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

August 2020

DOI:10.1101/2020.08.24.20180927

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Authors:

Jean-Philippe Rasigade

Claude Bernard University Lyon 1

Anais Barray

Université de Lyon

Julie Teresa Shapiro

Agence Nationale de Sécurité Sanitaire de l'Alimentation, de l'Environnement et du Travail

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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.

Selected large-scale non-pharmaceutical interventions against COVID-19.

…

Predicted reduction of the COVID-19 effective reproduction number under increasingly stringent combinations of non-pharmaceutical interventions. Probability of reducing í µí±¹ í µí² below 1

…

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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

Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome

coronavirus 2 (SARS-CoV-2), emerged in China in late 2019 (1–3). 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 (6–9).

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

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

= 𝑅⋅exp𝛽

󰆹. 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

𝑏⋅exp𝛽 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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. CC-BY-NC-ND 4.0 International licenseIt is made available under a

52. J. D. Silverman, N. Hupert, A. D. Washburne, Using influenza surveillance networks to

estimate state-specific prevalence of SARS-CoV-2 in the United States. Science

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53. Coronavirus Pandemic Data Explorer. Our World in Data, (available at

https://ourworldindata.org/coronavirus-data-explorer).

. CC-BY-NC-ND 4.0 International licenseIt is made available under a

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

References (37-53)

. CC-BY-NC-ND 4.0 International licenseIt is made available under a

On the Use of Phylogeographic Inference to Infer the Dispersal History of Rabies Virus: A Review Study

Article

Full-text available

Aug 2021

Rabies is a neglected zoonotic disease which is caused by negative strand RNA-viruses belonging to the genus Lyssavirus. Within this genus, rabies viruses circulate in a diverse set of mammalian reservoir hosts, is present worldwide, and is almost always fatal in non-vaccinated humans. Approximately 59,000 people are still estimated to die from rabies each year, leading to a global initiative to work towards the goal of zero human deaths from dog-mediated rabies by 2030, requiring scientific efforts from different research fields. The past decade has seen a much increased use of phylogeographic and phylodynamic analyses to study the evolution and spread of rabies virus. We here review published studies in these research areas, making a distinction between the geographic resolution associated with the available sequence data. We pay special attention to environmental factors that these studies found to be relevant to the spread of rabies virus. Importantly, we highlight a knowledge gap in terms of applying these methods when all required data were available but not fully exploited. We conclude with an overview of recent methodological developments that have yet to be applied in phylogeographic and phylodynamic analyses of rabies virus.

Modeling CoVid-19 Diffusion with Intelligent Computational Techniques is not Working. What Are We Doing Wrong?

Preprint

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May 2021

As Europe is experiencing a second violent CoVid-19 storm, with the PCR-based testing system deteriorating due to the high volumes of people to be tested daily, there is a general reconsideration of the mathematical theories at the basis of our contact tracing and testing approaches. Drawing upon the concept of super spreader, we propose the use of (less sensitive) rapid tests to detect those secondary infections that do not need the use of PCRs, thus saving the most part of PCR tests currently used. This before the system fails.

Modeling CoVid-19 Diffusion with Intelligent Computational Techniques is not Working. What Are We Doing Wrong?

Chapter

Full-text available

Apr 2021

Chopping the tail: how preventing superspreading can help to maintain COVID-19 control

Preprint

Full-text available

Jul 2020

Disease transmission is notoriously heterogeneous, and SARS-CoV-2 is no exception. A skewed distribution where few individuals or events are responsible for the majority of transmission can result in explosive, superspreading events, which produce rapid and volatile epidemic dynamics, especially early or late in epidemics. Anticipating and preventing superspreading events can produce large reductions in overall transmission rates. Here, we present a compartmental (SEIR) epidemiological model framework for estimating transmission parameters from multiple imperfectly observed data streams, including reported cases, deaths, and mobile phone-based mobility that incorporates individual-level heterogeneity in transmission using previous estimates for SARS-CoV-1 and SARS-CoV-2. We parameterize the model for COVID-19 epidemic dynamics by estimating a time-varying transmission rate that incorporates the impact of non-pharmaceutical intervention strategies that change over time, in five epidemiologically distinct settings---Los Angeles and Santa Clara Counties, California; Seattle (King County), Washington; Atlanta (Dekalb and Fulton Counties), Georgia; and Miami (Miami-Dade County), Florida. We find the effective reproduction number R E dropped below 1 rapidly following social distancing orders in mid-March, 2020 and remained there into June in Santa Clara County and Seattle, but climbed above 1 in late May in Los Angeles, Miami, and Atlanta, and has trended upward in all locations since April. With the fitted model, we ask: how does truncating the tail of the individual-level transmission rate distribution affect epidemic dynamics and control? We find interventions that truncate the transmission rate distribution while partially relaxing social distancing are broadly effective, with impacts on epidemic growth on par with the strongest population-wide social distancing observed in April, 2020. Given that social distancing interventions will be needed to maintain epidemic control until a vaccine becomes widely available, "chopping off the tail" to reduce the probability of superspreading events presents a promising option to alleviate the need for extreme general social distancing.

Forecasting unprecedented ecological fluctuations

Article

Full-text available

Jun 2020
PLOS COMPUT BIOL

Forecasting ‘Black Swan’ events in ecosystems is an important but challenging task. Many ecosystems display aperiodic fluctuations in species abundance spanning orders of magnitude in scale, which have vast environmental and economic impact. Empirical evidence and theoretical analyses suggest that these dynamics are in a regime where system nonlinearities limit accurate forecasting of unprecedented events due to poor extrapolation of historical data to unsampled states. Leveraging increasingly available long-term high-frequency ecological tracking data, we analyze multiple natural and experimental ecosystems (marine plankton, intertidal mollusks, and deciduous forest), and recover hidden linearity embedded in universal ‘scaling laws’ of species dynamics. We then develop a method using these scaling laws to reduce data dependence in ecological forecasting and accurately predict extreme events beyond the span of historical observations in diverse ecosystems.

Age-dependent effects in the transmission and control of COVID-19 epidemics

Article

Full-text available

Aug 2020
NAT MED

The COVID-19 pandemic has shown a markedly low proportion of cases among children1–4. Age disparities in observed cases could be explained by children having lower susceptibility to infection, lower propensity to show clinical symptoms or both. We evaluate these possibilities by fitting an age-structured mathematical model to epidemic data from China, Italy, Japan, Singapore, Canada and South Korea. We estimate that susceptibility to infection in individuals under 20 years of age is approximately half that of adults aged over 20 years, and that clinical symptoms manifest in 21% (95% credible interval: 12–31%) of infections in 10- to 19-year-olds, rising to 69% (57–82%) of infections in people aged over 70 years. Accordingly, we find that interventions aimed at children might have a relatively small impact on reducing SARS-CoV-2 transmission, particularly if the transmissibility of subclinical infections is low. Our age-specific clinical fraction and susceptibility estimates have implications for the expected global burden of COVID-19, as a result of demographic differences across settings. In countries with younger population structures—such as many low-income countries—the expected per capita incidence of clinical cases would be lower than in countries with older population structures, although it is likely that comorbidities in low-income countries will also influence disease severity. Without effective control measures, regions with relatively older populations could see disproportionally more cases of COVID-19, particularly in the later stages of an unmitigated epidemic. A new epidemiological study shows reduced susceptibility to SARS-CoV-2 and decreased risk of developing severe symptoms in people aged younger than 20 years, suggesting that children have limited contribution to spread of COVID-19.

Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe

Article

Full-text available

Aug 2020
NATURE

Following the emergence of a novel coronavirus¹ (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions such as closure of schools and national lockdowns. We study the impact of major interventions across 11 European countries for the period from the start of COVID-19 until the 4th of May 2020 when lockdowns started to be lifted. Our model calculates backwards from observed deaths to estimate transmission that occurred several weeks prior, allowing for the time lag between infection and death. We use partial pooling of information between countries with both individual and shared effects on the reproduction number. Pooling allows more information to be used, helps overcome data idiosyncrasies, and enables more timely estimates. Our model relies on fixed estimates of some epidemiological parameters such as the infection fatality rate, does not include importation or subnational variation and assumes that changes in the reproduction number are an immediate response to interventions rather than gradual changes in behavior. Amidst the ongoing pandemic, we rely on death data that is incomplete, with systematic biases in reporting, and subject to future consolidation. We estimate that, for all the countries we consider, current interventions have been sufficient to drive the reproduction number

{R}_{t}

below 1 (probability

{R}_{t}\,

< 1.0 is 99.9%) and achieve epidemic control. We estimate that, across all 11 countries, between 12 and 15 million individuals have been infected with SARS-CoV-2 up to 4th May, representing between 3.2% and 4.0% of the population. Our results show that major non-pharmaceutical interventions and lockdown in particular have had a large effect on reducing transmission. Continued intervention should be considered to keep transmission of SARS-CoV-2 under control.

Effects of non-pharmaceutical interventions on COVID-19 cases, deaths, and demand for hospital services in the UK: a modelling study

Article

Full-text available

Jun 2020

Background Non-pharmaceutical interventions have been implemented to reduce transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in the UK. Projecting the size of an unmitigated epidemic and the potential effect of different control measures has been crucial to support evidence-based policy making during the early stages of the epidemic. This study assesses the potential impact of different control measures for mitigating the burden of COVID-19 in the UK. Methods We used a stochastic age-structured transmission model to explore a range of intervention scenarios, tracking 66·4 million people aggregated to 186 county-level administrative units in England, Wales, Scotland, and Northern Ireland. The four base interventions modelled were school closures, physical distancing, shielding of people aged 70 years or older, and self-isolation of symptomatic cases. We also modelled the combination of these interventions, as well as a programme of intensive interventions with phased lockdown-type restrictions that substantially limited contacts outside of the home for repeated periods. We simulated different triggers for the introduction of interventions, and estimated the impact of varying adherence to interventions across counties. For each scenario, we projected estimated new cases over time, patients requiring inpatient and critical care (ie, admission to the intensive care units [ICU]) treatment, and deaths, and compared the effect of each intervention on the basic reproduction number, R0. Findings We projected a median unmitigated burden of 23 million (95% prediction interval 13–30) clinical cases and 350 000 deaths (170 000–480 000) due to COVID-19 in the UK by December, 2021. We found that the four base interventions were each likely to decrease R0, but not sufficiently to prevent ICU demand from exceeding health service capacity. The combined intervention was more effective at reducing R0, but only lockdown periods were sufficient to bring R0 near or below 1; the most stringent lockdown scenario resulted in a projected 120 000 cases (46 000–700 000) and 50 000 deaths (9300–160 000). Intensive interventions with lockdown periods would need to be in place for a large proportion of the coming year to prevent health-care demand exceeding availability. Interpretation The characteristics of SARS-CoV-2 mean that extreme measures are probably required to bring the epidemic under control and to prevent very large numbers of deaths and an excess of demand on hospital beds, especially those in ICUs. Funding Medical Research Council.

No evidence of secondary transmission of COVID-19 from children attending school in Ireland, 2020

Article

Full-text available

May 2020
Euro Surveill

As many countries begin to lift some of the restrictions to contain COVID-19 spread, lack of evidence of transmission in the school setting remains. We examined Irish notifications of SARS-CoV2 in the school setting before school closures on 12 March 2020 and identified no paediatric transmission. This adds to current evidence that children do not appear to be drivers of transmission, and we argue that reopening schools should be considered safe accompanied by certain measures. © 2020 European Centre for Disease Prevention and Control (ECDC). All rights reserved.

Serologic responses to SARS-CoV-2 infection among hospital staff with mild disease in eastern France

Preprint

Full-text available

May 2020

Background: The serologic response of individuals with mild forms of SARS-CoV-2 infection is poorly characterized. Methods: Hospital staff who had recovered from mild forms of PCR-confirmed SARS-CoV-2 infection were tested for anti-SARS-CoV-2 antibodies using two assays: a rapid immunodiagnostic test (99.4% specificity) and the S-Flow assay (~99% specificity).The neutralizing activity of the sera was tested with a pseudovirus-based assay. Results: Of 162 hospital staff who participated in the investigation, 160 reported SARS-CoV- 2 infection that had not required hospital admission and were included in these analyses. The median time from symptom onset to blood sample collection was 24 days (IQR: 21-28, range 13-39). The rapid immunodiagnostic test detected antibodies in 153 (95.6%) of the samples and the S-Flow assay in 159 (99.4%), failing to detect antibodies in one sample collected 18 days after symptom onset (the rapid test did not detect antibodies in that patient). Neutralizing antibodies (NAbs) were detected in 79%, 92% and 98% of samples collected 13-20, 21-27 and 28-41 days after symptom onset, respectively (P=0.02). Conclusion: Antibodies against SARS-CoV-2 were detected in virtually all hospital staff sampled from 13 days after the onset of COVID-19 symptoms. This finding supports the use of serologic testing for the diagnosis of individuals who have recovered from SARS-CoV-2 infection. The neutralizing activity of the antibodies increased overtime. Future studies will help assess the persistence of the humoral response and its associated neutralization capacity in recovered patients.

Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions

Article

Full-text available

May 2020

Keeping the lid on infection spread From February to April 2020, many countries introduced variations on social distancing measures to slow the ravages of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Publicly available data show that Germany has been particularly successful in minimizing death rates. Dehning et al. quantified three governmental interventions introduced to control the outbreak. The authors predicted that the third governmental intervention—a strict contact ban since 22 March—switched incidence from growth to decay. They emphasize that relaxation of controls must be done carefully, not only because there is a 2-week lag between a measure being enacted and the effect on case reports but also because the three measures used in Germany only just kept virus spread below the growth threshold. Science , this issue p. eabb9789

Estimating the burden of SARS-CoV-2 in France

Article

Full-text available

May 2020

COVID-19 pandemic in France Coronavirus disease 2019 (COVID-19) exacted a heavy toll in France during March and April 2020. Quarantine measures were effective in reducing transmission by 84%, and some relaxation of social isolation was expected in May. Salje et al. fit transmission models for the epidemic in France to hospital admissions. The authors forecast that 2.9 million people will have been infected by 11 May, representing 4.4% of the population—a value inadequate for herd immunity. Daily critical care hospitalizations should reduce from several hundreds to tens of cases, but control will remain a delicate balancing act. Any relaxation of lockdown in France will have to be carefully controlled and monitored to avoid undermining more optimistic forecasts. Science , this issue p. 208

Changes in contact patterns shape the dynamics of the COVID-19 outbreak in China

Article

Full-text available

Apr 2020

Who and what next? The coronavirus 2019 (COVID-19) pandemic has brought tighter restrictions on the daily lives of millions of people, but we do not yet understand what measures are the most effective. Zhang et al. modeled virus transmission in Wuhan, China, in February 2020, investigating the effects of interventions ranging from patient management to social isolation. Age-mixing patterns were estimated by contact surveys conducted in Wuhan and Shanghai at the beginning of February 2020. Once people reduced their average daily contacts from 14 to 20 down to 2, transmission rapidly fell below the epidemic threshold. The model also showed that preemptive school closures helped to reduce transmission, although alone they would not prevent a COVID-19 outbreak. Limiting human mixing to within households appeared to be the most effective measure. Science , this issue p. 1481

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

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