Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study

Abstract

Background:
Since Dec 31, 2019, the Chinese city of Wuhan has reported an outbreak of atypical pneumonia caused by the 2019 novel coronavirus (2019-nCoV). Cases have been exported to other Chinese cities, as well as internationally, threatening to trigger a global outbreak. Here, we provide an estimate of the size of the epidemic in Wuhan on the basis of the number of cases exported from Wuhan to cities outside mainland China and forecast the extent of the domestic and global public health risks of epidemics, accounting for social and non-pharmaceutical prevention interventions.

Methods:
We used data from Dec 31, 2019, to Jan 28, 2020, on the number of cases exported from Wuhan internationally (known days of symptom onset from Dec 25, 2019, to Jan 19, 2020) to infer the number of infections in Wuhan from Dec 1, 2019, to Jan 25, 2020. Cases exported domestically were then estimated. We forecasted the national and global spread of 2019-nCoV, accounting for the effect of the metropolitan-wide quarantine of Wuhan and surrounding cities, which began Jan 23-24, 2020. We used data on monthly flight bookings from the Official Aviation Guide and data on human mobility across more than 300 prefecture-level cities in mainland China from the Tencent database. Data on confirmed cases were obtained from the reports published by the Chinese Center for Disease Control and Prevention. Serial interval estimates were based on previous studies of severe acute respiratory syndrome coronavirus (SARS-CoV). A susceptible-exposed-infectious-recovered metapopulation model was used to simulate the epidemics across all major cities in China. The basic reproductive number was estimated using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credibile interval (CrI).

Findings:
In our baseline scenario, we estimated that the basic reproductive number for 2019-nCoV was 2·68 (95% CrI 2·47-2·86) and that 75 815 individuals (95% CrI 37 304-130 330) have been infected in Wuhan as of Jan 25, 2020. The epidemic doubling time was 6·4 days (95% CrI 5·8-7·1). We estimated that in the baseline scenario, Chongqing, Beijing, Shanghai, Guangzhou, and Shenzhen had imported 461 (95% CrI 227-805), 113 (57-193), 98 (49-168), 111 (56-191), and 80 (40-139) infections from Wuhan, respectively. If the transmissibility of 2019-nCoV were similar everywhere domestically and over time, we inferred that epidemics are already growing exponentially in multiple major cities of China with a lag time behind the Wuhan outbreak of about 1-2 weeks.

Interpretation:
Given that 2019-nCoV is no longer contained within Wuhan, other major Chinese cities are probably sustaining localised outbreaks. Large cities overseas with close transport links to China could also become outbreak epicentres, unless substantial public health interventions at both the population and personal levels are implemented immediately. Independent self-sustaining outbreaks in major cities globally could become inevitable because of substantial exportation of presymptomatic cases and in the absence of large-scale public health interventions. Preparedness plans and mitigation interventions should be readied for quick deployment globally.

Funding:
Health and Medical Research Fund (Hong Kong, China).

Full text

Articles
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
1
Nowcasting and forecasting the potential domestic and
international spread of the 2019-nCoV outbreak originating
in Wuhan, China: a modelling study
Joseph T Wu*, Kathy Leung*, Gabriel M Leung
Summary
Background Since Dec 31, 2019, the Chinese city of Wuhan has reported an outbreak of atypical pneumonia caused by
the 2019 novel coronavirus (2019-nCoV). Cases have been exported to other Chinese cities, as well as internationally,
threatening to trigger a global outbreak. Here, we provide an estimate of the size of the epidemic in Wuhan on the
basis of the number of cases exported from Wuhan to cities outside mainland China and forecast the extent of the
domestic and global public health risks of epidemics, accounting for social and non-pharmaceutical prevention
interventions.
Methods We used data from Dec 31, 2019, to Jan 28, 2020, on the number of cases exported from Wuhan
internationally (known days of symptom onset from Dec 25, 2019, to Jan 19, 2020) to infer the number of infections
in Wuhan from Dec 1, 2019, to Jan 25, 2020. Cases exported domestically were then estimated. We forecasted the
national and global spread of 2019-nCoV, accounting for the eect of the metropolitan-wide quarantine of Wuhan
and surrounding cities, which began Jan 23–24, 2020. We used data on monthly flight bookings from the Ocial
Aviation Guide and data on human mobility across more than 300 prefecture-level cities in mainland China from
the Tencent database. Data on confirmed cases were obtained from the reports published by the Chinese Center
for Disease Control and Prevention. Serial interval estimates were based on previous studies of severe acute
respiratory syndrome coronavirus (SARS-CoV). A susceptible-exposed-infectious-recovered metapopulation model
was used to simulate the epidemics across all major cities in China. The basic reproductive number was estimated
using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credibile
interval (CrI).
Findings In our baseline scenario, we estimated that the basic reproductive number for 2019-nCoV was 2·68
(95% CrI 2·47–2·86) and that 75 815 individuals (95% CrI 37 304–130 330) have been infected in Wuhan as of
Jan 25, 2020. The epidemic doubling time was 6·4 days (95% CrI 5·8–7·1). We estimated that in the baseline
scenario, Chongqing, Beijing, Shanghai, Guangzhou, and Shenzhen had imported 461 (95% CrI 227–805),
113 (57–193), 98 (49–168), 111 (56–191), and 80 (40–139) infections from Wuhan, respectively. If the transmissibility
of 2019-nCoV were similar everywhere domestically and over time, we inferred that epidemics are already
growing exponentially in multiple major cities of China with a lag time behind the Wuhan outbreak of about
1–2 weeks.
Interpretation Given that 2019-nCoV is no longer contained within Wuhan, other major Chinese cities are probably
sustaining localised outbreaks. Large cities overseas with close transport links to China could also become outbreak
epicentres, unless substantial public health interventions at both the population and personal levels are implemented
immediately. Independent self-sustaining outbreaks in major cities globally could become inevitable because of
substantial exportation of presymptomatic cases and in the absence of large-scale public health interventions.
Preparedness plans and mitigation interventions should be readied for quick deployment globally.
Funding Health and Medical Research Fund (Hong Kong, China).
Copyright © 2020 Elsevier Ltd. All rights reserved.
Published Online
January 31, 2020
https://doi.org/10.1016/
S0140-6736(20)30260-9
*Contributed equally
WHO Collaborating Centre for
Infectious Disease
Epidemiology and Control,
School of Public Health,
Li Ka Shing Faculty of Medicine,
University of Hong Kong,
Hong Kong, China
(Prof J T Wu PhD, K Leung PhD,
Prof G M Leung MD)
Correspondence to:
Prof Joseph T Wu, School of
Public Health, Li Ka Shing Faculty
of Medicine, University of
Hong Kong, Hong Kong, China
joewu@hku.hk
Introduction
Wuhan, the capital of Hubei province in China, is
investigating an outbreak of atypical pneumonia caused
by the zoonotic 2019 novel coronavirus (2019-nCoV). As
of Jan 29, 2020 (1100 h Hong Kong time), there have
been 5993 cases of 2019-nCoV infections confirmed in
mainland China (figure 1), including 132 deaths. As of
Jan 28, 2020 (1830 h Hong Kong time), there have been
78 exported cases from Wuhan to areas outside mainland
China (appendix p 2–4).
The National Health Commission of China has devel-
oped a case-definition system to facilitate the classification
of patients (panel). To mitigate the spread of the virus, the
Chinese Government has pro gressively implemented
metro politan-wide quarantine of Wuhan and several
nearby cities since Jan 23–24, 2020. Numerous domestic
See Online for appendix

Articles
2
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
airports and train stations, as well as international airports,
have adopted temperature screening measures to detect
individuals with fever.
Two other novel coronaviruses (CoVs) have emerged as
major global health threats since 2002, namely severe
acute respiratory syndrome coronavirus (SARS-CoV;
in 2002) that spread to 37 countries, and Middle East
respiratory syndrome coronavirus (MERS-CoV; in 2012)
that spread to 27 countries. SARS-CoV caused more than
8000 infections and 800 deaths, and MERS-CoV infected
2494 individuals and caused 858 deaths worldwide to
date. Both are zoonotic viruses and epidemiologically
similar, except that SARS-CoV has virtually no subclinical
manifestation, whereas MERS-CoV behaves more simi-
larly to the other four commonly circulating human
CoVs, with a substantial proportion of asymptomatic
infections (table 1). Symptomatic cases of both viruses
usually present with moderate-to-severe respiratory
symptoms that often progress to severe pneumonia.
A notable common characteristic of both SARS-CoV
and MERS-CoV is that they have low potential for
sustained community transmission (ie, low basic repro-
ductive number).15,28,29 However, the most worrisome
aspect is the ability of the viruses to cause unusually
large case clusters via superspreading, which can exceed
100 individuals and are apparently seeded by a single
index case.5,28–31
In this study, we provide a nowcast of the probable size
of the epidemic, recognising the challenge of complete
ascertainment of a previously unknown pathogen with
an unclear clinical spectrum and testing capacity, even
after identification of the aetiological cause. More
importantly, from a public health control viewpoint, we
then forecast the probable course of spread domes tically
and inter nationally, first by assuming similar trans-
missibility as the initial phase in Wuhan (ie, little or no
mitigation interventions), then accounting for the
potential impact of the various social and personal non-
pharmaceutical interventions that have been progres-
sively and quickly implemented in January, 2020.
Methods
Data sources and assumptions
In this modelling study, we first inferred the basic repro-
ductive number of 2019-nCoV and the outbreak size in
Wuhan from Dec 1, 2019, to Jan 25, 2020, on the basis of
the number of cases exported from Wuhan to cities
outside mainland China. We then estimated the number
of cases that had been exported from Wuhan to other
cities in mainland China. Finally, we forecasted the
spread of 2019-nCoV within and outside mainland China,
accounting for the Greater Wuhan region quarantine
implemented since Jan 23–24, 2020, and other public
health interventions.
Wuhan is the major air and train transportation hub of
central China (figure 1). We estimated the daily number of
outbound travellers from Wuhan by air, train, and road
with data from three sources (see appendix p 1 for details):
(1) the monthly number of global flight bookings to Wuhan
for January and February, 2019, obtained from the Ocial
Aviation Guide (OAG); (2) the daily number of domestic
passengers by means of transportation recorded by the
location-based services of the Tencent (Shenzhen, China)
database from Wuhan to more than 300 prefecture-level
Research in context
Evidence before this study
In central China, Wuhan is investigating an outbreak of atypical
pneumonia caused by the zoonotic 2019 novel coronavirus
(2019-nCoV). Few data and details are currently available.
Two other novel coronaviruses (CoVs) have emerged as major
global epidemics in recent decades; in 2002, severe acute
respiratory syndrome coronavirus (SARS-CoV) spread to
37 countries and caused more than 8000 cases and almost
800 deaths, and in 2012, Middle East respiratory syndrome
coronavirus (MERS-CoV) spread to 27 countries, causing
2494 cases and 858 deaths worldwide to date. These CoVs are
both zoonotic and have low potential for sustained community
transmission. However, larger clusters involving superspreading
events were observed for SARS in 2003 and MERS in 2014–17.
As of Jan 25, 2020, the scale and geographical extent of the
2019-nCoV outbreak both within and outside mainland China
are highly uncertain. National and global spread of this disease is
particularly concerning given that chunyun, a 40-day period with
extremely high air and train traffic across China because of the
lunar new year Spring Festival, began on Jan 10, 2020.
We searched PubMed and preprint archives for articles published
up to Jan 25, 2020, that contained information about the Wuhan
outbreak using the terms “coronavirus”, “CoV”, “2019-nCoV”,
“Wuhan”, “transmission”, “China”, “superspreading”, and
“Chinese New Year”. We found six studies that reported the
relative risks of case exportation from Wuhan to areas outside
mainland China.
Added value of this study
In the absence of a robust and complete line list for characterising
the epidemiology of this novel pathogen, we inferred the
outbreak size of 2019-nCoV in Wuhan from the number of
confirmed cases that have been exported to cities outside
mainland China. We used this outbreak size estimate to project
the number of cases that have been exported to other Chinese
cities. We forecasted the spread of 2019-nCoV both within and
outside of mainland China.
Implications of all the available evidence
Preparedness plans should be readied for quick deployment
worldwide, especially in cities with close travel links with
Wuhan and other major Chinese cities.
For the Tencent database see
https://heat.qq.com/
For the Official Aviation Guide
see https://www.oag.com/

Articles
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
3
cities in main land China from Jan 6 to March 7, 2019;
and (3) the domestic passenger volumes from and to
Wuhan during chunyun 2020 (Spring Festival travel
season; appendix p 1) estimated by Wuhan Municipal
Transportation Management Bureau and press-released in
December, 2019.32
On Jan 19, 2020, the Chinese Center for Disease Control
and Prevention (CDC) reported that only 43 (22%) of the
198 confirmed cases in its outbreak investigation had
been exposed to the Huanan seafood wholesale market,33
the most probable index source of zoonotic 2019-nCoV
infections, which was closed and disinfected on
Jan 1, 2020. As such, and because of the diculties of
tracing all infections, we assumed that during
Dec 1–31, 2019, the epidemic in Wuhan was seeded by a
constant zoonotic force of infection that caused 86 cases
(ie, twice the 43 confirmed cases with zoonotic exposure)
in our baseline scenario. For the sensitivity analysis, we
assumed 129 and 172 cases (50% and 100% higher than
the baseline scenario value). Given that both 2019-nCoV
and SARS-CoV could cause self-sustaining human-to-
human transmission in the community, we assumed that
the serial interval of 2019-nCoV was the same as that of
SARS-CoV in Hong Kong (mean 8·4 days; table 1).4 We
assumed that the incubation period of 2019-nCoV was
similar to that of SARS-CoV and MERS-CoV (mean
6 days; table 1). These assumptions are consistent with
preliminary estimates of the serial interval (mean 7·5 days)
and incubation period (mean 6·1 days) using line-list data
from China CDC.34
Estimating the transmissibility and outbreak size of
2019-nCoV in Wuhan
We assumed that the catchment population size of the
Wuhan Tianhe International Airport at Wuhan was
19 million (ie, Greater Wuhan region with 11 million
people from Wuhan city plus 8 million from parts of
several neighbouring cities). We estimated the number of
cases in Greater Wuhan on the basis of the number of
confirmed cases exported to cities outside mainland
China whose symptom onset date had been reported to
fall from Dec 25, 2019, to Jan 19, 2020 (appendix pp 2–4).
The start date of this period (day Ds) corresponded to one
mean incubation period before the Wuhan outbreak was
announced on Dec 31, 2019, whereas the end date (day De)
was 7 days before the time of writing (Jan 26, 2020). This
end date was chosen to minimise the eect of lead time
bias on case confirmation (the time between onset and
case confirmation was ≤7 days in 46 [80%] of 55 cases
exported to cities outside mainland China; see appendix
pp 2–4). We let χd to be the number of such case
exportation on day d.
Our 2019 OAG data indicated that for cities outside
mainland China excluding Hong Kong, the daily
average number of international outbound air passengers
was LW,I =3633 and that of international inbound air
passengers was LI,W=3546 in Greater Wuhan during
January–Feb ru ary, 2019 (table 2). We excluded Hong
Kong in this estimate because travel from mainland
China to Hong Kong had dropped sharply since
August, 2019, because of social unrest in Hong Kong. Our
calibrated Tencent mobility data indicated that for cities
Figure 1: Risk of spread outside Wuhan
(A) Cumulative number of confirmed cases of 2019 novel coronavirus as of Jan 28, 2020, in Wuhan, in mainland
China (including Wuhan), and outside mainland China. (B) Major routes of outbound air and train travel
originating from Wuhan during chunyun, 2019. Darker and thicker edges represent greater numbers of passengers.
International outbound air travel (yellow) constituted 13·5% of all outbound air travel, and the top 40 domestic
(red) outbound air routes constituted 81·3%. Islands in the South China Sea are not shown.
B
A
Dec 31,
2019
Jan 5,
2020
Jan 10,
2020
Jan 15,
2020
Jan 20,
2020
Jan 25,
2020
Jan 30,
2020
Date
0
7000
6000
5000
4000
3000
2000
1000
0
70
80
90Wuhan
Mainland China
Outside mainland China
60
50
40
30
20
10
Number of confirmed cases in Wuhan or mainland China
Number of confirmed cases outside mainland China (green)
International air outbound travel
Domestic air outbound travel
Domestic train outbound travel

Articles
4
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
in mainland China, the daily number of all domestic
outbound travellers was LW,C (t)=502 013 and that of all
domestic inbound travellers was LC,W(t)=487 310 in Wuhan
at time t before chunyun (Jan 10). During chunyun, these
estimates were LW,C (t)=717 226 and LC,W(t)=810 500.
We used the following susceptible-exposed-infectious-
recovered (SEIR) model to simulate the Wuhan epidemic
since it was established in December, 2019:
where S(t), E(t), I(t), and R(t) were the number of
susceptible, latent, infectious, and removed individuals
at time t; DE and DI were the mean latent (assumed to be
the same as incubation) and infectious period (equal to
the serial interval minus the mean latent period4); R0 was
the basic reproductive number; z(t) was the zoonotic
SARS-CoV MERS-CoV Commonly circulating human CoVs (229E, NL63,
OC43, HKU1)
Basic reproductive
number, mean
(95% CI), or prevalence
of infection
(for commonly
circulating human
CoVs)
Beijing: 1·88 overall,1 0·94 after generation 1
(excluding SSE).1 Hong Kong: 1·70 (0·44–2·29)*
overall,2 2·7 (2·2–3·7) in the early phase (excluding
SSE),3 range 0·14–1 in the later phase (excluding
SSE).3 Singapore: 1·63 overall1 or 1·83 (0·47–2·47)*
overall,2 range 2·2–3·6 in the early phase (including
SSE).4 Toronto 0·86 (0·24–1·18)* overall.2
Worldwide: 0·95 (0·67–1·23) overall.5
Middle East: 0·47 (0·29–0·80) overall.6 Saudi Arabia: 0·45
(0·33–0·58) overall.7 Middle East and South Korea: 0·91
(0·36–1·44) overall.5 South Korea: range 2·0–8·1 in early
phase (including SSE).8
229E and OC43 in USA:9 annual infection attack
rates of 2·8% to 26·0% in prospective cohorts.
Guangzhou, China:10 CoVs detected in 2·25% of
adults and children with fever and upper respiratory
infection symptoms, among which 60% were OC43,
17% were 229E, 15% were NL63, and 7·8% were
HKU1. UK:11 CoVs detected in all age groups, most
frequently in children aged 7–12 months (4·86%)
Incubation period,
days, mean (SD) or
mean (95% CI)
Hong Kong:12 4·6 (3·8–5·8). Hong Kong:13 4·4 (4·6).
Beijing:13 5·7 (9·7). Taiwan:13 6·9 (6·1)
Saudi Arabia:14 5·0 (4·0–6·6). South Korea:14 6·9 (6·3–7·5). OC43 and other common human CoVs:15 range 2–4.
common human CoVs:16 range 2–5. Common human
CoVs:17 range 3–4.
Serial interval, days,
mean (SD)
Singapore:4 8·4 (3·8). Saudi Arabia:7 6·8 (4·1). South Korea:18 12·4 (2·8). ··
Seroprevalence
among non-cases
Hong Kong, among close contacts:19 around 0%. Qatar:20 0·21% (10 of 4719) among healthy blood donors,
0·74% (1 of 135) among individuals who are close contacts
of cases but not sick. Arabian Peninsula:21 0·15% (15 of
10 365) among general population, 6·2% (68 of 1090)
among individuals exposed to camels.
OC43 and 229E:22 86–100%. HKU1, S-protein-based
ELISA:23 0% in children aged <10 years, to a plateau
of 21·6% in adults aged 31–40 years.
Case-hospitalisation
probability, mean
(95% CI)
Around 100%.12 South Korea:24 around 100%. OC43 in Canada:25 12·6% among older and disabled
adults in a long-term care facility. 229E and OC43 in
USA:9 prevalence of 3·3–11·1% in a hospitalised
cohort. Brazil:26 11% among children aged <3 years
attending the paediatric emergency room with acute
lower respiratory infection and hospitalised.
Case-fatality
proportion
Worldwide (WHO): 9·6% among probable cases.
mainland China:27 6·4% among probable cases.
Hong Kong:12 17% among laboratory-confirmed
cases.
Worldwide (WHO): 34·5% among laboratory-confirmed
cases. South Korea:24 20·4% among laboratory-confirmed
cases.
··
CoV=coronavirus. SARS=severe acute respiratory syndrome. MERS=Middle East respiratory syndrome. SSE=superspreading event. *Data are mean (IQR).
Table 1: Epidemiological characteristics of human CoVs
=S(t)
N
–
dS(t)
dt
(
R0
DI
I(t) + z(t)
(
+ LI,W + LC,W(t)
–
(
LW,I
N
+
(
LW,C(t)
N
S(t)
=S(t)
N
dE
dt
(
R0
DI
I(t) + z(t)
(
–
(
LW,I
N
+
(
LW,C(t)
N
E(t)
E(t)
DE
–
=E(t)
DE
dI(t)
dt–
(
LW,I
N+
(
LW,C(t)
NI(t)
I(t)
DI
–
Panel: Case definitions of 2019 novel coronavirus (2019-nCoV)
The case definition of 2019-nCoV differs depending on the context in which it is used.
Case definition of the Chinese Center for Disease Control and Prevention (CDC)
A suspected or probable case is defined as a case that meets: (1) three clinical criteria or
(2) two clinical criteria and one epidemiological criterion. Clinical criteria are: fever;
radiographic evidence of pneumonia or acute respiratory distress syndrome; and low or
normal white blood cell count or low lymphocyte count. Epidemiological criteria are: living
in Wuhan or travel history to Wuhan within 14 days before symptom onset; contact with
patients with fever and symptoms of respiratory infection within 14 days before symptom
onset; and a link to any confirmed cases or clusters of suspected cases.
The definition of a confirmed case, for the first case in a province, is a suspected or
probable case with detection of viral nucleic acid at the city CDC and provincial CDC.
For the second case and all subsequent cases, the definition is a suspected or probable
case with detection of virus nucleic acid at the city CDC.
Case definition used in the case exportation model in this study
We defined cases as individuals who were symptomatic, who could be detected by
temperature screening at international borders, or who had a disease severity requiring
hospital admission, or both, plus travel history to Wuhan.

Articles
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
5
force of infection equal to 86 cases per day in the baseline
scenario before market closure on Jan 1, 2020, and equal
to 0 thereafter. The cumulative number of infections and
cases that had occurred in Greater Wuhan up to time t
was obtained from the SEIR model.
We assumed that travel behaviour was not aected by
disease and hence international case exportation occurred
according to a non-homogeneous process with rate
As such, the expected number of international case
exportation on day d was
Taken together, the likelihood function was
We estimated R0 using Markov Chain Monte Carlo
methods with Gibbs sampling and non-informative flat
prior. For a given R0 from the resulting posterior distri-
bution, we used the same SEIR model to estimate the
corresponding outbreak size in Wuhan and the probability
distribution of the number of cases that had been exported
domestically to other cities in mainland China (on the
basis of the destination distribution in our calibrated
Tencent mobility data). Point estimates were presented
using posterior means, and statistical uncertainty was
presented using 95% credible intervals (CrIs).
Nowcasting and forecasting the spread of 2019-nCoV in
China and worldwide
We extended the above SEIR model into a SEIR-meta-
population model to simulate the spread of 2019-nCoV
across mainland China, assuming the trans missibility
of 2019-nCoV was similar across all cities.35 The
movements of individuals between more than
300 prefecture-level cities were modelled using the
daily average trac volumes in our calibrated Tencent
mobility data. Given that 2019-nCoV has caused
widespread outbreak awareness not only among public
health professionals (ie, WHO and government health
authorities), but also among the general public in
China and other countries, the transmissibility of the
epidemic might be reduced compared with its nascent
stage at Wuhan because of community-wide social
distancing measures and other non-pharmaceutical
interventions (eg, use of face masks and improved
personal hygiene). Previous studies sug gested that
non-pharmaceutical interventions might be able to
reduce influenza transmission by up to 50%.36 As such,
we simulated local epidemics across mainland China
assuming that the transmissibility of 2019-nCoV was
reduced by 0%, 25%, and 50% after Wuhan was
quarantined on Jan 23, 2020. The epidemics would fade
out if transmissibility could be reduced by 1–1/R0.
Further more, we considered 50% reduction in inter-
city mobility. Finally, we hypothesised that citywide
population quarantine at Wuhan had negligible eect
on the epidemic trajectories of the rest of the country
and tested this hypothesis by making the extreme
assumption that all inbound and outbound mobility at
Wuhan were eliminated indefinitely on Jan 23, 2020.
Role of the funding source
The funder of the study had no role in study design, data
collection, data analysis, data interpretation, or writing of
the report. The corresponding author had full access to
all the data in the study and had final responsibility for
the decision to submit for publication.
Results
Figure 2 summarises our estimates of the basic repro-
ductive number R0 and the outbreak size of 2019-nCoV in
Wuhan as of Jan 25, 2020. In our baseline scenario, we
estimated that R0 was 2·68 (95% CrI 2·47–2·86) with an
epidemic doubling time of 6·4 days (95% CrI 5·8–7·1;
figure 2). We estimated that 75 815 individuals (95% CrI
37 304–130 330) individuals had been infected in
=
L
W,I
N
(E(t) + I(t))λ(t)

d = ∫d – 1(u)d
u
d
L
(R0) =
d
e– dx
d
xd!
D
e
d=D
s
Π
—
Number of air passengers per
month in 2019
Bangkok 16 202
Hong Kong* 7531
Seoul 5982
Singapore 5661
Tokyo 5269
Taipei 5261
Kota Kinabalu 4531
Phuket 4411
Macau 3731
Ho Chi Minh City 3256
Kaohsiung 2718
Osaka 2636
Sydney 2504
Denpasar-Bali 2432
Phnom Penh 2000
London 1924
Kuala Lumpur 1902
Melbourne 1898
Chiang Mai 1816
Dubai 1799
Data were obtained from the Official Airline Group. *Due to the ongoing social
unrest since June, 2019, we used actual flight volume based on local estimates in
the models.
Table 2: Cities outside of mainland China to which Wuhan had the
greatest volume of outbound air travel in January–February, 2019

Articles
6
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
Greater Wuhan as of Jan 25, 2020. We also estimated
that Chongqing, Beijing, Shanghai, Guangzhou, and
Shenzhen, had imported 461 (227–805), 113 (57–193),
98 (49–168), 111 (56–191), and 80 (40–139) infections from
Wuhan, respectively (figure 3). Beijing, Shanghai,
Guangzhou, and Shenzhen were the mainland Chinese
cities that together accounted for 53% of all outbound
international air travel from China and 69% of inter-
national air travel outside Asia, whereas Chongqing is a
large metropolis that has a population of 32 million and
very high ground trac volumes with Wuhan. Substantial
epidemic take-o in these cities would thus contribute to
the spread of 2019-nCoV within and outside mainland
China.
If the zoonotic force of infection that initiated the
Wuhan epidemic was 50% and 100% higher than the
baseline scenario value, then R0 would be 2·53 (95% CrI
2·32–2·71) and 2·42 (2·22–2·60), respectively. The cor-
responding estimate of the number of infections in
Wuhan would be 38% and 56% lower than baseline. The
number of exported cases and infections in Chongqing,
Beijing, Shanghai, Guangzhou, and Shenzhen would be
similarly reduced in magnitude (figure 3).
Figure 4 shows the epidemic curves for Wuhan,
Chongqing, Beijing, Shanghai, Guangzhou, and Shenzhen
with a R0 of 2·68, assuming 0%, 25%, or 50% decrease
in transmissibility across all cities, together with 0% or
50% reduction in inter-city mobility after Wuhan was
quarantined on Jan 23, 2020. The epidemics would
fade out if transmissibility was reduced by more than
1–1/R0=63%. Our estimates suggested that a 50% reduc-
tion in inter-city mobility would have a negligible eect
on epidemic dynamics. We estimated that if there was
no reduction in trans missibility, the Wuhan epidemic
would peak around April, 2020, and local epidemics across
cities in mainland China would lag by 1–2 weeks.
If transmissibility was reduced by 25% in all cities
domestically, then both the growth rate and magnitude of
local epidemics would be substantially reduced; the
epidemic peak would be delayed by about 1 month and its
magnitude reduced by about 50%. A 50% reduction in
transmissibility would push the viral reproductive number
to about 1·3, in which case the epidemic would grow
slowly without peaking during the first half of 2020.
However, our simulation suggested that wholesale
quarantine of population movement in Greater Wuhan
would have had a negligible eect on the forward
Figure 3: Estimated number of cases exported to the Chinese cities to which Wuhan has the highest outbound travel volumes
Estimates are as of Jan 26, 2020. Data are posterior means with 95% CrIs. FOI=force of infection.
0
100
200
300
400
500
600
700
800
Number of infections
City
Chongqing
Beijing
Shanghai
Guangzhou
Shenzhen
Chengdu
Zhengzhou
Changsha
Nanchang
Hefei
Nanjing
Hangzhou
Wenzhou
Kunming
Xiamen
Haikou
Tianjin
Nanning
Xi’an
Qingdao
Base case
50% higher zoonotic FOI
100% higher zoonotic FOI
Figure 2: Posterior distributions of estimated basic reproductive number and estimated outbreak size in
greater Wuhan
Estimates are as of Jan 25, 2020. Cases corresponded to infections that were symptomatic or infectious.
The number of cases was smaller than the number of infections because some individuals with the infection were
still in the incubation period. We assumed that infected individuals were not infectious during the incubation
period (ie, similar to severe acute respiratory syndrome-related coronavirus37). PDF=probability density function.
FOI=force of infection.
2 2·5 3
0
1
2
3
4
5
6
7
PDF
Basic reproductive number
0 50 100
0
0·2
0·4
0·6
0·8
1·0
Number of cases (1000s)
0 100 10015050
0
0·1
0·2
0·3
0·4
0·5
Number of infections (1000s)
Base case
50% higher zoonotic FOI
100% higher zoonotic FOI

Articles
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
7
trajectories of the epidemic because multiple major
Chinese cities had already been seeded with more than
dozens of infections each (results not shown because they
are visually indistinguishable from figure 4). The proba-
bility that the chain of transmission initiated by an infected
case would fade out without causing exponential epidemic
growth decreases sharply as R0 increases (eg, <0·2 when
R0 >2).1,38 As such, given the substantial volume of case
importation from Wuhan (figure 3), local epidemics are
probably already growing exponentially in multiple major
Chinese cities. Given that Beijing, Shanghai, Guangzhou,
and Shenzhen together accounted for more than 50% of
all outbound interna tional air travel in mainland China,
other countries would likely be at risk of experiencing
2019-nCoV epidemics during the first half of 2020.
Discussion
During the period of an epidemic when human-to-human
transmission is established and reported case numbers
are rising exponentially, nowcasting and forecasting are
of crucial importance for public health planning and
control domestically and internationally. 39,40 In this study,
we have estimated the outbreak size of 2019-nCoV thus
far in Wuhan and the probable extent of disease spread to
other cities domestically. Our findings suggest that
independent self-sustaining human-to-human spread is
already present in multiple major Chinese cities, many of
which are global transport hubs with huge numbers of
both inbound and outbound passengers (eg, Beijing,
Shanghai, Guangzhou, and Shenzhen).
Therefore, in the absence of substantial public health
interventions that are immediately applied, further
international seeding and subsequent local establishment
of epidemics might become inevitable. On the present
trajectory, 2019-nCoV could be about to become a global
epidemic in the absence of mitigation. Nevertheless, it
might still be possible to secure containment of the
spread of infection such that initial imported seeding
cases or even early local transmission does not lead to a
large epidemic in locations outside Wuhan. To possibly
succeed, substantial, even draconian measures that limit
population mobility should be seriously and immediately
considered in aected areas, as should strategies to
drastically reduce within-population contact rates through
cancellation of mass gatherings, school closures, and
instituting work-from-home arrange ments, for example.
Precisely what and how much should be done is highly
contextually specific and there is no one-size-fits-all set of
prescriptive interventions that would be appropriate
across all settings. Should containment fail and local
transmission is established, mitigation measures
according to plans that had been drawn up and executed
during previous major outbreaks, such as those of SARS,
MERS, or pandemic influenza, could serve as useful
reference templates.
The overriding epidemiological priority to inform
public health control would be to compile and release a
line list of suspected, possible, probable, and confirmed
cases and close contacts that is updated daily and linked
to clinical outcomes and laboratory test results. A robust
line list is essential for the generation of accurate and
precise epidemiological parameters as inputs into
transmission models to inform situational awareness
and optimising the responses to the epidemic.41 Addi-
tionally, given the extent of spread and level of public
concern it has already generated, the clinical spectrum
and severity profile of 2019-nCoV infections needs rapid
ascertainment by unbiased and reliable methods in
unselected samples of cases, especially those with mild
or subclinical presentations.
The modelling techniques that we used in this study are
very similar to those used by other researchers who are
working towards the same goal of characterising the
epidemic dynamics of 2019-nCoV (Zhanwei Du, University
of Texas at Austin, personal communication).42–45 The
consensus on our methodology provides some support for
the validity of our nowcasts and forecasts. An additional
strength of our study is that our model is parameterised
with the latest mobility data from OAG and Tencent.
Nonetheless, our study has several major limitations.
First, we assumed that travel behaviour was not aected
by disease status and that all infections eventually
have symptoms (albeit possibly very mild). We would
have underestimated the outbreak size in Greater Wuhan
if individuals with increased risk of infection (eg,
confounded by socioeconomic status) were less likely to
travel internationally or if the proportion of asymptomatic
0
10
20
30
40
Daily incidence
(per 1000 population)
0% transmissibility reduction
50% mobility reduction
25% transmissibility reduction
50% mobility reduction
Jan 1, 2020
Feb 1, 2020
March 1, 2020
April 1, 2020
May 1, 2020
June 1, 2020
July 1, 2020
Jan 1, 2020
Feb 1, 2020
March 1, 2020
April 1, 2020
May 1, 2020
June 1, 2020
July 1, 2020
Jan 1, 2020
Feb 1, 2020
March 1, 2020
April 1, 2020
May 1, 2020
June 1, 2020
July 1, 2020
50% transmissibility reduction
50% mobility reduction
0
10
20
30
40
Daily incidence
(per 1000 population)
0% transmissibility reduction
No mobility reduction
25% transmissibility reduction
No mobility reduction
50% transmissibility reduction
No mobility reduction
Wuhan Chongqing Beijing Shanghai Guangzhou Shenzhen
Figure 4: Epidemic forecasts for Wuhan and five other Chinese cities under different scenarios of reduction in
transmissibility and inter-city mobility

Articles
8
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
infections were substantial. Second, our estimate of
transmis sibility and outbreak size was somewhat sensitive
to our assumption regarding the zoonotic mechanism
that initiated the epidemic at Wuhan. However, our overall
conclusion regarding the extent of case exportation in
major Chinese cities would remain the same even for our
lowest estimate of transmissibility (figure 3). Third, our
epidemic forecast was based on inter-city mobility data
from 2019 that might not necessarily reflect mobility
patterns in 2020, especially in the presence of current
public vigilance and response regarding the health threat
posed by 2019-nCoV (appendix p 5). Fourth, little is known
regarding the seasonality of coro navirus transmission. If
2019-nCoV, similar to influenza, has strong seasonality in
its transmission, our epidemic forecast might not be
reliable.
Identifying and eliminating the zoonotic source
remains an important task to prevent new animal-to-
human seeding events. The renewal of a complete ban
on market trading and sale of wild game meat in China
on Jan 26 can provide only temporary suspension of
demand, even if completely adhered to.46 Vaccine
platforms should be accelerated for real-time deployment
in the event of a second wave of infections. Above all, for
health protection within China and internationally,
especially those loca tions with the closest travel links
with major Chinese ports, preparedness plans should
be readied for deploy ment at short notice, including
securing supply chains of pharmaceuticals, personal
pro tective equipment, hospital supplies, and the
necessary human resources to deal with the
consequences of a global outbreak of this magnitude.
Contributors
JTW, GML, and KL designed the experiments. KL collected data.
JTW and KL analysed data. KL, JTW, and GML interpreted the results
and wrote the manuscript.
Declaration of interests
We declare no competing interests.
Data sharing
Data obtained for this study will not be made available to others.
Acknowledgments
We thank Chi-Kin Lam and Miky Wong from School of Public Health,
The University of Hong Kong (Hong Kong, China) for technical support.
This research was supported by a commissioned grant from the Health
and Medical Research Fund from the Government of the Hong Kong
Special Administrative Region.
Editorial note: the Lancet Group takes a neutral position with respect to
territorial claims in published maps and institutional aliations.
References
1 Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. Superspreading
and the eect of individual variation on disease emergence. Nature
2005; 438: 355–59.
2 Chowell G, Castillo-Chavez C, Fenimore PW, Kribs-Zaleta CM,
Arriola L, Hyman JM. Model parameters and outbreak control for
SARS. Emerg Infect Dis 2004; 10: 1258–63.
3 Riley S, Fraser C, Donnelly CA, et al. Transmission dynamics of the
etiological agent of SARS in Hong Kong: impact of public health
interventions. Science 2003; 300: 1961–66.
4 Lipsitch M, Cohen T, Cooper B, et al. Transmission dynamics and
control of severe acute respiratory syndrome. Science 2003;
300: 1966–70.
5 Chowell G, Abdirizak F, Lee S, et al. Transmission characteristics of
MERS and SARS in the healthcare setting: a comparative study.
BMC Med 2015; 13: 210.
6 Kucharski AJ, Althaus C. The role of superspreading in Middle East
respiratory syndrome coronavirus (MERS-CoV) transmission.
Euro Surveill 2015; 20: 14–18.
7 Cauchemez S, Nouvellet P, Cori A, et al. Unraveling the drivers of
MERS-CoV transmission. Proc Natl Acad Sci USA 2016; 113: 9081–86.
8 Park J-E, Jung S, Kim A, Park JE. MERS transmission and risk
factors: a systematic review. BMC Public Health 2018; 18: 574.
9 Walsh EE, Shin JH, Falsey AR. Clinical impact of human
coronaviruses 229E and OC43 infection in diverse adult
populations. J Infect Dis 2013; 208: 1634–42.
10 Zhang SF, Tuo JL, Huang XB, et al. Epidemiology characteristics of
human coronaviruses in patients with respiratory infection
symptoms and phylogenetic analysis of HCoV-OC43 during
2010-2015 in Guangzhou. PLoS One 2018; 13: e0191789.
11 Gaunt ER, Hardie A, Claas EC, Simmonds P, Templeton KE.
Epidemiology and clinical presentations of the four human
coronaviruses 229E, HKU1, NL63, and OC43 detected over 3 years
using a novel multiplex real-time PCR method. J Clin Microbiol
2010; 48: 2940–47.
12 Leung GM, Hedley AJ, Ho LM, et al. The epidemiology of severe
acute respiratory syndrome in the 2003 Hong Kong epidemic:
an analysis of all 1755 patients. Ann Intern Med 2004; 141: 662–73.
13 Lau EH, Hsiung CA, Cowling BJ, et al. A comparative epidemiologic
analysis of SARS in Hong Kong, Beijing and Taiwan. BMC Infect Dis
2010; 10: 50.
14 Virlogeux V, Fang VJ, Park M, Wu JT, Cowling BJ. Comparison of
incubation period distribution of human infections with
MERS-CoV in South Korea and Saudi Arabia. Sci Rep 2016;
6: 35839.
15 Vijgen L, Keyaerts E, Moës E, et al. Complete genomic sequence of
human coronavirus OC43: molecular clock analysis suggests a
relatively recent zoonotic coronavirus transmission event. J Virol
2005; 79: 1595–604.
16 Lessler J, Reich NG, Brookmeyer R, Perl TM, Nelson KE,
Cummings DA. Incubation periods of acute respiratory viral
infections: a systematic review. Lancet Infect Dis 2009; 9: 291–300.
17 Mason R, Broaddus VC, Martin T, et al. Murray and Nadel’s textbook
of respiratory medicine, 5th edn. Amsterdam: Elsevier, 2010.
18 Cowling BJ, Park M, Fang VJ, Wu P, Leung GM, Wu JT. Preliminary
epidemiological assessment of MERS-CoV outbreak in South Korea,
May to June 2015. Euro Surveill 2015; 20: 7–13.
19 Leung GM, Lim WW, Ho LM, et al. Seroprevalence of IgG
antibodies to SARS-coronavirus in asymptomatic or subclinical
population groups. Epidemiol Infect 2006; 134: 211–21.
20 Al Kahlout RA, Nasrallah GK, Farag EA, et al. Comparative
serological study for the prevalence of anti-MERS coronavirus
antibodies in high-and low-risk groups in Qatar. J Immunol Res
2019; published online Feb 18. DOI:10.1155/2019/1386740.
21 Abbad A, Perera RA, Anga L, et al. Middle East respiratory
syndrome coronavirus (MERS-CoV) neutralising antibodies in a
high-risk human population, Morocco, November 2017 to
January 2018. Euro Surveill 2019; 24: 1900244.
22 Gill EP, Dominguez EA, Greenberg SB, et al. Development and
application of an enzyme immunoassay for coronavirus OC43
antibody in acute respiratory illness. J Clin Microbiol 1994;
32: 2372–76.
23 Chan CM, Tse H, Wong SS, et al. Examination of seroprevalence of
coronavirus HKU1 infection with S protein-based ELISA and
neutralization assay against viral spike pseudotyped virus.
J Clin Virol 2009; 45: 54–60.
24 Oh MD, Park WB, Park SW, et al. Middle East respiratory
syndrome: what we learned from the 2015 outbreak in the Republic
of Korea. Korean J Intern Med 2018; 33: 233–46.
25 Patrick DM, Petric M, Skowronski DM, et al. An outbreak of human
coronavirus OC43 infection and serological cross-reactivity with
SARS coronavirus. Can J Infect Dis Med Microbiol 2006; 17: 330–36.
26 Matsuno AK, Gagliardi TB, Paula FE, et al. Human coronavirus
alone or in co-infection with rhinovirus C is a risk factor for severe
respiratory disease and admission to the pediatric intensive care
unit: a one-year study in Southeast Brazil. PLoS One 2019;
14: e0217744.

Articles
www.thelancet.com Published online January 31, 2020 https://doi.org/10.1016/S0140-6736(20)30260-9
9
27 Jia N, Feng D, Fang LQ, et al. Case fatality of SARS in mainland
China and associated risk factors. Trop Med Int Health 2009;
14 (suppl 1): 21–27.
28 Breban R, Riou J, Fontanet A. Interhuman transmissibility of
Middle East respiratory syndrome coronavirus: estimation of
pandemic risk. Lancet 2013; 382: 694–99.
29 Cauchemez S, Fraser C, Van Kerkhove MD, et al. Middle East
respiratory syndrome coronavirus: quantification of the extent of
the epidemic, surveillance biases, and transmissibility.
Lancet Infect Dis 2014; 14: 50–56.
30 Hung LS. The SARS epidemic in Hong Kong: what lessons have we
learned? J R Soc Med 2003; 96: 374–78.
31 McDonald LC, Simor AE, Su IJ, et al. SARS in healthcare facilities,
Toronto and Taiwan. Emerg Infect Dis 2004; 10: 777–81.
32 People’s Daily Online. Wuhan is expected to send 15 million
passengers during Spring Festival in 2020 (in Chinese).
Dec 28, 2019. http://hb.people.com.cn/n2/2019/1228/c194063-
33671662.html (accessed Jan 2, 2020).
33 The 2019-nCoV Outbreak Joint Field Epidemiology Investigation
Team, Li Q. An outbreak of NCIP (2019-nCoV) infection in China—
Wuhan, Hubei Province, 2019–2020. China CDC Weekly 2020;
2: 79–80.
34 Li Q, Guan X, Wu P, et al. Early transmission dynamics in Wuhan,
China, of novel coronavirus-infected pneumonia. N Engl J Med
2020; published online Jan 29. DOI:10.1056/NEJMoa2001316.
35 Wang L, Wu JT. Characterizing the dynamics underlying global
spread of epidemics. Nat Commun 2018; 9: 218.
36 Bootsma MC, Ferguson NM. The eect of public health measures
on the 1918 influenza pandemic in U.S. cities.
Proc Natl Acad Sci USA 2007; 104: 7588–93.
37 Centers for Disease Control and Prevention. Frequently asked
questions about SARS. 2005. https://www.cdc.gov/sars/about/faq.
html (accessed Jan 25, 2020).
38 Diekmann O, Heesterbeek JAP. Mathematical epidemiology of
infectious diseases: model building, analysis and interpretation.
Chichester: John Wiley, 2000.
39 Desai AN, Kraemer MUG, Bhatia S, et al. Real-time epidemic
forecasting: challenges and opportunities. Health Secur 2019;
17: 268–75.
40 Polonsky JA, Baidjoe A, Kamvar ZN, et al. Outbreak analytics:
a developing data science for informing the response to emerging
pathogens. Philos Trans R Soc Lond B Biol Sci 2019; 374: 20180276.
41 Lipsitch M, Finelli L, Heernan RT, Leung GM, Redd SC. Improving
the evidence base for decision making during a pandemic: the example
of 2009 influenza A/H1N1. Biosecur Bioterror 2011; 9: 89–115.
42 Imai N, Cori A, Dorigatti I, et al. MRC Centre for Global Infectious
Disease Analysis: Wuhan coronavirus reports 1–3. January, 2020.
https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/
news--wuhan-coronavirus (accessed Jan 25, 2020).
43 Read JM, Bridgen JRE, Cummings DAT, Ho A, Jewell CP.
Novel coronavirus 2019-nCoV: early estimation of epidemiological
parameters and epidemic predictions. medRxiv 2020; published
online Jan 24. DOI:10.1101/2020.01.23.20018549 (preprint).
44 Liu T, Hu J, Kang M, et al. Transmission dynamics of 2019 novel
coronavirus (2019-nCoV). bioRxiv 2020; published online Jan 26.
DOI:10.1101/2020.01.25.919787 (preprint).
45 Zhao S, Ran J, Musa SS, et al. Preliminary estimation of the basic
reproduction number of novel coronavirus (2019-nCoV) in China,
from 2019 to 2020: a data-driven analysis in the early phase of the
outbreak. bioRxiv 2020; published online Jan 24.
DOI:10.1101/2020.01.23.916395 (preprint).
46 State Administration for Market Regulation. Announcement of the
State Administration of Market Supervision, Ministry of Agriculture
and Rural Aairs, and the National Forestry and Grass Bureau on
banning wildlife trading (in Chinese). Jan 26, 2020. http://gkml.
samr.gov.cn/nsjg/wjs/202001/t20200126_310742.html (accessed
Jan 25, 2020).