Impact of delays on effectiveness of contact tracing strategies for COVID-19: a modelling study

Abstract

Background
In countries with declining numbers of confirmed cases of COVID-19, lockdown measures are gradually being lifted. However, even if most physical distancing measures are continued, other public health measures will be needed to control the epidemic. Contact tracing via conventional methods or mobile app technology is central to control strategies during de-escalation of physical distancing. We aimed to identify key factors for a contact tracing strategy to be successful.

Methods
We evaluated the impact of timeliness and completeness in various steps of a contact tracing strategy using a stochastic mathematical model with explicit time delays between time of infection and symptom onset, and between symptom onset, diagnosis by testing, and isolation (testing delay). The model also includes tracing of close contacts (eg, household members) and casual contacts, followed by testing regardless of symptoms and isolation if testing positive, with different tracing delays and coverages. We computed effective reproduction numbers of a contact tracing strategy (RCTS) for a population with physical distancing measures and various scenarios for isolation of index cases and tracing and quarantine of their contacts.

Findings
For the most optimistic scenario (testing and tracing delays of 0 days and tracing coverage of 100%), and assuming that around 40% of transmissions occur before symptom onset, the model predicts that the estimated effective reproduction number of 1·2 (with physical distancing only) will be reduced to 0·8 (95% CI 0·7–0·9) by adding contact tracing. The model also shows that a similar reduction can be achieved when testing and tracing coverage is reduced to 80% (RCTS 0·8, 95% CI 0·7–1·0). A testing delay of more than 1 day requires the tracing delay to be at most 1 day or tracing coverage to be at least 80% to keep RCTS below 1. With a testing delay of 3 days or longer, even the most efficient strategy cannot reach RCTS values below 1. The effect of minimising tracing delay (eg, with app-based technology) declines with decreasing coverage of app use, but app-based tracing alone remains more effective than conventional tracing alone even with 20% coverage, reducing the reproduction number by 17·6% compared with 2·5%. The proportion of onward transmissions per index case that can be prevented depends on testing and tracing delays, and given a 0-day tracing delay, ranges from up to 79·9% with a 0-day testing delay to 41·8% with a 3-day testing delay and 4·9% with a 7-day testing delay.

Interpretation
In our model, minimising testing delay had the largest impact on reducing onward transmissions. Optimising testing and tracing coverage and minimising tracing delays, for instance with app-based technology, further enhanced contact tracing effectiveness, with the potential to prevent up to 80% of all transmissions. Access to testing should therefore be optimised, and mobile app technology might reduce delays in the contact tracing process and optimise contact tracing coverage.

Funding
ZonMw, Fundação para a Ciência e a Tecnologia, and EU Horizon 2020 RECOVER.

Full text

www.thelancet.com/public-health Published online July 16, 2020 https://doi.org/10.1016/S2468-2667(20)30157-2
1
Articles
Lancet Public Health 2020
Published Online
July 16, 2020
https://doi.org/10.1016/
S2468-2667(20)30157-2
See Online/Comment
https://doi.org/10.1016/
S2468-2667(20)30160-2
Julius Center for Health
Sciences and Primary Care
(Prof M E Kretzschmar PhD,
G Rozhnova PhD,
M C J Bootsma PhD,
M van Boven PhD,
Prof J H H M van de Wijgert PhD,
Prof M J M Bonten MD) and
Department of Medical
Microbiology (Prof M Bonten),
University Medical Center and
Mathematical Institute
(M Bootsma), Utrecht
University, Utrecht,
Netherlands; BioISI—
Biosystems & Integrative
Sciences Institute, Faculdade
de Ciências, Universidade de
Lisboa, Lisboa, Portugal
(G Rozhnova); and Institute of
Infection and Global Health,
University of Liverpool,
Liverpool, UK
(Prof J H H M van de Wijgert)
Correspondence to:
Prof Mirjam E Kretzschmar,
Julius Center for Health Sciences
and Primary Care, University
Medical Center Utrecht, Utrecht
3584CX, Netherlands
m.e.e.kretzschmar@
umcutrecht.nl
Impact of delays on effectiveness of contact tracing
strategies for COVID-19: a modelling study
Mirjam E Kretzschmar, Ganna Rozhnova, Martin C J Bootsma, Michiel van Boven, Janneke H H M van de Wijgert, Marc J M Bonten
Summary
Background In countries with declining numbers of confirmed cases of COVID-19, lockdown measures are gradually
being lifted. However, even if most physical distancing measures are continued, other public health measures will be
needed to control the epidemic. Contact tracing via conventional methods or mobile app technology is central to
control strategies during de-escalation of physical distancing. We aimed to identify key factors for a contact tracing
strategy to be successful.
Methods We evaluated the impact of timeliness and completeness in various steps of a contact tracing strategy using
a stochastic mathematical model with explicit time delays between time of infection and symptom onset, and between
symptom onset, diagnosis by testing, and isolation (testing delay). The model also includes tracing of close contacts
(eg, household members) and casual contacts, followed by testing regardless of symptoms and isolation if testing
positive, with dierent tracing delays and coverages. We computed eective reproduction numbers of a contact
tracing strategy (RCTS) for a population with physical distancing measures and various scenarios for isolation of index
cases and tracing and quarantine of their contacts.
Findings For the most optimistic scenario (testing and tracing delays of 0 days and tracing coverage of 100%), and
assuming that around 40% of transmissions occur before symptom onset, the model predicts that the estimated
eective reproduction number of 1·2 (with physical distancing only) will be reduced to 0·8 (95% CI 0·7–0·9) by
adding contact tracing. The model also shows that a similar reduction can be achieved when testing and tracing
coverage is reduced to 80% (RCTS 0·8, 95% CI 0·7–1·0). A testing delay of more than 1 day requires the tracing delay
to be at most 1 day or tracing coverage to be at least 80% to keep RCTS below 1. With a testing delay of 3 days or longer,
even the most ecient strategy cannot reach RCTS values below 1. The eect of minimising tracing delay (eg, with app-
based technology) declines with decreasing coverage of app use, but app-based tracing alone remains more eective
than conventional tracing alone even with 20% coverage, reducing the reproduction number by 17·6% compared
with 2·5%. The proportion of onward transmissions per index case that can be prevented depends on testing and
tracing delays, and given a 0-day tracing delay, ranges from up to 79·9% with a 0-day testing delay to 41·8% with a
3-day testing delay and 4·9% with a 7-day testing delay.
Interpretation In our model, minimising testing delay had the largest impact on reducing onward transmissions.
Optimising testing and tracing coverage and minimising tracing delays, for instance with app-based technology,
further enhanced contact tracing eectiveness, with the potential to prevent up to 80% of all transmissions. Access to
testing should therefore be optimised, and mobile app technology might reduce delays in the contact tracing process
and optimise contact tracing coverage.
Funding ZonMw, Fundação para a Ciência e a Tecnologia, and EU Horizon 2020 RECOVER.
Copyright © 2020 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY-NC-ND
4.0 license.
Introduction
Many countries are preparing so-called exit strategies
from the COVID-19 lockdown while attempting to
successfully control transmission. Contact tracing, in
combination with the quarantine and potential testing of
contacts, is considered a key component in a phase when
lockdown measures are gradually lifted.1–8 Contact tracing
is an intervention where an index case with confirmed
infection is asked to provide information about contact
people who were at risk of acquiring infection from the
index case within a given time period before the positive
test result. These contacts are then traced and informed
about their risk, quarantined, and tested if eligible for
testing according to national testing guidelines. This
requires upscaling of conventional contact tracing
capacity. The potential of mobile device apps to support
contact tracing is widely discussed and such technology
has been used in several countries such as South Korea
and Taiwan. Although these countries have successfully
reduced case numbers, no causal relationship between
use of app technology and epidemic control has yet been
shown.9–14 Many uncertainties remain on the optimal
process of contact tracing with conventional methods or
mobile apps, on the timing of testing for current or past

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infection, and on the required coverage of contact tracing
needed.
Modelling studies have shown how mobile apps can
increase eectiveness of contact tracing compared with
conventional approaches, but eectiveness depends on
what proportion of the population will use the app
consistently for a suciently long period of time.9
Modelling studies have predicted that contact tracing
alone cannot control an outbreak if tracing coverage is
too low.2,15 The tracing coverage needed depends on how
much transmission occurs before symptom onset, and
on the details of the tracing process.
In previous work, we have investigated the impact of
timeliness and completeness of case reporting on the
eectiveness of surveillance and interventions,16,17 and we
quantified the timeliness of contact tracing of infected
passengers during an airline flight for the 2009 influenza
pandemic.18 In all of these studies, the timing of various
steps in the monitoring and intervention chain emerged
as a key factor for eectiveness of a public health
response. Usually, there are identifiable delays in the
response chain that might be crucial to the overall
eectiveness of a strategy.
Here, we analyse in detail the process chain of iden-
tifying index cases by symptom reporting, testing of
index cases, and subsequent contact tracing, with the
aim to inform policy makers on the relative importance
of key steps in the process. We use a mathematical
model that reflects the various steps and delays in
the contact tracing process to quantify how delays
aect the eective repro duction number and the frac-
tion of onward transmission prevented per diagnosed
index case.5,19
Methods
Time delays in contact tracing
Our starting point is an assumed eective reproduction
number (Re) for COVID-19 of around 1, describing a
situation with physical distancing but measures lifted to
some extent. We then quantify the relative contribution
of the individual components of a contact tracing strategy
required to bring and maintain the eective reproduction
number with contact tracing (RCTS) to a value below 1. For
simplicity, we do not include transmission in health-care
settings, because in settings such as nursing homes,
which can be viewed as closed populations, other
interventions might be more appropriate.
We break down the process of contact tracing into
two steps (figure 1; appendix p 6). In the first step, an index
case acquires the infection (at time T0), then after a short
latent period becomes infectious (at time T1) and then
possibly symptomatic (at time T2), which here is defined as
being eligible for testing. Subsequently, a proportion of
these symptomatic individ uals, determined by the testing
coverage, gets tested and diagnosed (at time T3). The time
between T2 and T3 is called the testing delay (D1
= T3
− T2)
and can vary between 0 and 7 days, and in this period
individuals might self-quarantine. We define testing
See Online for appendix
Research in context
Evidence before this study
We searched PubMed, bioRxiv, and medRxiv for articles
published in English from Jan 1 to June 20, 2020, with the
following keywords: (“2019-nCoV” OR “novel coronavirus” OR
“COVID-19” OR “SARS-CoV-2”) AND “contact tracing” AND
“model*”. Population-level modelling studies of severe acute
respiratory syndrome coronavirus 2 (SARS-CoV-2) have
suggested that isolation and tracing alone might not be
sufficient to control outbreaks and additional measures might
be required. However, few studies have focused on the effects
of lifting individual measures once the first wave of the
epidemic has been controlled. Lifting measures must be
accompanied by effective contact tracing strategies to keep the
effective reproduction number below 1. A detailed analysis,
with special emphasis on the effects of time delays in testing of
index patients and tracing of contacts, has not been done.
Added value of this study
We did a systematic analysis of the various steps required in the
process of testing and diagnosing an index case as well as tracing
and isolating possible secondary cases of the index case. We then
used a stochastic transmission model that distinguishes between
close contacts (eg, household members) and casual contacts to
assess which steps and (possible) delays are crucial in determining
the effectiveness of a contact tracing strategy. We evaluated how
delays and the level of contact tracing coverage influence the
effective reproduction number, and how fast contact tracing
needs to be to keep the reproduction number below 1. We also
analysed what proportion of onward transmission can be
prevented with short testing and tracing delays and high contact
tracing coverage. Assuming that around 40% of transmission
occurs before symptom onset, we estimate that keeping the time
between symptom onset and testing and isolation of an index
case short (<3 days) is imperative for successful contact tracing.
This implies that the process leading from symptom onset to
receiving a positive test should be minimised by providing a
sufficient number of easily accessible testing facilities. In addition,
reducing contact tracing delays also helps to keep the
reproduction number below 1.
Implications of all the available evidence
Our analyses highlight that a contact tracing strategy will only
contribute to containment of COVID-19 if it can be organised
such that delays in the process from symptom onset to
isolation of the index case and their contacts are very short.
The process of conventional contact tracing should be
reviewed and streamlined, while mobile app technology might
offer a tool for speeding up the process. Reducing delay in
testing individuals for SARS-CoV-2 should be a key objective of
a contact tracing strategy.

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3
coverage as the proportion of all symptomatic cases that
are tested. After being diagnosed, we assume index cases
are isolated with no further transmission.
The second step is tracing contacts of the index case,
which occurs at time T4. A fraction of those contacts,
determined by the tracing coverage, will be found and
tested. We assumed that all traced contacts do not
transmit any further, either because they are tested and
isolated if infected or because they are eectively
quarantined. The eectiveness of these measures are
therefore subsumed in the tracing coverage. The time
between T3 and T4 is the tracing delay (D2=T4 – T3), which
can range from 0 days (eg, with app technology) to 3 days
(with conventional approaches); this range was obtained
through personal communications with public health
professionals who are working with contact tracing in
practice, as well as existing estimates for influenza.18 In
this step, tracing coverage is defined as the proportion of
contacts detected, which either depends on the capacity
of conventional approaches or on the fraction of the
population using suitable app technology for screen ing.
Strategies considered
We considered two particular contact tracing strategies:
conven tional contact tracing and mobile app technology
contact tracing (reproduction number RCTS). We did not
consider hybrid approaches of combined conventional
and mobile app-based strategies. We compared these
strategies with a physical distancing strategy (reproduction
number Re) and an isolation strategy where symptomatic
individuals get tested and isolated without subsequent
contact tracing (repro duction number Riso).
As 100% testing and tracing coverages are dicult
to achieve, we defined a best-case scenario with 80%
testing and tracing coverage, where people eligible
for testing are immediately tested with a very fast test
result (testing delay 0 days) and immediate isolation
when testing positive. In contact tracing strategies, this is
followed by immediate tracing of contacts (tracing delay
0 days), who immediately adhere to isolation measures.
In our analyses, this best-case scenario can only be
achieved by mobile app use. We consider more realistic
scenarios where testing and tracing are suboptimal—
eg, a con ventional contact tracing strategy—and we vary
these parameters separately in a sensitivity analysis
(appendix pp 9–12).
Effectiveness of contact tracing at the population level
To analyse the impact of delays in testing and tracing on
the eectiveness of contact tracing strategies at the popu-
lation level, we use a model introduced by Kretzschmar
and colleagues,19 which was adapted for severe acute
respiratory syndrome coronavirus 2 (SARS-CoV-2).5 The
stochastic model describes an epidemic as a branching
process with progression through latent infection and an
infectious period in time steps of 1 day. Infectivity and
probability of symptom onset per day of the infectious
period and numbers of contacts per day were fitted to
distributions taken from published data.20–24 With these
distributions, around 40% of transmissions take place
before symp tom onset. We distinguish between close
contacts (eg, household contacts) and casual contacts,
which dier in the risk of acquiring infection from the
index case. Contact definitions were based on those used
in the Polymod study,23 where a contact is defined as
having a two-way con versation of three or more words in
physical presence or having physical contact with another
person. A high-risk contact is one that includes physical
contact, lasts more than 15 min, or occurs on a regular
basis. Additionally, the time required for tracing and
isolating infected contacts and the coverage of tracing
can dier between these types of contacts and between
dierent types of contact tracing (eg, conventional vs
mobile app supported). We assume that isolation is
perfect—ie, that isolated people do not transmit any
longer—and that all traced infected contacts are isolated,
regardless of whether they develop symptoms or not. The
model allows for explicit computation of the basic
reproduction number R0, Re, Riso, and RCTS. Reproduction
numbers were calculated as expectations, and distri-
butions of individual repro duction numbers were simu-
lated. The model was coded in Mathematica 12.1. Further
details are presented in the appendix (pp 3–9).
Parameter settings
We assumed that without physical distancing, individuals
have on average four close contacts and nine casual
contacts per day, with stochastic variability. The distri-
butions were fitted to data from the Polymod study for
the Netherlands.23 Transmission probability per contact
for close contacts was taken to be four times higher than
for casual contacts. We assumed that 80% of all infected
people develop symptoms at some time during their
infectious period and 20% remain asymptomatic.
Symptomatic and asymptomatic cases were assumed to
be equally infectious. Overall, the transmission prob-
ability was calibrated to R0=2·5. For physical distancing,
we assumed that close contacts were reduced by 40%
and casual contacts by 70%. The resulting eective
Figure 1: Schematic of the contact tracing process and its time delays
T0=time of infection of index case. T1=onset of infectiousness. T2=symptom onset. T3=time of positive diagnosis.
T4=time of tracing and quarantining of contacts.
Latent
Infectious
Recovering
Time
Contacts
traced
Positive test result
T0T1T2T3T4
X
X
X
X
X
X
Prevented by isolation
Prevented by contact tracing

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reproduction number was Re=1·2. More details on the
parameters are given in the appendix (pp 2–4).
Uncertainty of model outcomes
We considered uncertainty due to stochastic variability and
uncertainty due to possible variation in parameter esti-
mates. We dealt with stochastic variability by computing
individual reproduction numbers for 1000 individuals
for all scenarios and plotted their distributions as box-
plots. Parameter uncertainty was explored by performing
simulations using hypercube sampling for transmission
probabilities and probabilities of symptom onset per day of
the infectious period (appendix pp 9–10).
Scenarios modelled
For conventional contact tracing, we assumed baseline
values of 80% testing coverage and higher tracing
coverage for close contacts than for casual contacts, set at
80% and 50%, respectively. We analysed the eect of
various testing and tracing delays and tracing coverage
on RCTS while keeping the testing coverage at 80%. For
comparison, we also considered the isolation strategy
(Riso), again with testing coverage at 80%. In sensitivity
analyses, we varied the testing delay D1 between
0 and 7 days and the tracing delay D2 between 0 and 3 days;
furthermore, we varied both testing coverage and tracing
coverages separately between 20% and 80% in increments
of 20 percentage points.
We then compared the eectiveness of conventional
contact tracing alone with a scenario in which mobile
app technology is used for alerting people to be tested
and for tracing contacts; exact parameter values for this
comparison are shown in table 1. Dierences between
these strategies were taken as follows. The testing
delay (D1) is reduced by 4 days with mobile app
technology. We assumed a conventional contact tracing
setting in which symptomatic individuals need to
decide to seek health care to get tested, and we assumed
that with app technology, individuals reporting
symptoms to the app are automatically oered a test
without having to seek health care. For conventional
contact tracing, we assumed suboptimal coverage in
identifying contacts from the week before diagnosis
due to recall bias, especially for casual contacts. For
contact tracing with mobile app technology, we assume
80% tracing coverage of the contacts of symptomatic
people using mobile app technology as a best-case
scenario, but also consider other coverages as detailed
below and in table 1. We show also results for 100%
coverage, although realistically more than 80% is not
feasible because not all contacts will be correctly
identified and compliance with isolation of those tested
positive might not be perfect. We assume that tracing
goes back for 7 days before the positive test result for
both strategies.
Next, we quantified the impact of coverage of testing
and mobile app use on the eectiveness of dierent
strategies. We varied the percentage of app users in the
population between 20% and 100% in increments of
20 percentage points. We first considered the situation
where testing is provided for 80% of people with
symptoms independently of app use, and app use only
influences the fraction of contacts that are traced (ie,
tracing coverage varies between 20% and 100%). Alter-
natively, we assumed that only app users are tested
(ie, testing coverage varies between 20% and 100%), and
coverage of tracing also depends on fraction of app use.
In all cases, a contact could only be traced if both the
index case and the contact were app users—ie, the
probability of a contact being traced is given by the
square of the proportion of app users.
Isolation Conventional
contact tracing
Mobile app
contact tracing
Testing coverage 80% 80% 20%, 40%, 60%,
80%, 100%
Testing delay (D1), assuming immediate
isolation when testing positive
4 days 4 days 0 days
Time to trace close contacts (D2)·· 3 days 0 days
Time to trace other contacts, assuming testing
and isolation of those who test positive
·· 3 days 0 days
Tracing coverage of close contacts ·· 80% 20%, 40%, 60%,
80%, 100%
Tracing coverage of casual contacts ·· 50% 20%, 40%, 60%,
80%, 100%
Time traced back ·· 7 days 7 days
For isolation-only and conventional contact tracing strategies, we assumed a baseline testing coverage of 80%
(see appendix pp 11–12 for sensitivity analyses). For mobile app contact tracing strategies, we varied the testing
coverage between 20% and 100%, and assumed 80% as a best-case scenario. For conventional contact tracing,
delays and coverages were chosen to reflect current practice, whereas for mobile app contact tracing, we varied
coverages to reflect different levels of app use.
Table 1: Comparison of isolation, conventional contact tracing, and mobile app contact tracing strategies
Figure 2: Comparison of conventional and mobile app contact tracing strategies
For parameter values, see table 1. The isolation only strategy is shown in green
for comparison. We assumed that testing coverage is 80% for the conventional
contact tracing strategy and 60%, 80%, and 100% for the mobile app contact
tracing strategy. For the mobile app strategy, it is assumed that the tracing
coverage equals the testing coverage—ie, it is 60%, 80%, and 100%, respectively.
Expected reproduction numbers are shown as a function of testing delay D1.
Re=effective reproduction number.
Conventional
Mobile app: 60% testing and tracing
Mobile app: 80% testing and tracing
Mobile app: 100% testing and tracing
0 1 2 3 4 5 6 7
0·7
0·8
0·9
1·0
1·1
1·2
1·3
Testing delay D1 (days)
Reproduction number
Contact tracing strategy
Re
Isolation
strategy

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5
Finally, we quantified the fraction of transmissions of
an index case that can be prevented, and the contri-
bution to the fraction prevented from isolation and from
tracing contacts with decreasing delays. The number of
onward transmissions of an index case is, by definition,
described by the eective reproduction number Re of
the realised scenario. Therefore, the dierence of
reproduc tion numbers between two intervention
scenarios under the condition that an index case is
diagnosed will describe the fraction of onward
transmissions prevented. For contacts, this is the
fraction of the total infectivity that lies after the time of
isolation—ie, the part of infec tiousness that is prevented
by contact tracing. In other words, a contact person who
is detected and isolated before the start of their
infectious period is counted as a fully prevented
transmission, whereas a contact person who is only
traced and identified after 70% of their infectivity has
passed is counted as 0·3 of a prevented onward
transmission.
Role of the funding source
The funders of the study had no role in study design,
data collection, data analysis, data interpretation, writing
of the manuscript, or the decision to submit for publi-
cation. All authors had full access to all the data in the
study and were responsible for the decision to submit the
manuscript for publication.
Results
If 80% of infectious people who develop symptoms are
tested and isolated within 1 day after symptom onset, the
eective reproduction number Re is expected to decline
from 1·2 to an Riso of 1·0 (95% CI 0·9–1·1), using an
isolation strategy without contact tracing (figure 2).
Contact tracing has the potential to further decrease the
reproduction number to 0·8 (95% CI 0·7–0·9), as shown
by the mobile app contact tracing scenario with 100%
testing and tracing (figure 2). In our predefined best-case
scenario, with 80% testing coverage, testing and tracing
delays of 0 days, and a tracing coverage of 80%, the model
predicts a 30% reduction of Re, down to an RCTS of 0·8
(0·7–1·0). However, once the testing delay approaches
2 days, tracing delay needs to be at most 1 day or tracing
coverage needs to be at least 80% to keep RCTS below 1
(appendix p 10). From these scenarios, the reduction of
RCTS achieved by implementing the best-case scenario is
estimated at 17% (appendix p 10). Once testing delay
becomes 3 days or longer, even perfect contact tracing (ie,
100% testing and tracing coverage with no tracing delay)
cannot bring RCTS values below 1.
Our assumption that conventional contact tracing has
a longer tracing delay and lower tracing coverage than a
strategy based on mobile app technology resulted in
marked dierences in RCTS for the whole range of testing
delay (figure 2). With conventional contact tracing, RCTS
would remain above 1 if the testing delay exceeds 0 days,
whereas contact tracing based on mobile app technology
could still keep RCTS below 1 with a delay of up to 2 days,
as long as testing and tracing coverage are at least 80%,
or with a testing delay of 1 day if tracing coverage is at
least 60%. If the testing delay reaches 5 days or more,
app technology adds little eectiveness to conventional
contact tracing or just isolation of symptomatic cases.
The reductions of Re (based on physical distancing)
achieved by isolation of symptomatic cases only, conven-
tional contact tracing, and mobile app-based contact
tracing are shown in figure 3A. For isolation only and for
conventional contact tracing, we assumed a delay of 4 days
between symptom onset and isolation of the index case.
Figure 3: Estimated reduction of the effective reproduction number for
various contact tracing strategies
(A) RCTS is shown as a percentage of Re , where only physical distancing is
implemented. For the isolation scenario and conventional contact tracing
scenario, we assumed a 4-day delay between symptom onset and isolation of
the index case. For mobile app contact tracing, testing delay was assumed to be
0 days. Testing coverage was assumed to be 80% in the isolation and
conventional contact tracing scenarios; app use prevalence was assumed to be
60%, 80%, and 100% in the mobile app contact tracing scenario.
(B) Distributions of individual reproduction numbers for 1000 individuals in the
same scenarios as in described in panel A. Each boxplot shows the mean
(diamond, where the height of the diamond indicates the CI of the mean)
IQR, and upper fence (75% quartile + 1·5 × IQR) of the distribution. The dots are
outliers, where darker dots contain more datapoints than lighter dots. All
data points are integers. Re=effective reproduction number. RCTS=effective
reproduction number with contact tracing.
100·0 98·2 97·5
75·6 69·6
61·9
0
1
2
3
4
5
6
B
Reproduction number
0
20
40
60
80
100
A
Percentage of Re
Intervention
Physical distancing
Isolation
Interventions without
contact tracing
Conventional
Mobile app: 60% testing and tracing
Mobile app: 80% testing and tracing
Mobile app: 100% testing and tracing
Interventions with
contact tracing

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The relative reductions are independent of the level of Re,
with similar percentage reductions seen when starting
from R0—ie, in a situation without physical distancing
(appendix p 14). At 80% testing coverage, conventional
contact tracing, even if applied for all infected individuals
with symptoms, is less eective than mobile app-based
contact tracing (dierence 27·9 percentage points), due to
longer tracing delays and lower tracing coverage (figure 3;
table 1). When considering the distributions of individual
reproduction numbers for the assumed testing delays—
ie, 4 days for isolation and con ventional contact tracing
and 0 days for app-based contact tracing—we found that
the mean reproduction number was less than 1 only for
mobile app-based contact tracing (figure 3).
The eectiveness of mobile app-based technology
declines with lower fractions of the population using it
(figure 4). Yet, app-based tracing on its own remains
more eective than conventional tracing alone, even with
20% coverage, due to its inherent speed. Even with low
coverage, there is a reduction of Re, due to fast tracing of
a small part of the population. Depending on Re, such an
approach might be sucient to reduce RCTS to levels
below 1. This can be seen in the distributions of RCTS:
when the app is used only for contact tracing (ie, all
symptomatic individuals can be tested, regardless of
whether they use the app), the means of the RCTS
distributions are below 1 when at least 40% of the
population are using the app, whereas when the app is
used for contact tracing and testing (ie, only app users
can be tested), this is the case when at least 60% of the
population are using the app (figure 4).
We quantified proportions of transmissions per index
case that can be prevented depending on testing delay,
stratified by isolation of index cases and tracing delays
(table 2). In the best-case scenario, with testing and tracing
delays of 0 days, 79·9% of transmissions can be prevented
if the tracing coverage is 80%. When testing delay is
increased to 3 days with a tracing delay of 0 days, the
percentage of transmission prevented is almost halved to
41·8%. If tracing delay is also increased to 3 days, only
21·0% of onward transmissions can still be prevented.
Discussion
Using a mathematical model that describes the dierent
steps of a contact tracing strategy for COVID-19, we have
quantified the relevance of delays and coverage pro-
portions for controlling SARS-CoV-2 transmission. We
conclude that reducing the testing delay—ie, shortening
the time between symptom onset and a positive test
result, assuming immediate isolation—is the most
import ant factor for improving contact tracing eective-
ness. Reducing the tracing delay—ie, shortening the time
to trace contacts, assuming immediate testing and isola-
tion if found positive—might further enhance contact
tracing eectiveness. Yet this additional eect rapidly
declines with increasing testing delay. The eectiveness
of mobile app-based contact tracing declines with lower
app use coverage, but it remains more eective than
conventional contact tracing even with lower coverage,
due to its inherent speed. If an index case is tested positive
and enters this information into the app, other users who
have been in contact can be warned immediately, because
the app will have recorded these contacts via Bluetooth.
Figure 4: Impact of varying levels of mobile app use on RCTS
In panels A and B, we assume that there is also testing (at 80% coverage) of those who do not use the mobile app,
so app use only is used for tracing contacts. In panels C and D, only app users, who develop symptoms, are tested.
Panels A and C show percentage reductions of Re achieved by the mobile app contact tracing strategy;
panels B and D show the impact of various contact tracing strategies on distributions of individual reproduction
numbers, RCTS. Each boxplot shows the mean (diamond, where the height of the diamond indicates the CI of the
mean) IQR, and upper fence (75% quartile + 1·5 × IQR) of the distribution. The dots are outliers, where darker dots
contain more datapoints than lighter dots. All datapoints are integers. Re=effective reproduction number.
RCTS=effective reproduction number with contact tracing.
94·3 87·3
79·0
69·6
59·0
82·4 79·8 75·6 69·6
61·9
0
20
40
60
80
100
Percentage of Re
Testing of app users only
Percentage of the population
using the mobile app
0
1
2
3
4
5
6
CD
RCTS
0
20
40
60
80
100
Percentage of Re
Testing of whole population
0
1
2
3
4
5
6
AB
RCTS
Percentage of the population
using the mobile app
20% 40% 60% 80% 100%
Isolation only Isolation plus contact tracing
D2=3 D2=2 D2=1 D2=0
D1=0 50·4% 62·4% 67·8% 73·9% 79·9%
D1=1 35·7% 47·3% 53·4% 60·7% 68·5%
D1=2 23·4% 33·0% 38·9% 46·5% 55·4%
D1=3 14·2% 21·0% 26·0% 32·9% 41·8%
D1=4 7·8% 11·9% 15·7% 21·4% 29·1%
D1=5 3·8% 5·9% 8·4% 12·5% 18·4%
D1=6 1·6% 2·4% 3·8% 6·4% 10·4%
D1=7 0·5% 0·7% 1·3% 2·8% 4·9%
Interventions explored are isolation of only the index case or isolation of the index
case with tracing and isolation of 80% of infected contacts, according to tracing
delay D2, ranging from 0 to 3 days. All interventions are varied by testing delay D1,
ranging from 0 to 7 days.
Table 2: Percentage of onward transmissions prevented per diagnosed
index case for various interventions

Articles
www.thelancet.com/public-health Published online July 16, 2020 https://doi.org/10.1016/S2468-2667(20)30157-2
7
A contact tracing strategy therefore has the potential to
control virus transmission, and to enable alleviation of
other control measures, but only if all delays are maxi-
mally reduced. It should be noted that we simulated
two contact tracing systems—conventional contact
tracing with testing and tracing delays and app-based
contact tracing without delays—and ignored hybrid
approaches. At present, most European countries are
using conventional contact tracing strategies, but are
attempting to reduce delays (eg, by improving testing and
tracing capacity and by removing testing barriers), and
are piloting or planning the addition of app-based contact
tracing. Such hybrid contact tracing systems would fall
somewhere between the fully conventional and app-based
scenarios described in this Article.
Several factors can reduce the eectiveness of contact
tracing, such as large proportions of cases who remain
asymptomatic or are otherwise not diagnosed and large
proportions of contacts who cannot be traced. Mobile app-
based technology could increase the proportion of
traceable contacts because it does not rely on recall of
names and contact details, but this would require the
participation of a substantial proportion of the popu lation.
App use acceptance might be hampered by privacy
concerns and other ethical considerations. Also, app use
needs to continue over a long time period, requiring
sustained adherence by app users. Low participation does
not render contact tracing useless, however, because it
could help to locally extinguish clusters before they grow
larger. In addition, every measure that lowers the eective
reproduction number, even if it is already below 1, will
lower the cumulative case number and speed up the time
until elimination of the virus from the population.
A strength of our approach is that it explicitly takes
many details of the contact tracing process into account,
such that the key factors can be identified. A limitation of
our approach is that it does not take population age
structure into account, which might influence the
proportion of asymptomatic cases and mobile app use
coverage. Also, the willingness of a case to self-isolate
depends on age and social norms, might be influenced by
socioeconomic status, and is aected by perceived benefit
of isolation in relation to perceived risk of the infection to
others.25 We also excluded other hetero geneities while
assuming homogeneous mixing,26,27 and assumed homo-
geneously distributed use of app technology for dierent
coverage levels. Clustering of non-users could have
consequences for the overall eectiveness of contact
tracing, similar to clustering of non-vaccinated people.
Furthermore, we ignored that a sizeable portion of
transmissions might be acquired nosocomially when
population prevalence is still low.28 The model also
ignores that some contacts of the index case might have
self-quarantined with symptoms before they are traced,
which lowers the benefits of a contact tracing strategy.
Our study adds to results from other modelling studies,
which have shown that contact tracing can be an eective
intervention if tracing coverage is high and if the process
is fast.2,15 A determining factor is the proportion of
transmissions occurring before symptom onset, which
determines the urgency of tracing and isolating contacts
as fast as possible. Our study showed in detail what the
role is of each step in the contact tracing process in
making it successful. Our model diers from other
published models in that it makes a distinction between
close and casual contacts and we consider scenarios for
conventional contact tracing and mobile app-based
contact tracing characterised by specific delays and
coverages.
Our finding of the crucial importance of the first step
of contact tracing—establishing a diagnosis in cases with
symptoms—has important consequences. It requires an
infrastructure for testing that allows people with symp-
toms to be quickly tested and alerted to their results,
preferably within 1 day of symptom onset. For example,
walk-in or drive-in testing facilities could be set up on a
large scale and test results immediately communicated
via the tracing app. Studies have shown that the
sensitivity of current PCR tests is low during the first
3 days after infection due to low but steadily increasing
viral load in the respiratory tract;29,30 testing on the fourth
day after infection, regardless of symptoms, might
therefore be optimal. However, when more sensitive
PCR tests become available, earlier testing might further
enhance eectiveness. As the clinical symptoms of
COVID-19 are mostly mild and heterogeneous, many
people should be eligible for testing, resulting in a large
proportion of negative test results. Future work should
determine the optimal balance between the proportion of
negative tests and the eectiveness of contact tracing.
Our findings also provide strong support to optimise
contact tracing. In the Netherlands, the contact tracing
strategy was based on establishing contact between an
index case and a public health ocer, followed by an
interview after which contacts are traced. This procedure
is labour intensive, time consuming, prone to recall bias,
incomplete (anonymous contacts cannot be traced), and
usually takes several days. Optimising this process by
improving testing and tracing capacity, removing testing
barriers, and by adding app-based or other digital tech-
nologies to minimise tracing delay is needed to establish
optimal control of transmission. These improve ments
are currently being implemented or considered. Overall,
our findings suggest that an optimised contact tracing
strategy, with short delays and high coverage for testing
and tracing, could substantially reduce the reproduction
number, which would allow alleviation of more stringent
control measures.
Contributors
MEK and MJMB conceived the study. MEK designed and programmed
the model and produced the output. MvB, MCJB, and GR helped with
the analysis and literature research. JHHMvdW contributed to data
interpretation and writing. All authors interpreted the results,
contributed to writing the manuscript, and approved the final version
for submission.

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8
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20 Bi Q, Wu Y, Mei S, et al. Epidemiology and transmission of
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Declaration of interests
We declare no competing interests.
Data sharing
The Mathematica code used for the analysis are available on GitHub.
Acknowledgments
MEK received funding from ZonMw (projects number 91216062 and
number 10430022010001). GR received funding from Fundação para a
Ciência e a Tecnologia (project reference 131_596787873). MJMB received
funding from EU Horizon 2020 grant RECOVER (H2020-101003589).
We thank Patricia Bruijning-Verhagen (University Medical Center
Utrecht) and Hans Heesterbeek (Utrecht University) for useful
discussions. This work forms part of RECOVER (Rapid European
COVID-19 Emergency Response research). RECOVER is funded by
the EU Horizon 2020 research and innovation programme under grant
agreement number 101003589.
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For the Mathematica code see
https://github.com/
mirjamkretzschmar/
ContacttracingModel