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| DATE | 2020-10-15 |
| FROM | Ruben Safir
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| SUBJECT | Subject: [Hangout - NYLXS] Mathmatics of Social Distancing and results
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https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30457-6/fulltext
Articles| Volume 20, ISSUE 10, P1151-1160, October 01, 2020
Effectiveness of isolation, testing, contact tracing, and physical
distancing on reducing transmission of SARS-CoV-2 in different settings:
a mathematical modelling study
Effectiveness of isolation, testing, contact tracing, and physical
distancing on reducing transmission of SARS-CoV-2 in different settings:
a mathematical modelling study
Adam J Kucharski, PhD
Petra Klepac, PhD
Andrew J K Conlan, PhD
Stephen M Kissler, PhD
Maria L Tang, MMath
Hannah Fry, PhD
et al.
Show all authors
Open AccessPublished:June 16,
2020DOI:https://doi.org/10.1016/S1473-3099(20)30457-6
Effectiveness of isolation, testing, contact tracing, and physical
distancing on reducing transmission of SARS-CoV-2 in different settings:
a mathematical modelling study
Summary
Introduction
Methods
Results
Discussion
Supplementary Material
References
Article Info
Figures
Tables
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Summary
Background
The isolation of symptomatic cases and tracing of contacts has been used
as an early COVID-19 containment measure in many countries, with
additional physical distancing measures also introduced as outbreaks
have grown. To maintain control of infection while also reducing
disruption to populations, there is a need to understand what
combination of measures—including novel digital tracing approaches and
less intensive physical distancing—might be required to reduce
transmission. We aimed to estimate the reduction in transmission under
different control measures across settings and how many contacts would
be quarantined per day in different strategies for a given level of
symptomatic case incidence.
Methods
For this mathematical modelling study, we used a model of
individual-level transmission stratified by setting (household, work,
school, or other) based on BBC Pandemic data from 40 162 UK
participants. We simulated the effect of a range of different testing,
isolation, tracing, and physical distancing scenarios. Under optimistic
but plausible assumptions, we estimated reduction in the effective
reproduction number and the number of contacts that would be newly
quarantined each day under different strategies.
Results
We estimated that combined isolation and tracing strategies would reduce
transmission more than mass testing or self-isolation alone: mean
transmission reduction of 2% for mass random testing of 5% of the
population each week, 29% for self-isolation alone of symptomatic cases
within the household, 35% for self-isolation alone outside the
household, 37% for self-isolation plus household quarantine, 64% for
self-isolation and household quarantine with the addition of manual
contact tracing of all contacts, 57% with the addition of manual tracing
of acquaintances only, and 47% with the addition of app-based tracing
only. If limits were placed on gatherings outside of home, school, or
work, then manual contact tracing of acquaintances alone could have an
effect on transmission reduction similar to that of detailed contact
tracing. In a scenario where 1000 new symptomatic cases that met the
definition to trigger contact tracing occurred per day, we estimated
that, in most contact tracing strategies, 15 000–41 000 contacts would
be newly quarantined each day.
Interpretation
Consistent with previous modelling studies and country-specific COVID-19
responses to date, our analysis estimated that a high proportion of
cases would need to self-isolate and a high proportion of their contacts
to be successfully traced to ensure an effective reproduction number
lower than 1 in the absence of other measures. If combined with moderate
physical distancing measures, self-isolation and contact tracing would
be more likely to achieve control of severe acute respiratory syndrome
coronavirus 2 transmission.
Funding
Wellcome Trust, UK Engineering and Physical Sciences Research Council,
European Commission, Royal Society, Medical Research Council.
• View related content for this article
Introduction
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spread
rapidly across multiple countries in early 2020.1
, 2
, 3
A staple public health control measure for outbreaks of emerging,
directly transmitted infections involves the isolation of symptomatic
cases as well as the tracing, testing, and quarantine of their contacts.2
The effectiveness of this measure in containing new outbreaks depends on
both the transmission dynamics of the infection and the proportion of
transmission that occurs from infections without symptoms.4
Evidence exists that SARS-CoV-2 has a reproduction number (R) of about
2–3 in the early stages of an outbreak,1
, 5
and many infections can occur without symptoms,6
which means isolation of symptomatic cases and contact tracing alone are
unlikely to contain an outbreak unless a high proportion of cases are
isolated and contacts successfully traced and quarantined.7
Several countries have used combinations of non-pharmaceutical
interventions to reduce SARS-CoV-2 transmission.3
, 8
As well as isolating symptomatic individuals and tracing and
quarantining their contacts, measures have included general physical
distancing, school closures, remote working, community testing, and
cancellation of events and mass gatherings. It has also been suggested
that the effectiveness of contact tracing could be enhanced through
app-based digital tracing.9
The effectiveness of contact tracing and the extent of resources
required to implement it successfully will depend on the social
interactions within a population.10
Targeted interventions such as contact tracing also need to consider
individual-level variations in transmission: high variation can lead to
superspreading events, which could result in larger numbers of contacts
needing to be traced.11
Several examples exist of such events occurring for COVID-19, including
meals, parties, and other gatherings involving close contacts.12
Research in context
Evidence before this study
We searched PubMed, BioRxiv, and MedRxiv for articles published in
English from inception to April 15, 2020, with the following keywords:
“2019-nCoV”, “novel coronavirus”, “COVID-19”, “SARS-CoV-2” AND “contact
tracing” AND “model*”. Early modelling studies of severe acute
respiratory syndrome coronavirus 2 (SARS-CoV-2) suggested that isolation
and tracing alone might not be sufficient to control outbreaks and
additional measures might be required; these measures have since been
explored in population-level models. However, an analysis with
setting-specific social contact data to quantify the potential effect of
combined contact tracing and physical distancing measures on reducing
individual-level transmission of SARS-CoV-2 has not been done.
Added value of this study
We use data from more than 40 000 individuals to assess contact patterns
and potential SARS-CoV-2 transmission in different settings and compare
how combinations of self-isolation, contact tracing, and physical
distancing could reduce secondary cases. We assessed a range of combined
physical distancing and testing and tracing measures, including
app-based tracing, remote working, limits on different sized gatherings,
and mass population-based testing. We also estimated the number of
contacts that would be quarantined under different strategies.
Implications of all the available evidence
Several characteristics of SARS-CoV-2 make effective isolation and
contact tracing challenging, including high transmissibility, a
relatively short serial interval, and transmission that can occur
without symptoms. Combining isolation and contact tracing with physical
distancing measures—particularly measures that reduce contacts in
settings that would otherwise be difficult to trace—could therefore
increase the likelihood of achieving sustained control of SARS-CoV-2
transmission.
We used social-contact data from a large-scale UK study of over 40 000
participants13
to explore a range of different control measures for SARS-CoV-2,
including self-isolation of symptomatic cases; household quarantine;
manual tracing of acquaintances (ie, contacts that have been met
before); manual tracing of all contacts; app-based tracing; mass testing
regardless of symptoms; limits on daily contacts made outside home,
school, and work; and having a proportion of the adult population work
from home. We estimated the reduction in transmission under different
scenarios, and we estimated how many primary cases and contacts would be
quarantined per day in different strategies for a given level of
symptomatic case incidence.
Methods
Transmission model
For this mathematical modelling study, our analysis was based on data of
40 162 UK participants with recorded social contacts from the BBC
Pandemic dataset.13
In the BBC Pandemic dataset, collected in 2017–18, a contact was defined
as an interaction that either involved a face-to-face conversation or
physical contact, which broadly reflect the types of close contact that
have been linked to SARS-CoV-2 transmission clusters to date.12
Using these data, we simulated 25 000 individual-level transmission
events by repeatedly generating contact distributions for a primary case
and randomly generating infections among these contacts. In each
simulation, we randomly specified a primary case as either younger than
18 years or aged 18 years and older, on the basis of UK demography, in
which 21% of the population are younger than 18 years.14
We then generated contacts by randomly sampling values from the marginal
distributions of daily contacts made in three different settings for
their age group (ie, younger than 18 years or adults): in household
(defined as household size minus one), at work or school, and in other
settings (figure 1A, B). We used the marginal distributions rather than
raw participant data to ensure non-identifiability and reproducibility
in our model code. Information was provided and consent obtained from
all participants in the BBC Pandemic study before the app recorded any
data. Our study was approved by the London School of Hygiene & Tropical
Medicine Observational Research Ethics Committee (ref 14400).
Figure thumbnail gr1
Figure 1Model of social interactions and SARS-CoV-2 transmission and control
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In our model, we assumed infected individuals had a certain probability
of being symptomatic and of being tested if symptomatic, as well as an
infectious period that depended on when or if they self-isolated after
the onset of symptoms (table 1). We assumed a mean delay of 2·6 days
from onset to isolation in our baseline scenario (appendix, p 2). We
assumed individuals became infectious 1 day before onset of symptoms.
During each day of the effective infectious period, individuals made a
given number of contacts equal to their simulated daily contacts. To
avoid double-counting household members, household contacts were not
tallied over the entire infectious period, but instead were fixed. Once
individual-level contacts had been defined, we generated secondary
infections at random on the basis of assumed secondary attack rates
among contacts made in different settings, and we estimated how many
contacts would be successfully traced in each of these settings under
different scenarios (full description in the appendix, p 1). First, we
generated the number of secondary cases without any control measures in
place. Second, we randomly sampled the proportion of these secondary
cases that were either successfully traced and quarantined, and hence
removed from the potentially infectious pool, or averted through
isolation of the primary case. The difference between these two values
gave the overall number of secondary cases that would contribute to
further transmission, the effective R (Reff; figure 1C, D).
Table 1Parameter definitions and assumptions for the baseline model
Assumed value Details and references
Individual-level dynamics
R in absence of control measures 2·6 SARs were chosen to be consistent
with empirical estimates (table 2) and produce an R consistent with a
meta-analysis of early studies;15
sensitivity analysis shown in the appendix (p 4)
Duration of infectiousness 5 days (for cases that will become
symptomatic, first day is pre-symptomatic) Given incubation period of
about 5 days, this assumption implies serial interval of about 6·5 days;16
Relative infectiousness of asymptomatic cases 50% One published point
estimate was 65%,17
but secondary cases from asymptomatic individuals were more likely to,
in turn, be asymptomatic, suggesting lower contribution to transmission;
sensitivity analysis shown in the appendix (p 3)
Proportion of cases who are eventually symptomatic 30% of children, 70%
of adults Based on evidence synthesis of age-stratified COVID-19 data;18
sensitivity analysis shown in the appendix (p 3)
Probability that symptomatic individual will eventually self-isolate and
be tested 90% We assumed that the virus is only detectable by PCR during
the infectious period; 90% of UK survey respondents said they would
likely comply with app request to self-isolate if rapid test available19
Effective duration of infectiousness if an individual self-isolates when
symptomatic Mean delay from onset to isolation of 2·6 days; distribution
shown in the appendix (p 2) We assumed that individuals are most likely
to self-isolate 0–4 days after onset (ie, 1–5 days after becoming
infectious); for 269 cases with known date of onset and confirmation in
Singapore, of those who were confirmed within 5 days, 2% were confirmed
on date of onset, 26% on day 2, 27% on day 3, 14% on day 4, and 31% on
day 5;20
we assumed that isolation could occur 1 day before confirmation;
sensitivity analysis shown in the appendix (p 5)
SAR among contacts in home 20% Details in the SAR section of the Methods
SAR among other contacts 6% Details in the SAR section of the Methods
Contact tracing
Proportion of contacts who are acquaintances (ie, have been met before)
100% in household, 90% at school, 79% at work, 52% in other settings
Data from BBC Pandemic dataset;13
for each contact reported, participants were asked “have you met this
person before?”
Proportion of potentially traceable household contacts who are
successfully traced 100% Assumed
Proportion of potentially traceable workplace, school, or other scenario
contacts who are successfully traced 95% Assumed, with sensitivity
analysis shown in figure 2
Probability that traced contacts adhere to quarantine 90% Proportion of
traced contacts who are successfully removed from the potentially
infectious group; we assumed virus is only detectable by PCR during the
infectious period; 90% of UK survey respondents said they would likely
comply with app request to self-isolate if rapid test available;19
we assumed contacts traced by app would be quarantined immediately and
manually traced contacts would take 2 days to quarantine after isolation
of the index case9
, 16
App-based tracing
Proportion of population that would have the app installed 53% We
assumed that 71% of the population were smartphone users (details in
appendix, p 1); 75% of UK survey respondents said they would probably or
definitely download the app;19
therefore, we assume that 71% × 75% = 53% of the population would have
the app installed.
Mass testing
Proportion of the population that are tested per week 5% (ie, 460 000
tests per day for UK) 0·7% of the population tested per day, which is
equal to the highest number of daily per person tests done anywhere in
world as of mid-April, 2020 (details in appendix, p 1)
R=reproduction number. SAR=secondary attack rate.
Open table in a new tab
Secondary attack rate data sources
To estimate the risk of transmission per contact in different community
settings, we collated contact tracing studies for COVID-19 from multiple
settings that stratified contacts within and outside households (table
2). Across studies, the estimated secondary attack rate within
households was 10–20%, with a much smaller secondary attack rate
(ranging from 0% to 5%) estimated among close contacts made outside
households. However, all these studies were done in a so-called under
control scenario (ie, effective R<1) and some reported relatively few
contacts (ie, fewer than ten per case), which might omit superspreading
events, and isolation outside of household. These findings suggest that
SARS-CoV-2 infection might be driven by community transmission events as
well as household contacts. In our main analysis, we assumed a secondary
attack rate of 20% for households and 6% for all contacts, which led to
an overall R of 2·6 in our model when no control measures were in place.
This value is consistent with the estimated R values in the early stages
of the epidemic.1
, 5
Table 2Secondary attack rates estimated from COVID-19 contact tracing
studies by location
Secondary attack rate among household contacts (%) Secondary attack
rate among close contacts outside household (%) Contacts traced per case
Observed reproduction number
Shenzhen16
12·9% 0·9% 3·0 0·4
USA21
10·5% 0·0% 44·5 0·20
Guangzhou22
10·1% 0·5% 14·3 0·34
Taiwan23
6·6% 0·4% 27·6 0·21
Ningbo17
13·3% 5·1% 11·2 0·69
Guangzhou24
19·3% 5·3% 9·8 0·62
Table includes two separate analyses of contact tracing data from
Guangzhou and differing estimates are likely to be influenced by control
measures in place at the time.
Open table in a new tab
Scenarios
We considered several scenarios, both individually and in combination
(appendix, p 2). These scenarios included no control, self-isolation of
symptomatic cases within and away from household, household quarantine,
quarantine of work or school contacts, manual tracing of acquaintances
(ie, contacts that have been met before), manual tracing of all
contacts, app-based tracing, mass testing of cases regardless of
symptoms, a limit on daily contacts made in other settings (with the
baseline limit being four contacts, equal to the mean number reported by
adults in the BBC Pandemic data), and a proportion of the population
with no school or work contacts. In the self-isolation only scenario, we
assumed that individuals who were successfully isolated either had no
risk of onward transmission (even to household members) or had no risk
to contacts outside the household, but household members could still be
infected. Otherwise, we assumed household quarantine was in place
alongside other measures. For app-based tracing to be successfully
implemented in a given simulation, both the infectious individual and
their contacts needed to have and use the app. We assumed that
individuals younger than 10 years or older than 80 years would not use a
smartphone app (table 1). In the scenario with mass testing of cases
regardless of symptoms, we assumed that infected individuals would be
identified and immediately self-isolate at a random point during or
after their 5-day infectious period. We assumed that infected
individuals would not test positive if they were tested during the
latent period. No other measures (eg, self-isolation when symptomatic)
were in place for this scenario. In the baseline scenario for reduced
work contacts, we assumed that 50% of the population had no work
contacts because 54% of respondents in a UK social contact survey
reported not visiting work in the days after lockdown was introduced on
March 23, 2020.25
For each intervention scenario, we simulated 25 000 primary cases,
generating individual-level contact distributions and secondary cases
with and without the control measure in place, as previously described.
The model code is available online.
Role of the funding source
The sponsor of the study had no role in study design, data collection,
data analysis, data interpretation, or writing of the report. The
corresponding author had full access to all the data in the study and
had final responsibility for the decision to submit for publication.
Results
Under the control measures considered, we found that combined testing
and tracing strategies reduced the Reff more than mass testing or
self-isolation alone (table 3). If self-isolation of symptomatic cases
alone was included, our optimistic scenario resulted in a mean
transmission reduction of 29% if self-isolation was within the household
and 35% if self-isolation was outside the household. The addition of
household quarantine resulted in an overall mean reduction of 37%. In
simulations, self-isolation and household quarantine with the addition
of manual contact tracing of all contacts reduced transmission by 64%;
the addition of manual tracing of acquaintances only led to a 57%
reduction in transmission. We estimated that the addition of app-based
tracing only, with our baseline assumption of 53% coverage, reduced
transmission by 47%. Contact tracing measures also substantially reduced
the probability that a primary symptomatic case would generate more than
one secondary case (table 3).
Table 3Mean reduction in Reff under different control measures
Self-Isolation Contact tracing Non-HH contacts who are potentially
traceable (%) Cases who have R>1 (%) Reff Mean reduction in Reff
No control No No NA 50% 2·6 0%
Self-isolation within home Yes No NA 40% 1·8 29%
Self-isolation outside home Yes NA NA 37% 1·7 35%
Self-isolation plus HHQ Yes HH NA 35% 1·6 37%
Self-isolation plus HHQ plus work or school contact tracing Yes HH and
work or school 100% 27% 1·2 53%
Self-isolation plus HHQ plus manual contact tracing of acquaintances Yes
All 90% school, 79% work, and 52% other 26% 1·1 57%
Self-isolation plus HHQ plus manual contact tracing of all contacts Yes
All 100% 21% 0·94 64%
Self-isolation plus HHQ plus app-based tracing Yes All 53% 30% 1·4 47%
Self-isolation plus HHQ plus manual contact tracing of acquaintances
plus app-based tracing Yes All 90% school, 79% work, and 52% other with
manual tracing; 53% with app tracing 23% 1 61%
Self-isolation plus HHQ plus manual contact tracing of acquaintances
plus limit to four daily contacts with other individuals Yes All 90%
school, 79% work, and 52% other 21% 0·93 64%
Self-isolation plus HHQ plus manual contact tracing of acquaintances
plus app-based tracing plus limit to four daily contacts with other
individuals Yes All 90% school, 79% work, and 52% other with manual
tracing; 53% with app tracing 20% 0·87 66%
Mass testing of 5% of population per week No NA NA 49% 2·5 2%
Results from 20 000 simulated setting-specific secondary transmissions,
assuming a secondary attack rate of 20% among household contacts and 6%
among other contacts. Results under the assumption of some workplace
restrictions remaining in place are shown in table 4. Estimates are
shown to two significant figures. HH=household. HHQ=household
quarantine. NA=not applicable. Reff=effective reproduction number.
Open table in a new tab
We estimated that if some level of physical distancing were maintained,
it could supplement reductions in transmission from contact tracing. For
example, if daily contacts in other settings (ie, outside the home,
work, and school) were limited to four people (the mean number in our
dataset), manual tracing of acquaintances only led to a mean 64%
reduction in transmission, and the addition of app-based tracing
alongside this gave a mean 66% reduction overall. We estimated that mass
random testing of 5% of the population each week would reduce
transmission by only 2%, because substantially fewer infections would be
detected than in other scenarios and many of those that were would have
already transmitted infection.
We also considered the number of contacts that would be traced under
different strategies. In a scenario where 20 000 new symptomatic cases
occurred per day, most contact tracing strategies would require over
500 000 contacts to be newly quarantined each day on average (table 4).
We should note that if contact tracing is triggered on the basis of
suspected COVID-19-like symptoms rather than confirmation of COVID-19,
the number of symptomatic cases in these scenarios would reflect the
total incidence of illness and not just of confirmed COVID-19 cases.
Although we estimated a similar reduction in transmission from manual
tracing of all contacts and from manual tracing of only acquaintances
with a limit to four daily contacts in other settings (table 3), manual
tracing of acquaintances with a four-person limit required fewer people
to be quarantined each day (table 4). We obtained similar results for
the relative reductions in transmission and number of contacts traced
when we assumed a higher secondary attack rate within household or among
other contacts, which corresponded to baseline R values of 2·6–2·9
(appendix, p 4).
Table 4Number of additional people quarantined per symptomatic case
under different scenarios for the absolute number of new symptomatic
cases per day
Median number of people quarantined per detected case (90% prediction
interval) Mean newly quarantined people per day assuming 20 000 new
symptomatic cases per day Mean newly quarantined people per day assuming
5000 new symptomatic cases per day Mean newly quarantined people per day
assuming 1000 new symptomatic cases per day
SI and HHQ 2 (0–4) 38 000 9400 1900
SI plus HHQ plus work or school CT 13 (1–110) 540 000 140 000 27 000
SI plus HHQ plus manual CT of acquaintances 22 (1–120) 650 000 160 000
32 000
SI plus HHQ plus manual CT of all contacts 29 (1–140) 830 000 210 000 41 000
SI plus HHQ plus app-based CT 4 (1–69) 310 000 76 000 15 000
SI plus HHQ plus manual CT of acquaintances plus app-based CT 25 (1–130)
740 000 180 000 37 000
SI plus HHQ plus manual CT of acquaintances plus limit to four daily
contacts with other individuals 17 (1–110) 560 000 140 000 28 000
SI plus HHQ plus manual CT of acquaintances plus app-based CT plus limit
to four daily contacts with other individuals 21 (1–110) 630 000 160 000
32 000
We assumed that quarantined contacts are independent. Estimates shown to
two significant figures. If contact tracing is initiated on the basis of
suspected rather than confirmed COVID-19 cases, the symptomatic case
numbers here would reflect total incidence of COVID-19-like illness,
which might be considerably higher than the number of confirmed cases.
CT=contact tracing. HHQ=household quarantine. SI=self isolation.
Open table in a new tab
We found that the effectiveness of manual contact-tracing strategies was
highly dependent on how many contacts were successfully traced, with a
high level of tracing required to ensure Reff lower than 1 in our
baseline scenario (figure 2A). If contact tracing was combined with a
maximum limit to daily contacts made in other settings (eg, by
restricting gatherings), we found that this limit would have to be small
(ie, fewer than ten or 20 contacts) before a discernible effect could be
seen on Reff. The limit would have to be small (ie, fewer than about ten
contacts) to ensure Reff lower than 1 for app-based tracing, even if
half of adults also had no work contacts (figure 2B). When app-based
tracing was in place, we estimated that if work contacts alone were
restricted, a substantial proportion of the adult population would need
to have zero work contacts to ensure Reff lower than 1 (figure 2C).
Under our baseline assumptions, we estimated that app-based tracing
would require a high level of coverage to ensure Reff lower than 1
(figure 2D) because both primary case and contacts would need to install
and use the app.
Figure thumbnail gr2
Figure 2Impact of contact tracing effectiveness and physical distancing
on reduction in R (baseline R 2·6)
Show full caption
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We also considered the effect of the proportion of infections assumed to
be symptomatic and the relative contribution of asymptomatic individuals
to transmission. We estimated that if a high proportion of cases were
symptomatic, self-isolation and contact tracing measures would lead to a
greater relative reduction in transmission (appendix, p 3); this is
mostly because more primary cases would be detected. Control measures
were slightly less effective if the relative transmissibility of
asymptomatic infections was higher (appendix, p 3) because it would mean
more undetectable transmission occurring. However, because our baseline
scenario assumed that 70% of adults were symptomatic, the overall effect
of asymptomatic individuals on transmission was less than it would be if
most cases were asymptomatic. We estimated that if individuals
self-isolated rapidly (ie, with 1·2 days on average rather than 2·6
days), self-isolation and household quarantine would lead to a larger
reduction in transmission (appendix, p 5); correspondingly, if we
assumed cases took longer to self-isolate after becoming symptomatic
(ie, 3·6 days on average), these measures were less effective. However,
the estimated overall reduction from self-isolation and manual contact
tracing was similar across the three scenarios because although more
secondary infections occurred before isolation, a large proportion of
them would be traced under our baseline model assumptions.
Discussion
Using a model of setting-specific interactions, we estimated that
strategies that combined isolation of symptomatic cases with tracing and
quarantine of their contacts reduced the Reff more than mass testing or
self-isolation alone. The effectiveness of these isolation and tracing
strategies was further enhanced when combined with physical distancing
measures, such as a reduction in work contacts, or a limit to the number
of contacts made outside of home, school, or work settings. Not only
does physical distancing reduce transmission, but it is also likely to
reduce the number of unknown contacts who can be harder to trace.
Several countries have achieved a prolonged suppression of SARS-CoV-2
transmission using a combination of case isolation, contact tracing, and
physical distancing. In Hong Kong, isolation of cases and tracing of
contacts was combined with other physical distancing measures, which
resulted in an estimated Reff near 1 throughout February and March, 2020.26
In South Korea, testing and tracing has been combined with school
closures and remote working.27
In our analysis, we estimated that many contacts would need to be traced
and tested if the incidence of symptomatic cases was high. This
logistical constraint might influence how and when it is possible to
transition from ensuring an Reff lower than 1 through extensive physical
distancing measures to reducing transmission predominantly through
targeted isolation and tracing measures. Our estimate of many contacts
potentially being traced per case in the manual tracing strategies we
considered (table 4) suggests that any planning for ongoing control
based on isolation and tracing should consider the probable need to do
at least 30–50 additional tests for each symptomatic case reported. If
contact tracing is initiated on the basis of suspected rather than
confirmed SARS-CoV-2 infections, then the number of symptomatic cases
that require follow-up tracing and testing might be considerably higher
than the level of confirmed COVID-19 incidence. Given the role of
pre-symptomatic transmission for SARS-CoV-2, the quarantine of these
contacts rather than symptom monitoring alone is likely to be more
effective at reducing onward transmission.28
Our analysis has several limitations. We focused on individual-level
transmission between a primary case and their contacts rather than
considering higher degree network effects. Therefore, our results
focused on possible reductions in transmission rather than temporal
ranges of outbreak size or dynamics. Network structure might also
influence specific interventions. If contacts were clustered (ie, know
each other), the number of contacts that would need to be traced over
multiple generations of transmission could be reduced. Additionally, if
an inverse relationship exists between the probability of detectable
symptoms and app coverage, as might be the case for young children, it
could reduce the effectiveness of symptom-based tracing for such index
cases. We also assumed that contacts made within the home are the same
people daily, but contacts outside home are made independently each day.
Repeated contacts would also reduce the number of people that need to be
traced. However, our estimates are consistent with the upper bound of
numbers traced in empirical studies (table 2), as well as the analysis
of UK social interactions that accounted for contacts of contacts.10
Because our data were not stratified beyond the four contact settings we
considered (home, work, school, and other), we could not consider
additional specific settings, such as mass gatherings. However, our
finding that gatherings in other settings needed to be restricted to
small sizes before a noticeable effect on transmission occurred is
consistent with findings that groups between ten and 50 people have a
larger effect on SARS-CoV-2 dynamics than groups of more than 50.29
In our main analysis, we used a limit of four daily contacts as an
illustrative example. In reality, any control strategies would also need
to consider the probable behaviour of a population in complying with
social restrictions.
Our baseline assumptions were plausible but optimistic. Particularly, we
assumed a delay of symptom onset to isolation of 2·6 days in the
baseline scenario, and quarantine within 2 days for successfully
manually traced contacts and immediately for app-based tracing, with 90%
of contacts assumed to adhere to quarantine. For context, on the basis
of viral shedding dynamics, onset of infectiousness typically occurs 2–3
days after exposure.6
In our model, we considered self-isolation both within and outside the
household, finding that isolation outside household led to slightly
higher reduction in onward transmission than within; this reduction was
not larger because some pre-symptomatic transmission had often already
occurred. However, our conclusions about onwards transmission in the
different control tracing scenarios were not dependent on assumptions
about household transmission, because in these scenarios, we assumed
that household quarantine would be in place too. We also simulated
contact patterns at random for each individual in our population,
whereas in an outbreak, a correlation between number of contacts and
infection risk is likely to occur; individuals with multiple contacts
might be more likely to acquire infection and transmit it to others. If
this were the case, and we assume the same secondary attack rates, the
overall reduction might be lower than we have estimated; however, to
keep the baseline R consistent, this correlation would have to be offset
by a lower secondary attack rate among contacts. We also did not include
the potential for imported infections; when local infection prevalence
is low, additional screening or restrictions might need to be considered
to reduce the risk of new importations of cases.
Our results highlight the challenges involved in controlling SARS-CoV-2.
Consistent with previous modelling studies7
, 10
and observed early global outbreak dynamics, our analysis suggests
that—depending on the overall effectiveness of testing, tracing,
isolation, and quarantine—a combination of self-isolation, contact
tracing, and physical distancing might be required to maintain Reff
lower than 1. Additionally, in a scenario where incidence is high, a
considerable number of individuals might need to be quarantined to
achieve control with use of strategies that involve contact tracing.
Contributors
AJK, PK, and WJE designed the analysis. AJK developed the model. AJK,
PK, AJKC, SMK, MT, HF, and JRG contributed to collection, processing,
and interpretation of the original BBC Pandemic dataset, as well as
interpretation of the study findings. The CMMID COVID-19 working group
members contributed to interpretation of the study results. All authors
contributed to writing the manuscript and approved the final version.
Declaration of interests
We declare no competing interests.
Acknowledgments
AJK was supported by a Sir Henry Dale Fellowship jointly funded by the
Wellcome Trust and the Royal Society ( grant 206250/Z/17/Z ). MT was
supported by the UK Engineering and Physical Sciences Research Council (
grant EP/N509620/1 ). PK acknowledges support from the Royal Society
(0RP\EA\180004). WJE was supported by the Medical Research Council (
grant MC_PC_19065 ). We would like to thank Stephen Eglen for doing an
independent CODECHECK on our model code.
Supplementary Material
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Publication History
Published: June 16, 2020
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DOI: https://doi.org/10.1016/S1473-3099(20)30457-6
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Figures
Figure thumbnail gr1
Figure 1Model of social interactions and SARS-CoV-2 transmission and
control
Figure thumbnail gr2
Figure 2Impact of contact tracing effectiveness and physical
distancing on reduction in R (baseline R 2·6)
Tables
Table 1Parameter definitions and assumptions for the baseline model
Table 2Secondary attack rates estimated from COVID-19 contact
tracing studies by location
Table 3Mean reduction in Reff under different control measures
Table 4Number of additional people quarantined per symptomatic case
under different scenarios for the absolute number of new symptomatic
cases per day
Linked Articles
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of COVID-19 pandemic control, not optional choices
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