and the recovery rate 𝑔 governs the transitions
from 𝐼 to 𝑅 (we avoid the standard notation 𝛽 and 𝛾 for infection and recovery rates to prevent
confusion with Cox model parameters). The SIR model describes the transition rates between
compartments as a set of differential equations with respect to time 𝑡,
d𝑆
d𝑡 = −𝑏𝑆𝐼, d𝐼
d𝑡 = 𝑏𝑆𝐼 −𝑔𝐼, d𝑅
d𝑡 = 𝑔𝐼.
The transition rates of the SIR model define the basic reproduction number of the epidemic,
𝑅= 𝑏/𝑔. From a phylodynamic standpoint, if the population dynamics of a pathogen is described
as a birth-death model with divergence rate 𝜆 and extinction rate 𝜇, then 𝑅= 𝜆 𝜇
or, alternatively,
𝑅=
+1 (51). We simulated the epidemiological impact of each individual intervention in
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SIR models with 𝑅= 3 and 𝑔 = 2 weeks based on previous estimates (25, 26), yielding a
baseline infection rate 𝑏 = 𝑔𝑅= 6. In each model, the effective infection rate changed from 𝑏 to
𝑏exp𝛽 on the implementation date of an intervention with log-hazard ratio 𝛽. To determine
realistic implementation delays, the starting time of the simulation was set at the date of the first
local divergence event in each country and the implementation date was set to the observed median
delay across countries (see Fig. 3A). All models started with 100 infected individuals at 𝑡 = 0, a
value assumed to reflect the number of unobserved cases at the date of the first divergence event,
based on the temporality between the divergence events and the reported cases (Fig. S3) and on a
previous estimate from the U.S. suggesting that the total number of cases might be two orders of
magnitude larger than the reported count (52). Evaluation of the SIR models used the R package
deSolve.
Data and software availability
All data and software code used to generate the results are available at
github.com/rasigadelab/covid-npi.
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Acknowledgements:
We thank Philip Supply, François Vandenesch, Jean-Sébastien Casalegno, Vanessa Escuret, and
Christophe Ramière for fruitful discussions and reviews of our work. We thank the GISAID,
Nextstrain and OxCGRT teams for making their high-quality datasets available to the community.
A list of authors and laboratories contributing SARS-CoV-2 genome sequences is shown in Data
S3.
Funding: JPR received support from the FINOVI Foundation (grant R18037CC).
Author contributions: JPR, LJ, TW designed research. JPR, ABarray, JTS, CQ, YV, GD, LJ
conducted research. JPR, TW analyzed the data. JPR created figures. JPR, Abal, GD, LJ, PV, BL,
TW interpreted the data. All authors wrote the paper.
Competing interests: BL is currently active in groups advising the French government for which
BL is not receiving payment.
Data and material availability: Both data and analysis code are available online at
https://github.com/rasigadelab/covid-npi.
Supplementary Materials:
Figures S1-S8
Tables S1-S2
External Databases S1-S3
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