Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing
Identifieur interne : 001472 ( Pmc/Corpus ); précédent : 001471; suivant : 001473Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing
Auteurs : Luca Ferretti ; Chris Wymant ; Michelle Kendall ; Lele Zhao ; Anel Nurtay ; Lucie Abeler-Dörner ; Michael Parker ; David Bonsall ; Christophe FraserSource :
- Science (New York, N.y.) [ 0036-8075 ] ; 2020.
Abstract
The newly emergent human virus SARS-CoV-2 is resulting in high fatality rates and incapacitated health systems. Preventing further transmission is a priority. We analyzed key parameters of epidemic spread to estimate the contribution of different transmission routes and determine requirements for case isolation and contact-tracing needed to stop the epidemic. We conclude that viral spread is too fast to be contained by manual contact tracing, but could be controlled if this process was faster, more efficient and happened at scale. A contact-tracing App which builds a memory of proximity contacts and immediately notifies contacts of positive cases can achieve epidemic control if used by enough people. By targeting recommendations to only those at risk, epidemics could be contained without need for mass quarantines (‘lock-downs’) that are harmful to society. We discuss the ethical requirements for an intervention of this kind.
Url:
DOI: 10.1126/science.abb6936
PubMed: 32234805
PubMed Central: 7164555
Links to Exploration step
PMC:7164555Le document en format XML
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<author><name sortKey="Wymant, Chris" sort="Wymant, Chris" uniqKey="Wymant C" first="Chris" last="Wymant">Chris Wymant</name>
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<author><name sortKey="Kendall, Michelle" sort="Kendall, Michelle" uniqKey="Kendall M" first="Michelle" last="Kendall">Michelle Kendall</name>
<affiliation><nlm:aff id="aff1">Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, University of Oxford, Oxford, UK.</nlm:aff>
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<author><name sortKey="Zhao, Lele" sort="Zhao, Lele" uniqKey="Zhao L" first="Lele" last="Zhao">Lele Zhao</name>
<affiliation><nlm:aff id="aff1">Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, University of Oxford, Oxford, UK.</nlm:aff>
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<author><name sortKey="Nurtay, Anel" sort="Nurtay, Anel" uniqKey="Nurtay A" first="Anel" last="Nurtay">Anel Nurtay</name>
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<author><name sortKey="Abeler Dorner, Lucie" sort="Abeler Dorner, Lucie" uniqKey="Abeler Dorner L" first="Lucie" last="Abeler-Dörner">Lucie Abeler-Dörner</name>
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<author><name sortKey="Parker, Michael" sort="Parker, Michael" uniqKey="Parker M" first="Michael" last="Parker">Michael Parker</name>
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<author><name sortKey="Bonsall, David" sort="Bonsall, David" uniqKey="Bonsall D" first="David" last="Bonsall">David Bonsall</name>
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<author><name sortKey="Fraser, Christophe" sort="Fraser, Christophe" uniqKey="Fraser C" first="Christophe" last="Fraser">Christophe Fraser</name>
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<affiliation><nlm:aff id="aff4">Wellcome Centre for Human Genetics, University of Oxford, Oxford, UK.</nlm:aff>
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<front><div type="abstract" xml:lang="en"><p>The newly emergent human virus SARS-CoV-2 is resulting in high fatality rates and
incapacitated health systems. Preventing further transmission is a priority. We analyzed key
parameters of epidemic spread to estimate the contribution of different transmission routes and
determine requirements for case isolation and contact-tracing needed to stop the epidemic. We
conclude that viral spread is too fast to be contained by manual contact tracing, but could be
controlled if this process was faster, more efficient and happened at scale. A contact-tracing
App which builds a memory of proximity contacts and immediately notifies contacts of positive
cases can achieve epidemic control if used by enough people. By targeting recommendations to
only those at risk, epidemics could be contained without need for mass quarantines
(‘lock-downs’) that are harmful to society. We discuss the ethical requirements
for an intervention of this kind.</p>
</div>
</front>
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<pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Science</journal-id>
<journal-id journal-id-type="iso-abbrev">Science</journal-id>
<journal-id journal-id-type="publisher-id">SCIENCE</journal-id>
<journal-title-group><journal-title>Science (New York, N.y.)</journal-title>
</journal-title-group>
<issn pub-type="ppub">0036-8075</issn>
<issn pub-type="epub">1095-9203</issn>
<publisher><publisher-name>American Association for the Advancement of Science</publisher-name>
</publisher>
</journal-meta>
<article-meta><article-id pub-id-type="pmid">32234805</article-id>
<article-id pub-id-type="pmc">7164555</article-id>
<article-id pub-id-type="publisher-id">abb6936</article-id>
<article-id pub-id-type="doi">10.1126/science.abb6936</article-id>
<article-categories><subj-group subj-group-type="article-type"><subject>Research Article</subject>
</subj-group>
<subj-group subj-group-type="heading"><subject>Research Articles</subject>
</subj-group>
<subj-group subj-group-type="legacy-article-type"><subject>R-Articles</subject>
</subj-group>
<subj-group subj-group-type="field"><subject>Epidemiology</subject>
</subj-group>
</article-categories>
<title-group><article-title>Quantifying SARS-CoV-2 transmission suggests epidemic control with digital
contact tracing</article-title>
</title-group>
<contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0001-7578-7301</contrib-id>
<name><surname>Ferretti</surname>
<given-names>Luca</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
<xref ref-type="author-notes" rid="afn1">*</xref>
</contrib>
<contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0002-9847-8226</contrib-id>
<name><surname>Wymant</surname>
<given-names>Chris</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
<xref ref-type="author-notes" rid="afn1">*</xref>
</contrib>
<contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0001-7344-7071</contrib-id>
<name><surname>Kendall</surname>
<given-names>Michelle</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0002-2807-1914</contrib-id>
<name><surname>Zhao</surname>
<given-names>Lele</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0001-7107-1656</contrib-id>
<name><surname>Nurtay</surname>
<given-names>Anel</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0003-3662-4192</contrib-id>
<name><surname>Abeler-Dörner</surname>
<given-names>Lucie</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Parker</surname>
<given-names>Michael</given-names>
</name>
<xref ref-type="aff" rid="aff2"><sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0003-2187-0550</contrib-id>
<name><surname>Bonsall</surname>
<given-names>David</given-names>
</name>
<xref ref-type="award" rid="award598662"></xref>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3"><sup>3</sup>
</xref>
<xref ref-type="author-notes" rid="afn2">†</xref>
</contrib>
<contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0003-2399-9657</contrib-id>
<name><surname>Fraser</surname>
<given-names>Christophe</given-names>
</name>
<xref ref-type="award" rid="award598658"></xref>
<xref ref-type="award" rid="award598661"></xref>
<xref ref-type="award" rid="award598660"></xref>
<xref ref-type="aff" rid="aff1"><sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff4"><sup>4</sup>
</xref>
<xref ref-type="author-notes" rid="afn2">†</xref>
<xref ref-type="corresp" rid="cor1">‡</xref>
</contrib>
<aff id="aff1"><label>1</label>
Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, University of Oxford, Oxford, UK.</aff>
<aff id="aff2"><label>2</label>
Wellcome Centre for Ethics and the Humanities and Ethox Centre, University of Oxford, Oxford, UK.</aff>
<aff id="aff3"><label>3</label>
Oxford University NHS Trust, University of Oxford, Oxford, UK.</aff>
<aff id="aff4"><label>4</label>
Wellcome Centre for Human Genetics, University of Oxford, Oxford, UK.</aff>
</contrib-group>
<author-notes><fn id="afn1" fn-type="equal"><label>*</label>
<p>These authors contributed equally to this work.</p>
</fn>
<fn id="afn2" fn-type="equal"><label>†</label>
<p>These authors contributed equally to this work.</p>
</fn>
<corresp id="cor1"><label>‡</label>
Corresponding author. Email: <email xlink:href="christophe.fraser@bdi.ox.ac.uk">christophe.fraser@bdi.ox.ac.uk</email>
</corresp>
</author-notes>
<pub-date pub-type="epub"><day>31</day>
<month>3</month>
<year>2020</year>
</pub-date>
<elocation-id>eabb6936</elocation-id>
<history><date date-type="received"><day>11</day>
<month>3</month>
<year>2020</year>
</date>
<date date-type="accepted"><day>27</day>
<month>3</month>
<year>2020</year>
</date>
</history>
<permissions><copyright-statement> Copyright © 2020 The Authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No claim to original U.S.
Government Works</copyright-statement>
<copyright-year>2020</copyright-year>
<copyright-holder>AAAS</copyright-holder>
<license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0/"><ali:license_ref specific-use="vor" start_date="2020-03-04">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This open access article is distributed under <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License
4.0 (CC BY)</ext-link>
.</license-p>
</license>
</permissions>
<abstract><p>The newly emergent human virus SARS-CoV-2 is resulting in high fatality rates and
incapacitated health systems. Preventing further transmission is a priority. We analyzed key
parameters of epidemic spread to estimate the contribution of different transmission routes and
determine requirements for case isolation and contact-tracing needed to stop the epidemic. We
conclude that viral spread is too fast to be contained by manual contact tracing, but could be
controlled if this process was faster, more efficient and happened at scale. A contact-tracing
App which builds a memory of proximity contacts and immediately notifies contacts of positive
cases can achieve epidemic control if used by enough people. By targeting recommendations to
only those at risk, epidemics could be contained without need for mass quarantines
(‘lock-downs’) that are harmful to society. We discuss the ethical requirements
for an intervention of this kind.</p>
</abstract>
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</front>
<body><p>COVID-19 is a rapidly spreading infectious disease caused by the novel coronavirus SARS-COV-2,
a betacoronavirus, which has now established a global pandemic. Around half of infected
individuals become reported cases, and with intensive care support, the case fatality rate is
approximately 2% (<xref rid="R1" ref-type="bibr"><italic>1</italic>
</xref>
). More concerning is
that the proportion of cases requiring intensive care support is 5%, and patient management is
complicated by requirements to use personal protective equipment and engage in complex
decontamination procedures (<xref rid="R2" ref-type="bibr"><italic>2</italic>
</xref>
). Fatality
rates are likely to be higher in populations older than in Hubei province (such as in Europe),
and in low-income settings where critical care facilities are lacking (<xref rid="R3" ref-type="bibr"><italic>3</italic>
</xref>
). In (<xref rid="R4" ref-type="bibr"><italic>4</italic>
</xref>
) the public health cost of failing to achieve sustained epidemic
suppression was estimated as 250,000 lives lost in the next few months in Great Britain, and
1.1-1.2 million in the USA, even with the strongest possible mitigation action to ‘flatten
the curve’. Even modest outbreaks will see fatality rates climb as hospital capacity is
overwhelmed, and the indirect effects caused by compromised health care services have yet to be
quantified.</p>
<p>No treatment is currently available, and a vaccine will not be available for several months (as
of March 2020) at the earliest. The only approaches that we currently have available to stop the
epidemic are those of classical epidemic control, such as case isolation, contact tracing and
quarantine, physical distancing and hygiene measures.</p>
<p>The basic reproduction number R<sub>0</sub>
is the typical number of infections caused by an
individual in the absence of widespread immunity. Once immunity becomes widespread, the effective
reproduction number R will become lower than R<sub>0</sub>
and once R is less than 1, the
population has herd immunity and the epidemic declines. Immunity can only safely be obtained by
vaccination. Here we use the term “sustained epidemic suppression” to mean a
reduction of the reproduction number R to less than 1 by changing non-immunological conditions of
the population that affect transmission, such as social contact patterns.</p>
<p>The biological details of transmission of betacoronaviruses are known in general terms: these
viruses can pass from one individual to another through exhaled droplets (<xref rid="R5" ref-type="bibr"><italic>5</italic>
</xref>
), aerosol (<xref rid="R6" ref-type="bibr"><italic>6</italic>
</xref>
), contamination of surfaces (<xref rid="R7" ref-type="bibr"><italic>7</italic>
</xref>
), and possibly through fecal-oral contamination (<xref rid="R8" ref-type="bibr"><italic>8</italic>
</xref>
). Here we compare different transmission
routes that are more closely aligned to their implications for prevention. Specifically, we
propose four categories:</p>
<p>I. <italic>Symptomatic transmission:</italic>
direct transmission from a symptomatic
individual, through a contact that can be readily recalled by the recipient.</p>
<p>II. <italic>Pre-symptomatic transmission:</italic>
direct transmission from an individual that
occurs before the source individual experiences noticeable symptoms. (Note that this definition
may be context specific, for example based on whether it is the source or the recipient who is
asked whether the symptoms were noticeable.)</p>
<p>III. <italic>Asymptomatic transmission:</italic>
direct transmission from individuals who never
experience noticeable symptoms. This can only be established by follow-up, as single time-point
observation cannot fully distinguish asymptomatic from pre-symptomatic individuals.</p>
<p>IV. <italic>Environmental transmission:</italic>
transmission via contamination, and
specifically in a way that would not typically be attributable to contact with the source in a
contact survey (i.e., this does not include transmission pairs who were in extended close
contact, but for whom in reality the infectious dose passed via the environment instead of more
directly). These could be identified in an analysis of spatial movements.</p>
<p>We acknowledge that boundaries between these categories may be blurred, but defined broadly
these categories have different implications for prevention, responding differently to classical
measures of case isolation and quarantining contacts (<xref rid="R9" ref-type="bibr"><italic>9</italic>
</xref>
, <xref rid="R10" ref-type="bibr"><italic>10</italic>
</xref>
) (and
for a specific application to COVID-19 see below (<xref rid="R11" ref-type="bibr"><italic>11</italic>
</xref>
)).</p>
<p>Evidence exists for each of these routes of transmission: symptomatic (<xref rid="R12" ref-type="bibr"><italic>12</italic>
</xref>
), pre-symptomatic (<xref rid="R13" ref-type="bibr"><italic>13</italic>
</xref>
); asymptomatic (<xref rid="R14" ref-type="bibr"><italic>14</italic>
</xref>
); and environmental (<xref rid="R12" ref-type="bibr"><italic>12</italic>
</xref>
). For prevention, the crucial information is the relative frequency
of different routes of transmission so as to allocate finite resources between different
intervention strategies.</p>
<p>Li <italic>et al</italic>
. (<xref rid="R12" ref-type="bibr"><italic>12</italic>
</xref>
)
presented self-reported data on exposure for the first 425 cases in Wuhan; some of these recorded
visits to the Huanan Seafood Wholesale Market. The generalizability of transmission in that
setting to other settings is highly uncertain, as this large-scale event seeded the epidemic in
the absence of any knowledge about the disease. After closure of the Huanan Seafood Wholesale
Market on January 1, 2020, of 240 cases with no exposure to any wet market, 200 individuals (83%)
reported no exposure to an individual with respiratory symptoms. Inaccurate recall may explain
some responses, including failing to notice symptoms were exceptional at a time before awareness
of the disease began, but it is unlikely to be as much as 83% of them, implying that many
individuals were infected by non-symptomatic individuals.</p>
<p>The situation in Singapore at first glance appears different, since unlike in Wuhan, many
individuals were linked to an identified symptomatic source. However, the main difference is that
the linkage was retrospective, such that linkage could be established even if transmission
occurred before a case was symptomatic. As of March 5, 2020, there were 117 cases, of which 25
were imported. By devoting considerable resources, including police investigation, 75 of the 92
cases of local transmission were traced back to their presumed exposure, either to a known case
or to a location linked to spread (<xref rid="R15" ref-type="bibr"><italic>15</italic>
</xref>
).
Linking cases via a location generally includes the possibility of environmentally mediated
transmission. Therefore, the large fraction of traceable transmission in Singapore does not
contradict the large fraction without symptomatic exposure in Wuhan. However, it does suggest
that transmission from asymptomatic, rather than pre-symptomatic, individuals is not a major
driver of spread. Although serological surveys are currently lacking, other lines of evidence
suggest that the scenario of many asymptomatic infections for each symptomatic one is unlikely.
Testing 1,286 close contacts of confirmed cases found that, among 98 individuals testing
positive, only 20% did not have symptoms at first clinical assessment (<xref rid="R16" ref-type="bibr"><italic>16</italic>
</xref>
). Among 634 individuals testing positive on board the
Diamond Princess cruise ship, the proportion of individuals without symptoms was found to be 52%;
the proportion who were asymptomatic (rather than pre-symptomatic) was estimated as 18% (<xref rid="R17" ref-type="bibr"><italic>17</italic>
</xref>
). Testing of passengers on board six
repatriation flights from Wuhan suggest that 40-50% of infections were not identified as cases
(<xref rid="R4" ref-type="bibr"><italic>4</italic>
</xref>
, <xref rid="R18" ref-type="bibr"><italic>18</italic>
</xref>
). Mild cases have been found to have viral loads 60-fold less than
severe cases (<xref rid="R19" ref-type="bibr"><italic>19</italic>
</xref>
) and it is likely that
the viral loads of asymptomatic individuals are lower still, with possible implications for
infectiousness and diagnosis.</p>
<p>The most accurate and robust quantification of the relative frequency of routes of transmission
would be a well-designed prospective cohort study with detailed journal and phylogenetic
investigations. However, the current global emergency requires timely estimates using imperfect
data sources. We performed a detailed analysis of the timing of events in defined transmission
pairs, derived the generation time distribution, and attributed a probability for each pair that
transmission was pre-symptomatic. We also fit a mathematical model of infectiousness through the
four routes discussed above, over the course of infection. This allowed us to calculate
R<sub>0</sub>
, estimate the proportion of transmission from different routes, and make
predictions about whether contact tracing and isolation of known cases is enough to prevent
spread of the epidemic.</p>
<sec sec-type="other1" disp-level="1"><title>Estimating SARS-CoV-2 transmission parameters</title>
<p>We used the exponential growth rate of the epidemic, <italic>r</italic>
, from the early stages
of the epidemic in China, such that the effect of control measures discussed later will be
relative to the early stages of an outbreak, exemplified by baseline contact patterns and
environmental conditions in Hubei during that period. We note that this assumption is implicit
in many estimates of R<sub>0</sub>
. The epidemic doubling time T<sub>2</sub>
is equal to
log<sub>e</sub>
(2) / <italic>r.</italic>
We used the value r = 0.14 per day (<xref rid="R20" ref-type="bibr"><italic>20</italic>
</xref>
), corresponding to a doubling time of 5.0
days.</p>
<p>The incubation period is defined as the time between infection and onset of symptoms. It is
estimated as the time between exposure and report of noticeable symptoms. We used the incubation
period distribution calculated by (<xref rid="R21" ref-type="bibr"><italic>21</italic>
</xref>
).
The distribution is lognormal with mean 5.5 days, median 5.2 days and standard deviation 2.1
days, and is included with our results in <xref ref-type="fig" rid="F1">Fig. 1</xref>
.</p>
<fig id="F1" fig-type="figure" orientation="portrait" position="float"><label>Fig. 1</label>
<caption><title>Quantifying transmission timing in 40 transmission pairs.</title>
<p>Left panel: our inferred generation time distributions, in black; thicker lines denote
higher support for the corresponding functional form, with the Weibull distribution being the
best fit. For comparison we also include the serial interval distributions previously reported
by (<xref rid="R12" ref-type="bibr"><italic>12</italic>
</xref>
) (in light blue) and (<xref rid="R22" ref-type="bibr"><italic>22</italic>
</xref>
) (in grey), and the incubation period
distribution we used here from (<xref rid="R21" ref-type="bibr"><italic>21</italic>
</xref>
)
(dashed red line). Right panel: the distribution of the posterior probability of
pre-symptomatic transmission for each of the 40 transmission pairs. The red vertical line
shows the mean probability.</p>
</caption>
<graphic xlink:href="abb6936-F1"></graphic>
</fig>
<p>The generation time is defined for source-recipient transmission pairs as the time between the
infection of the source and the infection of the recipient. Because time of infection is
generally not known, the generation time is often approximated by the serial interval, which is
defined as the time between the onset of symptoms of the source and the onset of symptoms of the
recipient. We did not take that approach here; instead, we directly estimated the generation
time distribution from 40 source-recipient pairs. These pairs were manually selected according
to high confidence of direct transmission inferred from publicly available sources at the time
of writing (March, 2020), and with known time of onset of symptoms for both source and
recipient. We combined dates of symptom onset with intervals of exposure for both source and
recipient (when available) and the above distribution of incubation times and from these
inferred the distribution of generation times. The distribution is best described by a Weibull
distribution (AIC=148.4, versus 149.9 for gamma and 152.3 for lognormal distribution) with mean
and median equal to 5.0 days and standard deviation of 1.9 days, shown in the left panel of
<xref ref-type="fig" rid="F1">Fig. 1</xref>
. We also show the results of sensitivity analysis
to different functional forms, and compare to two previously published serial interval
distributions in (<xref rid="R12" ref-type="bibr"><italic>12</italic>
</xref>
,<italic></italic>
<xref rid="R22" ref-type="bibr"><italic>22</italic>
</xref>
). Uncertainty in the fit
of the distribution is shown in fig. S1. Our distribution is robust with respect to the choice
of transmission events (fig. S2). Correlation in the uncertainty between the inferred mean and
standard deviation is shown in fig. S3. The distribution of serial intervals for these pairs is
shown in fig. S4. The countries from which the transmission pair data was obtained are shown in
fig. S5.</p>
<p>For each of the 40 transmission pairs we estimated the posterior probability that transmission
was pre-symptomatic, i.e., occurred before the onset of symptoms in the infector. We used a
Bayesian approach with an uninformative prior (transmission before or after symptoms equally
likely). The 40 probabilities inferred are shown in the right panel of <xref ref-type="fig" rid="F1">Fig. 1</xref>
; the mean probability is 37% (95% CI: 27.5% - 45%), which can be
interpreted as the fraction of pre-symptomatic transmission events out of pre-symptomatic plus
symptomatic transmission events. This mean probability over all pairs approximates our prior,
but the bimodal distribution of individual probabilities in <xref ref-type="fig" rid="F1">Fig.
1</xref>
shows that these are typically far from the prior, i.e., the data are strongly
informative. Uncertainty in the value of this fraction is shown in fig. S6. The value does not
depend significantly on the choice of prior (figs. S7 and S8), functional form of the
distribution of generation times (figs. S9 and S10), or on the choice of transmission events
(fig. S11).</p>
</sec>
<sec sec-type="other2" disp-level="1"><title>A general mathematical model of SARS-CoV-2 infectiousness</title>
<p>We use a mathematical formalism (<xref rid="R23" ref-type="bibr"><italic>23</italic>
</xref>
)
that describes how infectiousness varies as a function of time since infection, τ, for a
representative cohort of infected individuals. This includes heterogeneity between individuals,
and averages over those individuals who infect few others and those who infect many. This
average defines the function β(τ). Infectiousness may change with τ due to
both changing disease biology (notably viral shedding) and changing contact with others. The
area under the β curve is the reproduction number R<sub>0</sub>
.</p>
<p>We decompose β(τ) into four contributions that reflect our categorization above,
namely asymptomatic transmission, pre-symptomatic transmission, symptomatic transmission, and
environmental transmission. The area under the curve of one of these contributions gives the
mean total number of transmissions over one full infection, via that route - asymptomatic,
pre-symptomatic, symptomatic or environmental - which we define to be R<sub>A</sub>
,
R<sub>P</sub>
, R<sub>S</sub>
and R<sub>E</sub>
respectively. The sum of these is
R<sub>0</sub>
.</p>
<p>The mathematical form for β(τ) is:<disp-formula id="E"><mml:math id="m1"><mml:mrow><mml:mi>β</mml:mi>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mi>τ</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:munder><mml:munder><mml:mrow><mml:msub><mml:mi>P</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:msub><mml:mi>x</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:msub><mml:mi>β</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mi>τ</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo stretchy="true">︸</mml:mo>
</mml:munder>
<mml:mrow><mml:mtext>asymptomatic</mml:mtext>
</mml:mrow>
</mml:munder>
<mml:mo>+</mml:mo>
<mml:munder><mml:munder><mml:mrow><mml:mrow><mml:mo>(</mml:mo>
<mml:mrow><mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msub><mml:mi>P</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow><mml:mo>[</mml:mo>
<mml:mrow><mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:mi>s</mml:mi>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mi>τ</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:msub><mml:mi>β</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mi>τ</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo stretchy="true">︸</mml:mo>
</mml:munder>
<mml:mrow><mml:mtext>pre-symptomatic</mml:mtext>
</mml:mrow>
</mml:munder>
<mml:mo>+</mml:mo>
<mml:munder><mml:munder><mml:mrow><mml:mrow><mml:mo>(</mml:mo>
<mml:mrow><mml:mn>1</mml:mn>
<mml:mo>−</mml:mo>
<mml:msub><mml:mi>P</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>s</mml:mi>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mi>τ</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:msub><mml:mi>β</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mi>τ</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo stretchy="true">︸</mml:mo>
</mml:munder>
<mml:mrow><mml:mtext>symptomatic</mml:mtext>
</mml:mrow>
</mml:munder>
<mml:mo>+</mml:mo>
<mml:munder><mml:munder><mml:mrow><mml:mstyle displaystyle="true"><mml:mrow><mml:munderover><mml:mo>∫</mml:mo>
<mml:mrow><mml:mi>l</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mi>τ</mml:mi>
</mml:munderover>
<mml:mrow><mml:msub><mml:mi>β</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mrow><mml:mi>τ</mml:mi>
<mml:mo>−</mml:mo>
<mml:mi>l</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>E</mml:mi>
<mml:mrow><mml:mo>(</mml:mo>
<mml:mi>l</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mstyle>
<mml:mtext> </mml:mtext>
<mml:mi>d</mml:mi>
<mml:mi>l</mml:mi>
</mml:mrow>
<mml:mo stretchy="true">︸</mml:mo>
</mml:munder>
<mml:mrow><mml:mtext>environmental</mml:mtext>
</mml:mrow>
</mml:munder>
</mml:mrow>
</mml:math>
</disp-formula>
β<italic><sub>s</sub>
</italic>
(τ) is the infectiousness of an
individual currently either symptomatic or pre-symptomatic, at age-of-infection τ. Other
parameters in this expression, and those feeding into it indirectly, are listed in <xref rid="T1" ref-type="table">Table 1</xref>
. A detailed discussion of this expression including
its assumptions is found in the supplementary materials. The priors chosen for parameters not
directly calculated from data are shown in fig. S12. The infectiousness model result using
central values of all parameters is shown in <xref ref-type="fig" rid="F2">Fig. 2</xref>
.</p>
<table-wrap id="T1" orientation="portrait" position="float"><label>Table 1</label>
<caption><title>Parameters of the infectiousness model.</title>
</caption>
<table frame="hsides" rules="groups"><col width="12.32%" span="1"></col>
<col width="7.37%" span="1"></col>
<col width="27.04%" span="1"></col>
<col width="12.29%" span="1"></col>
<col width="20.49%" span="1"></col>
<col width="20.49%" span="1"></col>
<thead><tr><td valign="top" align="left" scope="col" rowspan="1" colspan="1"><bold>Name</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Symbol</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Description</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Central value</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Uncertainty</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Source</bold>
</td>
</tr>
</thead>
<tbody><tr><td colspan="6" valign="top" align="center" scope="col" rowspan="1"><italic>Parameters directly
calculated from data</italic>
</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Doubling time</td>
<td valign="top" align="center" rowspan="1" colspan="1">T<sub>2</sub>
</td>
<td valign="top" align="left" rowspan="1" colspan="1">The time taken for the epidemic to double in size during the
early uncontrolled phase of expansion</td>
<td valign="top" align="center" rowspan="1" colspan="1">5.0 days</td>
<td valign="top" align="left" rowspan="1" colspan="1">95% CI 4.2 - 6.4</td>
<td valign="top" align="left" rowspan="1" colspan="1">(<xref rid="R20" ref-type="bibr"><italic>20</italic>
</xref>
)</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Incubation period (2 parameters)</td>
<td valign="top" align="center" rowspan="1" colspan="1">s(τ)</td>
<td valign="top" align="left" rowspan="1" colspan="1">lognormal meanlog<break></break>
lognormal sdlog</td>
<td valign="top" align="center" rowspan="1" colspan="1">1.644<break></break>
0.363</td>
<td valign="top" align="left" rowspan="1" colspan="1">95% CI 1.495 - 1.798<break></break>
95% CI 0.201 - 0.521</td>
<td valign="top" align="left" rowspan="1" colspan="1">(<xref rid="R21" ref-type="bibr"><italic>21</italic>
</xref>
)</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Generation time (2 parameters)</td>
<td valign="top" align="center" rowspan="1" colspan="1">w(τ)</td>
<td valign="top" align="left" rowspan="1" colspan="1">Weibull shape<break></break>
Weibull scale</td>
<td valign="top" align="center" rowspan="1" colspan="1">2.826<break></break>
5.665</td>
<td valign="top" align="left" rowspan="1" colspan="1">95% CI 1.75 - 4.7<break></break>
95% CI 4.7 - 6.9</td>
<td valign="top" align="left" rowspan="1" colspan="1">This paper</td>
</tr>
<tr><td colspan="6" valign="top" align="center" scope="col" rowspan="1"><italic>Parameters with Bayesian
priors informed by anecdotal reports or indirect evidence</italic>
</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Proportion asymptomatic</td>
<td valign="top" align="center" rowspan="1" colspan="1">P<sub>a</sub>
</td>
<td valign="top" align="left" rowspan="1" colspan="1">The proportion of infected individuals who are
asymptomatic</td>
<td valign="top" align="center" rowspan="1" colspan="1">0.4</td>
<td valign="top" align="left" rowspan="1" colspan="1">Prior = beta(α=1.5, β = 1.75)<break></break>
Mode =
0.4<break></break>
Mean = 0.46</td>
<td valign="top" align="left" rowspan="1" colspan="1">Media reports (Diamond Princess)</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Relative infectiousness of asymptomatics</td>
<td valign="top" align="center" rowspan="1" colspan="1">x<sub>a</sub>
</td>
<td valign="top" align="left" rowspan="1" colspan="1">The ratio of infectiousness of asymptomatic individuals to
infectiousness of symptomatic individuals</td>
<td valign="top" align="center" rowspan="1" colspan="1">0.1</td>
<td valign="top" align="left" rowspan="1" colspan="1">Prior = beta(α=1.5, β=5.5)<break></break>
Mode =
0.1<break></break>
Mean = 0.21</td>
<td valign="top" align="left" rowspan="1" colspan="1">Observation of few missing links in Singapore outbreak to date.
Suggestion from (<xref rid="R19" ref-type="bibr"><italic>19</italic>
</xref>
)</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Fraction of all transmission that is
environmentally mediated</td>
<td valign="top" align="center" rowspan="1" colspan="1">R<sub>E</sub>
/R<sub>0</sub>
</td>
<td valign="top" align="left" rowspan="1" colspan="1">Self-explanatory</td>
<td valign="top" align="center" rowspan="1" colspan="1">0.1</td>
<td valign="top" align="left" rowspan="1" colspan="1">Prior = beta(α=1.5, β=5.5)<break></break>
Mode =
0.1<break></break>
Mean = 0.21</td>
<td valign="top" align="left" rowspan="1" colspan="1">Anecdotal observation that many infections can be traced to
close contacts once detailed tracing is completed.</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Environmental infectiousness</td>
<td valign="top" align="center" rowspan="1" colspan="1">E(l)</td>
<td valign="top" align="left" rowspan="1" colspan="1">Rate at which a contaminated environment infects new people
after a time lag l</td>
<td valign="top" align="center" rowspan="1" colspan="1">3</td>
<td valign="top" align="left" rowspan="1" colspan="1">Box function (0,n) days, Prior for n = Gamma(shape = 4, rate
=1)<break></break>
Mode = 3<break></break>
Mean = 4</td>
<td valign="top" align="left" rowspan="1" colspan="1">(<xref rid="R39" ref-type="bibr"><italic>39</italic>
</xref>
) -
variety of values for many different surfaces.</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F2" fig-type="figure" orientation="portrait" position="float"><label>Fig. 2</label>
<caption><p><bold>Our model of infectiousness</bold>
. The average infectiousness (rate of infecting
others), β, as a function of the amount of time since infection, τ. The total
colored area found between two values of τ is the number of transmissions expected in
that time window. The total colored area over all values of τ is the number of
transmissions expected over the full course of one infection, i.e., the basic reproduction
number R<sub>0</sub>
. The different colors indicate the contributions of the four routes of
transmission (stacked on top of one another), so that the total area of one color over all
values of τ is the average number of transmissions via that route over the whole course
of infection: R<sub>P</sub>
, R<sub>S</sub>
, R<sub>E</sub>
, and R<sub>A</sub>
for
pre-symptomatic, symptomatic, environmentally mediated, and asymptomatic transmission
respectively. Values are rounded to one decimal place. Stopping disease spread requires
reduction of R to less than 1: blocking transmission, from whatever combination of colors and
values of τ we can achieve, such that the total area is halved.</p>
</caption>
<graphic xlink:href="abb6936-F2"></graphic>
</fig>
<p>By drawing input parameter sets from the uncertainties shown in <xref rid="T1" ref-type="table">Table 1</xref>
, we quantified our uncertainty in R<sub>0</sub>
and its four
contributions. The resulting values are shown in <xref rid="T2" ref-type="table">Table 2</xref>
and their underlying distributions are shown in fig. S13. Two-dimensional distributions showing
correlations in uncertainty are shown in fig. S14.</p>
<table-wrap id="T2" orientation="portrait" position="float"><label>Table 2</label>
<caption><title>R<sub>0</sub>
and its components.</title>
</caption>
<table frame="hsides" rules="groups"><col width="10.64%" span="1"></col>
<col width="17.42%" span="1"></col>
<col width="16.66%" span="1"></col>
<col width="21.96%" span="1"></col>
<col width="17.42%" span="1"></col>
<col width="15.9%" span="1"></col>
<thead><tr><td valign="top" align="left" scope="col" rowspan="1" colspan="1"></td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Pre-symptomatic</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Symptomatic</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Environmental</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Asymptomatic</bold>
</td>
<td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>Total R<sub>0</sub>
</bold>
</td>
</tr>
</thead>
<tbody><tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Absolute</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.9<break></break>
Uncertainty median: 0.7<break></break>
CI:
0.2 - 1.1</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.8<break></break>
Uncertainty median: 0.6<break></break>
CI:
0.2 - 1.1</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.2<break></break>
Uncertainty median: 0.4<break></break>
CI:
0.0 - 1.3</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.1<break></break>
Uncertainty median: 0.2<break></break>
CI:
0.0 - 1.2</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 2.0<break></break>
Uncertainty median: 2.1<break></break>
CI:
1.7 - 2.5</td>
</tr>
<tr><td valign="top" align="left" scope="row" rowspan="1" colspan="1">Fraction of R<sub>0</sub>
</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.47<break></break>
Uncertainty median: 0.35<break></break>
CI:
0.11 - 0.58</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.38<break></break>
Uncertainty median: 0.28<break></break>
CI:
0.09 - 0.49</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.1 by assumption<break></break>
Uncertainty median:
0.19<break></break>
CI: 0.02 - 0.56</td>
<td valign="top" align="left" rowspan="1" colspan="1">Point estimate: 0.06<break></break>
Uncertainty median: 0.09<break></break>
CI:
0.00 - 0.57</td>
<td valign="top" align="left" rowspan="1" colspan="1">1 by definition</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The estimate of R<sub>P</sub>
/(R<sub>P</sub>
+R<sub>S</sub>
) obtained by this method is 0.55
(0.37 - 0.72), which is larger than the estimate of 0.37 (0.28 - 0.45) from our analysis of the
40 transmission pairs but with overlapping uncertainty.</p>
<p>We define θ as the fraction of all transmissions that do not come from direct contact
with a symptomatic individual: 1 –
<italic>R</italic>
<sub>S</sub>
/<italic>R</italic>
<sub>0</sub>
. This corresponds to the θ
of (<xref rid="R9" ref-type="bibr"><italic>9</italic>
</xref>
) in the case where there is only
pre-symptomatic and symptomatic transmission. From <xref rid="T2" ref-type="table">Table
2</xref>
this is 0.62 (0.50 - 0.92). The value of θ observed during an exponentially
growing epidemic will be distorted when the timing of the different contributions to
transmission occur at different stages of the infection, due to over-representation of recently
infected individuals. This effect can be calculated through use of the renewal equation, as was
recently done to calculate the distribution of time from onset of COVID-19 symptoms to recovery
or death (<xref rid="R20" ref-type="bibr"><italic>20</italic>
</xref>
) (see supplementary
materials). We calculated the θ that would be observed with the early exponential growth
seen in China as 0.68 (0.56 - 0.92). The correction due to the epidemic dynamics is small
compared to parameter uncertainties.</p>
<p>We developed our mathematical model of infectiousness into a web application where users can
test the effect of alternative parameter combinations (<xref rid="R24" ref-type="bibr"><italic>24</italic>
</xref>
).</p>
</sec>
<sec sec-type="cases" disp-level="1"><title>Modelling case isolation and contract tracing with quarantine</title>
<p>We modeled the combined impact of two interventions: (i) isolation of symptomatic individuals,
and (ii) tracing the contacts of symptomatic cases and quarantining them. These interventions
aim to stop the spread of the virus by reducing the number of transmissions from both
symptomatic individuals and from their contacts (who may not be symptomatic), while minimizing
the impact on the larger population. In practice, neither intervention will be successful or
possible for 100% of individuals. The success rate of these interventions determines the
long-term evolution of the epidemic. If the success rates are high enough, the combination of
isolation and contact tracing/quarantining could bring R below 1 and therefore effectively
control the epidemic.</p>
<p>An analytical mathematical framework for the combined impact of these two interventions on an
epidemic was previously derived in (<xref rid="R9" ref-type="bibr"><italic>9</italic>
</xref>
).
In the supplementary material, we solve these equations using our infectiousness model above,
i.e., quantifying how the SARS-CoV-2 epidemic is expected to be controlled or not by case
isolation and the quarantining of traced contacts. Our results are shown in <xref ref-type="fig" rid="F3">Fig. 3</xref>
. The black line shows the threshold for epidemic control: combined
success rates in the region to the upper right of the black line are sufficient to reduce R to
less than one. The <italic>x</italic>
axis is the success rate of case isolation, which can be
thought of either as the fraction of symptomatic individuals isolated, assuming perfect
prevention of transmission on isolation, or the degree to which infectiousness of symptomatic
individuals is reduced assuming all of them are isolated. The <italic>y</italic>
axis is the
success rate of contact tracing; similarly, this can be thought of as the fraction of all
contacts traced, assuming perfectly successful quarantine upon tracing, or the degree to which
infectiousness of contacts is reduced assuming all of them are traced. These results for
intervention effectiveness, and their dependence on all parameters in our combined analysis, can
be explored through the same web interface as for our model of infectiousness (<xref rid="R24" ref-type="bibr"><italic>24</italic>
</xref>
).</p>
<fig id="F3" fig-type="figure" orientation="portrait" position="float"><label>Fig. 3</label>
<caption><p><bold>Quantifying intervention success</bold>
. Heat map plot showing the exponential growth
rate of the epidemic <italic>r</italic>
as a function of the success rate of instant isolation
of symptomatic cases (x axis) and the success rate of instant contact tracing (y axis).
Positive values of <italic>r</italic>
(red) imply a growing epidemic; negative values of
<italic>r</italic>
(green) imply a declining epidemic, with greater negative values implying
faster decline. The solid black line shows <italic>r</italic>
=0, i.e., the threshold for
epidemic control. The dashed lines show uncertainty in the threshold due to uncertainty in
R<sub>0</sub>
(see figs. S15 to S17). The different panels show variation in the delay
associated with the intervention - from initiating symptoms to case isolation and quarantine
of contacts.</p>
</caption>
<graphic xlink:href="abb6936-F3"></graphic>
</fig>
<p>Delays in these interventions make them ineffective at controlling the epidemic (<xref ref-type="fig" rid="F3">Fig. 3</xref>
): traditional manual contact tracing procedures are not
fast enough for SARS-CoV-2. A delay from confirming a case to finding their contacts is not,
however, inevitable. Specifically, this delay can be avoided by using a mobile phone App.</p>
</sec>
<sec sec-type="other3" disp-level="1"><title>Epidemic control with instant digital contact tracing</title>
<p>A mobile phone App can make contact tracing and notification instantaneous upon case
confirmation. By keeping a temporary record of proximity events between individuals, it can
immediately alert recent close contacts of diagnosed cases and prompt them to self-isolate.</p>
<p>Apps with similar aims have been deployed in China. Public health policy was implemented using
an App which was not compulsory but was required to move between quarters and into public spaces
and public transport. The App allows a central database to collect data on user movement and
coronavirus diagnosis and displays a green, amber or red code to relax or enforce restrictions
on movement. The database is reported to be analyzed by an artificial intelligence algorithm
that issues the color codes (<xref rid="R25" ref-type="bibr"><italic>25</italic>
</xref>
). The
App is a plug-in for the WeChat and Alipay Apps and has been generally adopted.</p>
<p>Mainland China outside of Hubei province received significantly more introductions from Wuhan
than did anywhere else, following mass movements of people around Chinese New Year and the start
of the Wuhan lockdown (<xref rid="R26" ref-type="bibr"><italic>26</italic>
</xref>
). Despite
this, sustained epidemic suppression has been achieved in China: fewer than 150 new cases have
been reported each day from March 2 to March 23, down from thousands each day at the height of
the epidemic. South Korea has also achieved sustained epidemic suppression: 76 new cases on
March 24, down from a peak of 909 on February 29, and is also using a mobile phone App for
recommending quarantine. Both the Chinese and South Korean Apps have come under public scrutiny
over issues of data protection and privacy.</p>
<p>With our result in <xref ref-type="fig" rid="F3">Fig. 3</xref>
implying the need for extremely
rapid contact tracing, we set out to design a simple and widely acceptable algorithm from
epidemiological first principles, using common smartphone functionality. The method is shown in
<xref ref-type="fig" rid="F4">Fig. 4</xref>
. The core functionality is to replace a
week’s work of manual contact tracing with instantaneous signals transmitted to and from
a central server. Coronavirus diagnoses are communicated to the server, enabling recommendation
of risk-stratified quarantine and physical distancing measures in those now known to be possible
contacts, while preserving the anonymity of the infected individual. Tests can be requested by
symptomatic individuals through the App.</p>
<fig id="F4" fig-type="figure" orientation="portrait" position="float"><label>Fig. 4</label>
<caption><title>A schematic of app-based COVID-19 contact tracing.</title>
<p>Contacts of individual A (and all individuals using the app) are traced using GPS
co-localisations with other App users, supplemented by scanning QR-codes displayed on
high-traffic public amenities where GPS is too coarse. Individual A requests a SARS-COV-2 test
(using the app) and their positive test result triggers an instant notification to individuals
who have been in close contact. The App advises isolation for the case (individual A) and
quarantine of their contacts.</p>
</caption>
<graphic xlink:href="abb6936-F4"></graphic>
</fig>
<p>The simple algorithm can easily be refined to be more informative, for example quarantining
areas if local epidemics become uncontrolled, quarantining whole households, or performing
second- or third-degree contact tracing if case numbers are rising, which would result in more
people being preemptively quarantined. Algorithmic recommendations can also be manually
overridden, where public health officials gather more specific evidence. The App can serve as
the central hub of access to all COVID-19 health services, information and instructions, and as
a mechanism to request food or medicine deliveries during self-isolation.</p>
<p>In the context of a mobile phone App, <xref ref-type="fig" rid="F3">Fig. 3</xref>
paints an
optimistic picture. There is no delay between case confirmation and notification of contacts,
leaving the total delay for the contact quarantine process as that from an individual initiating
symptoms to their confirmation as a case, plus the delay for notified contacts to enter
quarantine. The delay between symptom development and case confirmation will decrease with
faster testing protocols, and indeed could become instant if presumptive diagnosis of COVID-19
based on symptoms were accepted in high-prevalence areas. The delay between contacts being
notified and entering quarantine should be minimal with high levels of public understanding, as
should the delay for case isolation. The efficacy of contact tracing (the <italic>y</italic>
axis of <xref ref-type="fig" rid="F3">Fig. 3</xref>
) can be identified with the square of the
proportion of the population using the App, multiplied by the probability of the App detecting
infectious contacts, multiplied by the fractional reduction in infectiousness resulting from
being notified as a contact.</p>
</sec>
<sec sec-type="other4" disp-level="1"><title>Ethical considerations</title>
<p>Successful and appropriate use of the App relies on it commanding well-founded public trust
and confidence. This applies to the use of the App itself and of the data gathered. There are
strong, well-established ethical arguments recognizing the importance of achieving health
benefits and avoiding harm. These arguments are particularly strong in the context of an
epidemic with the potential for loss of life on the scale possible with COVID-19. Requirements
for the intervention to be ethical and capable of commanding the trust of the public are likely
to comprise the following. i. Oversight by an inclusive and transparent advisory board, which
includes members of the public. ii. The agreement and publication of ethical principles by which
the intervention will be guided. iii. Guarantees of equity of access and treatment. iv. The use
of a transparent and auditable algorithm. v. Integrating evaluation and research in the
intervention to inform the effective management of future major outbreaks. vi. Careful oversight
of and effective protections around the uses of data. vii. The sharing of knowledge with other
countries, especially low- and middle-income countries. viii. Ensuring that the intervention
involves the minimum imposition possible and that decisions in policy and practice are guided by
three moral values: equal moral respect, fairness, and the importance of reducing suffering
(<xref rid="R27" ref-type="bibr"><italic>27</italic>
</xref>
). It is noteworthy that the
algorithmic approach we propose avoids the need for coercive surveillance, since the system can
have very large impacts and achieve sustained epidemic suppression, even with partial uptake.
People should be democratically entitled to decide whether to adopt this platform. The intention
is not to impose the technology as a permanent change to society, but we believe it is under
these pandemic circumstances it is necessary and justified to protect public health.</p>
</sec>
<sec sec-type="discussion" disp-level="1"><title>Discussion</title>
<p>In this study, we estimated key parameters of the SARS-CoV-2 epidemic, using an analytically
solvable model of the exponential phase of spread and of the impact of interventions. Our
estimate of R<sub>0</sub>
is lower than many previous published estimates, for example (<xref rid="R12" ref-type="bibr"><italic>12</italic>
</xref>
,<italic></italic>
<xref rid="R28" ref-type="bibr"><italic>28</italic>
</xref>
, <xref rid="R29" ref-type="bibr"><italic>29</italic>
</xref>
). These studies assumed SARS-like generation times; however, the
emerging evidence for shorter generation times for COVID-19 implies a smaller R<sub>0</sub>
.
This means a smaller fraction of transmissions need to be blocked for sustained epidemic
suppression (R < 1). However, it does not mean sustained epidemic suppression will be easier
to achieve because each individual’s transmissions occur in a shorter window of time
after their infection, and a greater fraction of them occurs before the warning sign of
symptoms. Specifically, our approaches suggest that between a third and a half of transmissions
occur from pre-symptomatic individuals. This is in line with estimates of 48% of transmission
being pre-symptomatic in Singapore and 62% in Tianjin, China (<xref rid="R30" ref-type="bibr"><italic>30</italic>
</xref>
), and 44% in transmission pairs from various countries (<xref rid="R31" ref-type="bibr"><italic>31</italic>
</xref>
). Our infectiousness model suggests that
the total contribution to R<sub>0</sub>
from pre-symptomatics is 0.9 (0.2 - 1.1), almost enough
to sustain an epidemic on its own. For SARS, the corresponding estimate was almost zero (<xref rid="R9" ref-type="bibr"><italic>9</italic>
</xref>
), immediately telling us that different
containment strategies will be needed for COVID-19.</p>
<p>Transmission occurring rapidly and before symptoms, as we have found, implies that the
epidemic is highly unlikely to be contained by solely isolating symptomatic individuals.
Published models (<xref rid="R9" ref-type="bibr"><italic>9</italic>
</xref>
–<xref rid="R11" ref-type="bibr"><italic>11</italic>
</xref>
, <xref rid="R32" ref-type="bibr"><italic>32</italic>
</xref>
) suggest that in practice manual contact tracing can only improve
on this to a limited extent: it is too slow, and cannot be scaled up once the epidemic grows
beyond the early phase, due to limited personnel. Using mobile phones to measure infectious
disease contact networks has been proposed previously (<xref rid="R33" ref-type="bibr"><italic>33</italic>
</xref>
–<xref rid="R35" ref-type="bibr"><italic>35</italic>
</xref>
). Considering our quantification of SARS-CoV-2 transmission, we
suggest that this approach, with a mobile phone App implementing instantaneous contact tracing,
could reduce transmission enough to achieve R < 1 and sustained epidemic suppression,
stopping the virus from spreading further. We have developed a web interface to explore the
uncertainty in our modelling assumptions (<xref rid="R24" ref-type="bibr"><italic>24</italic>
</xref>
). This will also serve as an ongoing resource as new data becomes
available and as the epidemic evolves.</p>
<p>We included environmentally mediated transmission and transmission from asymptomatic
individuals in our general mathematical framework. However, the relative importance of these
transmission routes remain speculative based on current data. Cleaning and decontamination are
being deployed to varying levels in different settings, and improved estimates of their relative
importance would help inform this as a priority. Asymptomatic infection has been widely reported
for COVID-19, e.g., (<xref rid="R14" ref-type="bibr"><italic>14</italic>
</xref>
), unlike for
SARS where this was very rare (<xref rid="R36" ref-type="bibr"><italic>36</italic>
</xref>
). We
argue that the reports from Singapore imply that even if asymptomatic infections are common,
onward transmission from this state is probably uncommon, since forensic reconstruction of the
transmission networks has closed down most missing links. There is an important caveat to this:
the Singapore outbreak to date is small and has not implicated children. There has been
widespread speculation that children could be frequent asymptomatic carriers and potential
sources of SARS-CoV-2 (<xref rid="R37" ref-type="bibr"><italic>37</italic>
</xref>
, <xref rid="R38" ref-type="bibr"><italic>38</italic>
</xref>
).</p>
<p>We calibrated our estimate of the overall amount of transmission based on the epidemic growth
rate observed in China not long after the epidemic started. Growth in Western European countries
so far appears to be faster, implying either shorter intervals between individuals becoming
infected and transmitting onwards, or a higher R<sub>0</sub>
. We illustrate the latter effect in
figs. S18 and S19. If this is an accurate picture of viral spread in Europe and not an artefact
of early growth, epidemic control with only case isolation and quarantining of traced contacts
appears implausible in this case, requiring near-universal App usage and near-perfect
compliance. The App should be one tool among many general preventative population measures such
as physical distancing, enhanced hand and respiratory hygiene, and regular decontamination.</p>
<p>An App-based intervention could be more powerful than our analysis here suggests, however. The
renewal equation mathematical framework we use, while well adapted to account for realistic
infectiousness dynamics, is not well adapted to account for benefits of recursion over the
transmission network. Once they have been confirmed as cases, individuals identified by tracing
can trigger further tracing, as can their contacts and so on. This effect was not modeled in our
analysis here. If testing capacity is limited, individuals who are identified by tracing may be
presumed confirmed upon onset of symptoms, since the prior probability of them being positive is
higher than for the index case, accelerating the algorithm further without compromising
specificity. With fast enough testing, even index cases diagnosed late in infection could be
traced recursively, to identify recently infected individuals before they develop symptoms, and
before they transmit. Improved sensitivity of testing in early infection could also speed up the
algorithm and achieve rapid epidemic control.</p>
<p>The economic and social impact caused by widespread lockdowns is severe. Individuals on low
incomes may have limited capacity to remain at home, and support for people in quarantine
requires resources. Businesses will lose confidence, causing negative feedback cycles in the
economy. Psychological impacts may be lasting. Digital contact tracing could play a critical
role in avoiding or leaving lockdown. We have quantified its expected success and laid out a
series of requirements for its ethical implementation. The App we propose offers benefits for
both society and individuals, reducing the number of cases and also enabling people to continue
their lives in an informed, safe, and socially responsible way. It offers the potential to
achieve important public benefits while maximising autonomy. Specific issues exist for groups
within the population that may not be amenable to such an approach, and these could be rapidly
refined in policy. Essential workers, such as health care workers, may need separate
arrangements.</p>
<p>Further modelling is needed to compare the number of people disrupted under different
scenarios consistent with sustained epidemic suppression. But a sustained pandemic is not
inevitable, nor is sustained national lockdown. We recommend urgent exploration of means for
intelligent physical distancing via digital contact tracing.</p>
</sec>
</body>
<back><ack><title>Acknowledgments</title>
<p>We thank Will Probert, Andrei Akhmetzhanov, Alice Ledda, Ben Cowling, Gabriel Leung and Yuan
Yang for helpful comments. <bold>Funding:</bold>
This work was funded by the Li Ka Shing
Foundation. AN is funded by the Artic Network (Wellcome Trust Collaborators Award
206298/Z/17/Z). The funders played no role in study conception or execution. <bold>Author
contributions:</bold>
Conceptualization: CF, DB. Data curation: LF, CW, AN, LZ. Funding
acquisition: CF, MP. Investigation: LF, CW, MK, CF. Methodology: LF, CW. Visualization: LF, CW,
MK, DB. Project administration: LA. Software: MK. Ethical analysis: MP, CF, DB. Writing,
original draft: LF, CW, MP, DB, CF. Writing, review and editing: all authors. <bold>Competing
interests:</bold>
None declared. <bold>Data and materials availability:</bold>
All data are
available in the manuscript or the supplementary material. The code used for our analyses is
publicly available at (<xref rid="R40" ref-type="bibr"><italic>40</italic>
</xref>
). This work is
licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original
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<app-group><app><title>Supplementary Materials</title>
<supplementary-material content-type="local-data"><p>science.sciencemag.org/cgi/content/full/science.abb6936/DC1</p>
<p>Materials and Methods</p>
<p>Figs. S1 to S21</p>
<p>References (<xref rid="R41" ref-type="bibr"><italic>41</italic>
</xref>
–<xref rid="R45" ref-type="bibr"><italic>45</italic>
</xref>
)</p>
<p>Data S1</p>
</supplementary-material>
<supplementary-material content-type="local-data" id="S1"><media xlink:href="abb6936_Ferretti_SM.pdf"><caption><p>Click here for additional data file.</p>
</caption>
</media>
</supplementary-material>
<supplementary-material content-type="local-data" id="S2"><media xlink:href="abb6936-Data-S1.csv"><caption><p>Click here for additional data file.</p>
</caption>
</media>
</supplementary-material>
</app>
</app-group>
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