QUANTIFYING DYNAMICS OF SARS-COV-2 TRANSMISSION SUGGESTS THAT EPIDEMIC CONTROL IS FEASIBLE THROUGH INSTANTANEOUS DIGITAL CONTACT TRACING
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Luca Ferretti
Quantifying dynamics of SARS-CoV-2 transmission
suggests that epidemic control is feasible
through instantaneous digital contact tracing
Luca Ferretti
Big Data Institute, Li Ka Shing Centre for Health Information and Discovery,
Nuffield Department of Medicine, University of Oxford
Luca Ferretti
of disruption imposed and the likely period over which the interventions can be maintained. In thi
COVID-19 impact on ICUs
scenario, interventions can limit transmission to the extent that little herd immunity is acquired
leading to the possibility that a second
(Imperial wavereport
College of infection is seen once interventions
9, Ferguson et al) are lifted
300
Surge critical care bed capacity
250
Critical care beds occupied
per 100,000 of population
Do nothing
200
Case isolation
150 Case isolation and household
quarantine
Closing schools and universities
100
Case isolation, home quarantine,
50 social distancing of >70s
0
Luca Ferretti
Doubling times in China …
4
r = 0.134 (0.121 − 0.146)
T2 = 5.2
3
log10(daily count)
r = 0.35 (0.28 − 0.42) count type:
T2 = 2 ● symptom onset, linked to wet markets
2 symptom onset, not linked to wet markets
r = 0.085 confirmed case
(0.078 − 0.093) death
T2 = 8.1
r = 0.3 (0.21 − 0.39)
1 T2 = 2.3
r = 0.44 (0.34 − 0.55)
T2 = 1.6
● ● ●
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0 ● ● ● ● ● ● ●● ●● ●
●●●●● ●●● ● ● ● ●●●●●●●●
Dec 15 Jan 01 Jan 15 Feb 01 Feb 15
Luca Ferretti
… and Europe
Abruzzo Basilicata P.A. Bolzano Calabria Campania Emilia−Romagna Friuli Venezia Giulia Lazio
3.0
3.5
3.0
4.0
3.0
2.0
3.0
2.0
1.5
2.0
2.5
2.0
3.0
2.0
2.0
1.0
1.0
1.0
1.0
1.0
1.5
1.0
2.0
0.5
0.0
0.0
0.0
0.0
0.0
0.0
0.5
1.0
0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50
Liguria Lombardia Marche 2.0 Molise Piemonte Puglia Sardegna Sicilia
3.0
3.0
3.5
3.0
3.0
1.5
2.0
4.0
2.0
2.0
2.5
2.0
2.0
1.0
1.0
3.0
1.0
1.0
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0.0
0.0
0.0
0.0
2.0
0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50
Toscana P.A. Trento Umbria Valle d'Aosta Veneto
3.0
3.0
3.5
3.0
2.0
2.0
2.0
2.0
2.5
1.0
1.0
1.0
1.0
1.5
0.0
0.0
0.0
0.0
0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50 0 10 30 50
Luca Ferretti
An epidemiological classification
of transmission modes for SARS-CoV-2
• Symptomatic (after symptom onset)
• Pre-symptomatic (before symptom onset)
• Asymptomatic (no symptom onset, or very mild symptoms)
• Environmental (fomites, ventilation systems…)
Decomposition of infectiousness (versus time post infection):
Luca Ferretti
An epidemiological classification
of transmission modes for SARS-CoV-2
• Symptomatic (after symptom onset)
• Pre-symptomatic (before symptom onset)
• Asymptomatic (no symptom onset, or very mild symptoms)
~40% but low infectiousness ?
• Environmental (fomites, ventilation systems…)
Decomposition of infectiousness (versus time post infection):
Luca Ferretti
An epidemiological classification
of transmission modes for SARS-CoV-2
• Symptomatic (after symptom onset)
• Pre-symptomatic (before symptom onset)
• Asymptomatic (no symptom onset, or very mild symptoms)
~40% but low infectiousness ?
• Environmental (fomites, ventilation systems…)
~10-20% ?
Decomposition of infectiousness (versus time post infection):Luca Ferretti
Incubation period and generation time
• Incubation period:
how long it takes to develop symptoms
versus
• Generation time (serial interval):
how long it takes to transmit the diseaseLuca Ferretti
Inference of generation time distribution
Maximum Composite Likelihood estimate
from times of exposure and onset of symptoms for infector-infected pairs
0.25
Generation time: Weibull Distribution of generation times
Generation time: gamma
Generation time: lognormal
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Serial interval: Li et al.
0.20
generation time
Serial interval: Nishiura et al. incubation time
Incubation period
15
number of transmission pairs
0.15
probability density
10
Density
5
0.10
0
0.0 0.2 0.4 0.6 0.8 1.0
0.05
Probability that transmission occurred before symptoms
0 5 10 15 20
0.00
0 5 10 15 20 Generation time
time since infection (days)Luca Ferretti
Pre-symptomatic transmission
8
About 30-45%
of all transmissions 6
posterior density
from symptomatic cases
are pre-symptomatic 4
2
15
number of transmission pairs
0
0.00 0.25 0.50 0.75
10
RP/(RP+RS)
5
0
0.0 0.2 0.4 0.6 0.8 1.0
Probability that transmission occurred before symptomsLuca Ferretti
How to reach epidemic control:
the reproduction numbers R0 and Reff
• R0 : average number of infections caused by an
infected individual in a naive population
• Reff : average number of infections caused by an
infected individual in the presence of interventions
The critical condition to control the epidemic is ReffLuca Ferretti
(⌧ ) and theEuler-Lotka
renewal equation
equation
In an epidemic which is growing exponentially, in a deterministic manne
human1 transmission, the incidence I(t) can be described by the renewa
Z 1
Classical renewal equation I(t) = I(t ⌧ ) (⌧ )d⌧,
0
Infectiousness
In words, Equation 7 says that the incidence now is set by the rat
w(⌧ ) is the
infected at generation
all previoustime distribution
times, weighted –by thehow
probability
infectious density
those functi
peopl
an individual becoming infected
Exponential ansatz and
with their
growth subsequent
rate r
mean rate at which an individual infects others a time ⌧ after being i onward transmi
basic reproduction
take number. If
(⌧ ) to be independent ofthe
theexponential
stage of thegrowth
epidemic rate(calendar
r and thetime genet
w(⌧ ) have been estimated, R 0 is determined by Equation
of susceptible individuals through acquired immunity, changing contact 8, i.e.
timescale of the data informing our estimations Z 1 of (⌧ ). After (⌧ ) ha
Classical Euler-Lotka equation r⌧
may consider how to change it through R 0 = 1/ e
interventions w(⌧to)d⌧,
reduce infectio
0
and indirect infectiousness is certain to be zero aftertime
Generation having been infect
distribution
onlyWe decompose
need (⌧ )previous
consider the without time
any loss of generality
window T of the into the following
epidemic – repla
the integral in Equation 7 by T for convenience. We take T to be infin
• Direct transmissions from asymptomatic individuals – those wh
(⌧ ) tending to zero at large times. Substituting into Equation 7 an
toms. The degreert to which individuals show symptoms is of cou
incidence, I(t) = I0 e , gives the conditionLuca Ferretti
An epidemiological classification
of transmission modes for SARS-CoV-2
• Symptomatic (after symptom onset)
• Pre-symptomatic (before symptom onset)
• Asymptomatic (no symptom onset, or very mild symptoms)
• Environmental (fomites, ventilation systems…)
The (⌧ ) we consider
Decomposition is therefore
of infectiousness (versus time post infection):
Z ⌧
(⌧ ) = Pa xa s (⌧ ) + (1 Pa )(1 s(⌧ )) s (⌧ ) + (1 Pa )s(⌧ ) s (⌧ ) + s (⌧ l)E(l)dl (13
| {z } | {z } | {z }
asymptomatic pre-symptomatic symptomatic | l=0 {z }
environmental
We solved for the form of (⌧ ) above first by fitting the shape of the pre-symptomatic pluLuca Ferretti
Decomposition of infectiousness
0.4
Pre-symptomatic transmission
β(τ) (transmissions per day)
0.3
Symptomatic transmission
R0 = 2.0:
Rp = 0.9 from pre−symptomatic
0.2 Rs = 0.8 from symptomatic
Re = 0.2 from environmental
Ra = 0.1 from asymptomatic
0.1
About half
of all transmissions
0.0
are pre-symptomatic
0 2 4 6 8 10 12
τ (days)rted
Lucashowing
Ferrettisymptoms, corresponding to their (1 S(⌧ )).
is solvedDecomposing
exactly by (⌧ ) exponential
into two factors – its growth,
integral Rinstead of beginning
0 , and the unit-normalised accordin
generation time
conditions
elude: describing Generalised Euler-Lotka equation
interval w(⌧ ) – the constraint above gives the relationship between r, R0 and w(⌧ ). Substituting
andepidemic
this solution
then tending
for y(⌧ ) growth
toward
back intowith no 16
equation
exponential
intervention
gives
growth as the boundar
ten).
Y (t, ⌧, ⌧ 0 )Translational invariance
for contact tracing
be the number2 of individuals at timetogether
0 t who r(⌧ 0 ⌧with
were )infected
0
exponential
atr(ta time
⌧) t ⌧ by growth with
Y (t, ⌧, ⌧ ) =0 . yY0 esatisfies Y(⌧(t + ⌧ )e 0 + dt) = (21)
ividuals who were in turn infected
eral 0 form as previously – equation=16 at a time t ⌧ – but dt, ⌧ + dt, ⌧
r(t ⌧ 0) 0with a di↵erent functional fo
t, ⌧, ⌧ ), ‘translational invariance’, because incrementing y e (⌧
0 all three arguments ⌧) by exactly the (22)
me Kermack-McKendrick
ngvalue
equation 16 into
means following equations
exactlyequation
the 23for
same cohort chains
ofgives
individuals theofthrough
infections
‘next-generation’ with moment
to a di↵erent contact tracing:for
equation
(Fraser el al PNAS 2004)
time. Equivalently,
The impact of case isolation, Z contact 1 ✓ tracing and quarantine ◆ 0)
In r⌧
the presence
@Y (t,of
⌧, ⌧ 0 ) isolation
case @Y (t, ⌧, of
⌧ 0 )efficacy
@Y ✏I⌧,and
(t, ⌧
1 s(⌧
0 ) contact tracing plus quarantine of efficacy 0 ✏T ,
y(⌧ ) = eequation(⌧15) is(1modified ✏I+s(⌧ )) + 1 ✏ T= +0
et al. 2004) to 1
✏ T 0 (14) y(⌧ ⌧ )d
@t (see @⌧
Fraser,
⌧ 0 =⌧
Riley @⌧ 0
s(⌧ ⌧)
Z
0 1 ✓Z 1✓ 0
1⌧ ) s(⌧ s(⇢)
)
◆ ◆
In the absence of any intervention, Y (t, ⌧, ⌧ ) satisfies the generalised
r⌧ Y (t, 0, ⌧ ) = (⌧ ) (1 ✏I s(⌧ )) s(⇢
1 ✏T + ✏T +Kermack-McKendrick
Y (t, ⌧, ⌧ 0
)d⌧ 0
(23)
=e
uations (also referred(⌧ ) (1 ✏I s(⌧ ))
to as the Von Foerster equations): ⌧1 ✏T 1 s(⌧ 0 ⌧ ) y(⇢)d⇢
Z ⇢=01
1 s(⇢)
Note that we Efficiency
take the of isolation
upper limit / contact
of the tracing 0 & quarantine
integral
0 here to be 1 rather than t (so that the
Y (t, 0, ⌧ ) = (⌧ ) Y (t, ⌧, ⌧ )d⌧ (15)
epidemic is solved exactly by exponential ⌧ 0 =⌧ 0 growth, instead of beginning according to specific
the integration
boundary variable
conditions andto be
then ⇢
tending = ⌧ toward ⌧ for convenience.
exponential growth as theHence,
boundary the grow
conditions
Theequation
words, generalised
15 says (functional)
that the incidence Euler-Lotka
of newly infected equation individuals at time t due to
entions corresponds
are
corresponds
forgotten).
to the to the
Translational
eigenvalue value
invarianceof r for
together which
with the functional
exponential growth with linear
t imply ‘nex
the
as previouslyequation
– equation(with eigenvalue 1) for this operator:
ividuals who were themselves infected a time ⌧ ago is given by the current infectiousness
same general form 16 – but with a di↵erent functional form for y(⌧ ).
0
Technically Y Substituting
is a double-density: one must
equation
an actual number of people at time t.
integrate
16 into equation Z
it over 23
a range
1✓ ✓
gives ofthe
⌧ values and a range of ⌧equation
‘next-generation’ ◆
values to for y:
r⌧ Z 1 s(⇢1 +s(⌧⌧0)) ◆ s(⇢)
Nr y = e y(⌧ ) (⌧ = e) (1r⌧ ✏I s(⌧
(⌧ ) (1 ✏I s(⌧)))) 11 ✏T + ✏T✏T y(⌧ 0
⌧ y(⇢)d⇢
)d⌧ 0
(24)
5 Z0⌧ 1
0 =⌧
✓
1 s(⌧1 ◆s(⇢)
0 ⌧)
r⌧ s(⇢ + ⌧ ) s(⇢)
=e (⌧ ) (1 ✏I s(⌧ )) 1 ✏T y(⇢)d⇢ (25)
⇢=0 1 s(⇢)
6
redefining the integration variable to be ⇢ = ⌧ 0 ⌧ for convenience. Hence, the growth rate after
the interventions corresponds to the value of r for which the functional linear ‘next-generation’Luca Ferretti
Is the COVID-19 epidemic controllable
via realistic contact tracing?
delay = 0 hours delay = 4 hours delay = 12 hours
% success in quarantining contacts
% success in quarantining contacts
% success in quarantining contacts
90 90 90
80 80 80
max R0 max R0 max R0
70 70 70
60
under control 60
under control 60
under control
50 4 50 4 50 4
40 3 40 3 40 3
30 2 30 2 30 2
20 1 20 1 20 1
10 10 10
10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90
% success in isolating cases % success in isolating cases % success in isolating cases
delay = 24 hours delay = 48 hours delay = 72 hours
% success in quarantining contacts
% success in quarantining contacts
% success in quarantining contacts
90 90 90
80 80 80
max R0 max R0 max R0
70 70 70
60
under control 60
under control 60
under control
50 4 50 4 50 4
40 3 40 3 40 3
30 2 30 2 30 2
20 1 20 1 20 1
10 10 10
10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90
% success in isolating cases % success in isolating cases % success in isolating casesLuca Ferretti
Why instant contact tracing matters?Luca Ferretti
Why instant contact tracing matters?
Isolation and contact tracing can stop the epidemic
only with high efficiency and short response times
antine3 days to1 isolation
day to isolation
and contact
and contact
quarantine
quarantine2 daysno
to delay
isolation
to isolation
and contact
and quarantine
contact quarantine1 day to isola
(manual contact tracing) (instantaneous contact tracing)
90 90 90 90 90
% success in quarantining contacts
% success in quarantining contacts
% success in quarantining contacts
% success in quarantining contacts
% success in quarantining contacts
80 80 80 80 80
70 70 70 70 70
r (per day)
60 60 60 60 60
0.1
50 50 50 50 50 0.0
−0.1
40 40 40 40 40 −0.2
30 30 30 30 30
20 20 20 20 20
10 10 10 10 10
90 10 20 1030 2040 3050 4060 5070 6080 7090 80 90 10 20 1030 2040 3050 4060 5070 6080 7090 80 90 10 20 30
% success
% in
success
isolating
in isolating
cases cases % success
% success
in isolating
in isolating
cases cases % sucLuca Ferretti
Why digital solutions?
Tools of classical epidemiology against COVID-19:
• Physical distancing/isolation/quarantine
• Either insufficient or high social&economic costs
• Mass screening/testing + contact tracing
• Hard to scale for a rapid response (HR, lab capacity)
• Vaccination
• Development/trial phase + time to scale production
Alternative digital technologies are needed for a fast, scalable responseLuca Ferretti
A mobile app for instant contact tracing
Subject A has COVID-19 infection. No symptoms
Home Train Work Home
A A A A
Day 1
E G
B C D F
Close B
Nearby
H I
Time
Report symptoms
A Request home test A
Awakes with Positive
Day 2
fever Covid-19
Instant signal
Automated test request
Self-isolate - 14 days B C D E F G
Advice on social distancing
Decontaminate
(lower risk contact) H I
TimeLuca Ferretti
Useful at all phases of the epidemic
• Prevent initial spread
• “Smart lockdown” to keep to economy afloat
• “Smart exit” from lockdown to prevent a second peak
• Control residual spreadLuca Ferretti
Challenges
• Limitations in smartphone coverage and contact technologies
(Bluetooth Low Energy). Integration of multiple approaches?
• >50% uptake required at population level
• Compliance with app recommendation to “stay at home” is key
• Scale-up of diagnostic testing across Europe is needed
• Some degree of physical distancing could still be required for
the fast-growing European epidemic
• Iterative improvements of app back-end and front-end, as
well as the science and technology behind app tracingLuca Ferretti
Ethical issues
• Building trust and confidence at every stage
• privacy and data usage concerns at the forefront
• adopting a transparent and auditable algorithm
• careful consideration of digital deployment
strategies to support specific groups, such as
health care workers, the elderly and the young
• deployed with individual consentLuca Ferretti
Challenges: voluntary uptakeLuca Ferretti
Challenges: voluntary uptakeLuca Ferretti
Challenges: voluntary uptakeLuca Ferretti
Challenges: voluntary uptakeLuca Ferretti
Recent developments
• Many privacy-preserving projects across the world - now
mostly concentrated in two main consortia for Europe and
North America (PEPP-PT and TCN)
• Bluetooth Low Energy as common choice of technology
(hence interoperability/roaming possible)
• Much movement at European level, different countries at
different stages
• Recent Google/Apple announcement: embedding contact
tracing APIs in the OS. Technical and political pros and cons.Luca Ferretti
What can you do?
• App-based contact tracing could potentially control the epidemic
and should be at the core of epidemic response.
Optimised contract-tracing algorithms? Learning from contact networks?
• It should not be a stand-alone solution!
Must be part of an integrated strategy (with epidemiological surveillance, risk
forecast, geolocation of hot spots, local lockdowns…).
Interplay with other interventions?
• Widespread diagnostic testing is critical
• Physical distancing still important
• Please support European governments and institutions
in their efforts towards app-based contact tracing
within an integrated strategy of epidemic controlLuca Ferretti
Based on: Ferretti, Wymant et al, Science 2020
Find out more about our research here:
http://www.coronavirus-fraser-group.orgYou can also read
