Abstract
73
Main: 2048
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Abstract
An outbreak of COVID-19 developed aboard the Princess Cruises Ship during
January-February 2020. Using mathematical modeling and time-series incidence data
describing the trajectory of the outbreak among passengers and crew members, we
characterize how the transmission potential varied over the course of the outbreak. Our
estimate of the mean reproduction number in the confined setting reached values as high
as ~11, which is higher than mean estimates reported from community-level transmission
dynamics in China and Singapore (approximate range: 1.1-7). Our findings suggest that
R
t decreased substantially compared to values during the early phase after the Japanese
government implemented an enhanced quarantine control. Most recent estimates of Rt
reached values largely below the epidemic threshold, indicating that a secondary
outbreak of the novel coronavirus was unlikely to occur aboard the Diamond Princess
Ship.
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Introduction
While the novel coronavirus (Covid-19) spread rapidly throughout China for several
weeks since December 2019, the virus had not taken off outside China in part due to the
unprecedented social distancing measures that the Chinese government put in place.
One exception is the outbreak of COVID-19 that developed aboard the Diamond
Princess Ship which was detected in early February when one of its passengers, a
traveler from Hong Kong, tested positive for the novel coronavirus. The number of
cases in the Diamond Princess Ship quickly jumped to 454 confirmed cases by February
18, 2020. In contrast, the total number of cases in Singapore, one of the countries with
the highest number of COVID-19 cases after China, was only 77 at the time [1].
Accumulating evidence indicates that the novel coronavirus can spread widely in
confined settings including hospitals [2], cruise ships [3], prisons, and churches [4-5]. In
Wuhan City, China, outbreaks inside health care settings led to the infection of
hundreds of health professionals [2]. In Tokyo, Japan, most of the reported infections
have been linked to a party inside a traditional wooden ship, called Yakatabune [6]
while most of the infections in Korea have affected members of one church and one
hospital.
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Tracking the evolution of the transmission potential of COVID-19 in different confined
settings and how it compares with that of other respiratory diseases such influenza has
public health implications. When outbreaks occur in confined settings, it is useful to
investigate how the effective reproduction number changes as a result of interventions
strategies such as the quarantine that the Japanese government imposed on travelers and
crew members aboard the Diamond Princess Ship.
In this study we sought to characterize the temporal variation in the transmission potential
of the COVID-19 outbreak aboard the Princess Cruises Ship using mathematical
modeling and time-series incidence data by dates of symptoms onset describing the
trajectory of the outbreak among passengers and crew members.
Epidemiological incidence cases
In Yokohama, Japan, an outbreak of COVID-19 has been unfolding on board the
Princess Cruise Ship, which has been under quarantine orders since February 5, 2020,
after a former passenger of the Diamond Princess Ship tested positive for the virus after
disembarking in Hong Kong [3,7]. As of February 22, 2020, two days after the
scheduled two-week quarantine came to an end, a total of 621 symptomatic and
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asymptomatic people including one quarantine officer, one nurse and one administrative
officer tested positive for COVID-19 out of the 3,711 passengers and crew members on
board. Laboratory tests by PCR that prioritize symptomatic or high-risk groups have
been conducted.
Incidence curves of laboratory-confirmed symptomatic cases of COVID-19
among passengers and crew members of the outbreak unfolding aboard the Princess
Cruises Ship are publicly available from the National Institute of Infectious Diseases,
Japan (NIID) website [3]. Daily time series of symptomatic patients, from January 20,
2020 to February 18, 2020 were extracted. However, to reconstruct the trajectory of the
epidemic, only 197 cases have dates of symptoms onset are available out of a total of
300 confirmed symptomatic cases.
Of the 103 symptomatic cases with missing onset dates, a total of the 79 cases
are passengers while 24 cases are crew members. Moreover, out of the 79 passenger
cases, 30 cases were reported from February 4, 2020 to February 6, 2020, 21 cases were
reported from February 7, 2020 to February 14, 2020, and 28 cases were reported from
February 14, 2020 to February 19, 2020. Of 24 crew member cases, 1 case was reported
from February 4, 2020 to February 6, 2020, 15 cases were reported from February 7,
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2020 to February 14, 2020, and 8 cases were reported from February 14, 2020 to
February 19, 2020.
Epidemiological modelling
We connected the daily incidence series with a discrete–time integral equation
to describe the epidemic dynamics aboard the Diamond Princess Ship. Specifically, let
f
s denote the probability mass function of the serial interval of COVID-19, where the
serial interval is defined as the time from illness onset in the primary case to time of
illness onset in the secondary case. Then f
s, of length s days, is given by
/g1858 /g2929/g3404/g1832 /g4666 s /g4667 /g3398/g1832 /g4666 s/g33981 /g4667 .
For s>0, F(s) represents the cumulative distribution function of the gamma distribution.
We characterized the expected number of new incident cases E[ci,t] in type i at symptom
onset week t as follows,
E /g3427 /g1855 /g3036,/g3047 /g3431 /g3404/g3533 /g1870 /g3036/g3037,/g3047
/g3037
/g3533/g1855 /g3037,/g3047/g2879/g3046, /g1858 /g3046
/g2998
/g3046/g2880/g2869
,
where rij denotes the average number of cases of type i infected by a single individual of
type j. Here we assume that the incidence, ci,t, follows a Poisson sampling process with
expected value E[ci,t].
The reproduction matrix for each type is given by
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M /g2930 /g3404/g4672 /g1870 /g2869/g2869,/g3047 /g1870 /g2869/g2870,/g3047
/g1870 /g2870/g2869,/g3047 /g1870 /g2870/g2870,/g3047
/g4673.
This matrix is referred to as a next-generation matrix (NGM) in a fully susceptible
population [8]. Using this matrix, we derive the instantaneous time-dependent effective
reproduction number, R
t, for the entire transmission dynamics from the largest
eigenvalue of the NGM. Under the assumption that the per-contact infection probability
and the generation interval are consistent over time regardless of the type of infection,
the NGM quantifies the within type and inter-type patterns of transmission [9]. The sum
of the value in column j is the reproduction number for a specific type j.
Serial interval estimates of COVID-19 were derived from previous studies of
COVID-19, indicating that it follows a gamma distribution with the mean and SD at 7.5
and 3.4 days, respectively, based on ref. [10]. The maximum value of the serial interval
was fixed at 20 days as the cumulative probability distribution of the gamma
distribution up to 20 days reaches 0.991.
We estimated model parameters and made projections using a Monte Carlo
Markov Chain (MCMC) method in a Bayesian framework. Point estimates and
corresponding 95% credibility intervals were drawn from the posterior probability
distribution. All statistical analyses were conducted in R version 3.5.2 (R Foundation
for Statistical Computing, Vienna, Austria) and the ‘rstan’ package
(No-U-Turn-Sampler (NUTS)).
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Result
A summary of the COVID-19 confirmed cases by age group and symptom
status onboard the Princess Cruises Ship is illustrated in Table 2. A total of 531 people
had tested positive for the illness as of February 5, 2020. Out of 531 cases, three cases
were aged 0-19 years, 117 were aged 20-58 years and 411 were aged 60 years and older.
Finally, the crude asymptomatic ratio, a simple proportion of asymptomatic infections
among all the infections was estimated as follows: 66.7% (95%Confidence Interval
(95%CI): 9.4%, 99.1%) for aged 0-19 years, 30.8% (95%CI: 22.6%, 40.0%) for aged
20-58 years and 52.8% (95%CI: 47.9%, 57.5%) for aged 60 years and older (95%CI is
based on binomial distribution).
The observed and estimated daily number of cases among passengers and crew
members from day 1 to day 29 (January 20, 2020–February 17, 2020) are shown in
Figure 1. The total number of cases for all and by type (passengers and crew members)
were estimated at 187.0 (95%CrI: 163.8, 212.3), 127.1 (95%CrI: 107.8, 148.9) and 59.6
(95%CrI: 47.3, 74.0), respectively. For comparison, the number of reported cases for all
and by type were 197, 149 and 48 respectively. The corresponding percentage coverage
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of the 95%CrI of estimated data for observed data, the number of days where the model
95% CrI overlapped with the observed data, is 54% (15/28) for all, and 50% (14/28) and
43% (12/28) for passenger and crew, respectively.
The time-dependent reproduction number for all and by type are presented in
Figure 2. For all, R
t rapidly increased at around day 12 (January 31, 2020) and reached
its maximum with the value of 11.2 (95%CrI: 7.5, 16.2) at day 19 (February 7, 2020). Rt
for passengers presented a similar pattern with the value of 12.1 (95%CrI: 8.2, 17.2) at
day 19 (February 7, 2020), while R
t for crew members only shows slight fluctuations
with the largest value reaching 1.56 (95%CrI: 0.07, 7.55) at day 23 (February 11, 2020).
Distributions of median Rt for entire study period for overall, for type and by
each transmission type are shown in Figure 3. Median Rt are 5.8 (95%CrI: 0.6-11.0), 6.1
(95%CrI: 0.5, 11.8), 0.9 (95%CrI: 0.3, 1.5) for overall and by type (passenger, crew).
Examining inter-type and within-type transmission, R
t estimates greatly vary across
transmission types: 5.6 (95%CrI: 0.3, 10.9) for passenger to passenger, 0.6 (95%CrI:
0.1, 1.1) for passenger to crew, 0.5 (95%CrI: 0.2, 0.8) for crew to passenger, 0.5
(95%CrI: 0.3, 0.8) for crew to crew. Although vaccines are still in early development
stages as of February 2020, based on our findings, the corresponding target vaccination
coverage to contain the outbreak in this confined setting were estimated at 91% and
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94% from the maximum value of the 50 percentile distribution and the 97.5 percentile
distribution, respectively.
Our latest estimate of the overall Rt is 0.35 (95%CrI: 0.02, 2.19), with only 2%
of Rt estimates lying above the epidemic threshold of 1.0. Passenger and crew also have
total (within-type and inter-type) Rt values largely below the epidemic threshold, with
only small percentages at 0% and 9% above the epidemic threshold, respectively (Table
3).
Discussion
This is the first study to assess the transmission potential of the COVID-19 outbreak that
unfolded aboard the Diamond Princess Ship, January-February 2020. The overall mean
reproduction number in the confined setting reached values as high as ~11, which is
higher than mean estimates reported from community-level transmission dynamics in
China and Singapore in the range 1.1-7 [10-16]. However, following the implementation
of the quarantine period, the overall R
t decreased substantially compared to values
estimated during the early stage, but it exhibited fluctuations around the epidemic
threshold, which likely prolonged the outbreak.
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Our results indicate that Rt declined following the quarantine measures implemented by
the Japanese government on February 5 relative to values during the early phase of the
outbreak [3]. Importantly, only those passengers and crew who tested positive for the
novel coronavirus were permitted to disembark the Diamond Princess Ship, with more
than 80 percentage of the passengers and crews still on board as of February 18, 2020.
Our latest overall estimate of R
t at 0.35 (95%CrI: 0.02, 2.19) with only 2% of Rt
estimates lying above the epidemic threshold of 1.0 suggested a low probability of
observing a subsequent outbreak aboard the Diamond Princess Ship.
Our findings indicate that the passenger-to-passenger transmission type dominated the
transmission dynamics aboard the Diamond Princess Ship. The rapid increase in the
overall R
t from day 12 (January 31, 2020) to day 19 (February 7, 2020) is greatly
influenced by the increase in passenger-to-passenger transmission, and this time period
covers the time lag between February 1, 2020 when the index COVID-19 case was
reported and February 5, 2020 when the Japanese government requested the passengers
to stay inside their cabin after the detection of a cluster of COVID-19 positive cases [3,
17]. Upon the implementation of the quarantine orders, the overall R
t and Rt for
passengers aboard the Diamond Princess Ship declined thereafter, while Rt among crew
maintained a steady level and only started to decline on day 25 of the outbreak
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(February 13, 2020). This is consistent with the fact that passengers staying inside their
cabins led to a substantial decline in passenger-to-passenger transmission type except
for their interaction with cabin mates. Indeed, the proportion of secondary infections
inside the cabins increased from 7% (1/15) on February 6, 43% (3/7) on February 10,
2020 to 100% (1/1) on February 14, 2020 [3]. Thus, a high proportion of the
symptomatic cases after the quarantine gradually shifted from largely passenger cases to
crew cases. Indeed, despite their potential risk of acquiring the infection, crews had to
continue to work to deliver services to isolated passengers. The distribution of the
median Re by transmission type suggests that other transmission types likely
contributed to this outbreak to some extent (Figure 3). Because one quarantine officer,
one nurse, and one administrative officer contracted COVID-19 aboard the Diamond
Princess Ship, the infection risk continued to be significant inside the Diamond Princess
Ship.
As for the crude asymptomatic ratios by age groups, they show significant differences
across age groups. However, these crude ratios are severely influenced by the timing of
specimen collection relative to the infection time [19]. Hence, these ratios could be
better ascertained if additional data with the timing of specimen collection becomes
available.
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Several limitations should be listed. First, a total of 103 laboratory-confirmed
symptomatic cases with unknown onset dates were not incorporated in our analysis.
Although the high proportion of unavailable data (34% (103/300)) likely influenced a
downward bias in estimates of transmission potential, our estimates still point to the
high transmission potential of COVID-19 inside confined settings. Second, it is possible
that reporting delays could have influenced our latest estimates of the effective
reproduction number. In fact, the US government recently sent a chartered flight to
transport the American passengers on board the Diamond Princess Ship, and after the
disembarkation process, a total of 14 American passengers tested positive for the
disease [18] on February 16, 2020. This event also contributes to a downward bias in R
although the number of cases does not exceed the peak of the outbreak, further
supporting the potent transmissibility of COVID-19 in confined settings.
Our most recent estimate of the effective reproduction number of the ongoing
COVID-19 epidemic on board the Diamond Princess Ship was largely below the
epidemic threshold of 1.0, which suggested a very low probability of observing
secondary outbreaks of the disease in the Diamond Princess Ship.
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Figure 1. Observed and estimated number of the New Coronavirus (COVID-19)
cases by type, onboard the Princess Cruises Ship, 2020 (n = 197)
(A) - (C) Comparison of observed and predicted daily numbers of new cases by type.
Black dots shows observed data, and light and dark indicates 95% and 50% credible
intervals for posterior estimates, respectively. Day 1 on horizontal axis corresponds to
January 20, 2020.
Figure 2. Time-dependent effective reproduction number of COVID-19 onboard
the Princess Cruises Ship, 2020
The overall effective reproduction number were calculated from the dominant
eigenvalue of next-generation matrix. Light and dark indicates 95% and 50% credible
intervals for posterior estimates, respectively. Day 1 on horizontal axis corresponds to
January 20, 2020. Horizontal grey dashed line shows the reproduction number at 1.0 for
reference, below which incidence declines. Vertical dashed line indicates the day when
quarantine was implemented (February 5, 2020).
Figure 3. Distribution of median effective reproduction number for overall and by
transmission type, onboard the Princess Cruises Ship, 2020
P: Passenger, C: Crew
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Tables
Table 1– The whole voyage of the Princess Cruises Ship and important events related to
the outbreak
Day Date Event
1 Jan/20/2020 Departed from the Port of Yokohama
Index case embarked
6 Jan/25/2020 Arrived at the Port of Hong Kong
Index case disembarked in Hong Kong
Departed from the Port of Hong Kong
8 Jan/27/2020
Arrived at the Port of Chan May (Vietnam)
Departed from the Port of Chan May (Vietnam)
9 Jan/28/2020 Arrived at the Port of Cai Lan (Vietnam)
Departed from the Port of Cai Lan (Vietnam)
12 Jan/31/2020 Arrived at the Port of Keelung (Taiwan)
Departed from the Port of Keelung (Taiwan)
13 Feb/1/2020 Arrived at the Port of Naha (Japan)
Departed from the Port of Naha (Japan)
Index case was confirmed
16 Feb/4/2020 Arrived at the Port of Yokohama (Japan)
Passengers and crews were asked to stay on the ship for
quarantine
Health status of all passengers and crew members were
checked by questionnaire by quarantine officers
17 Feb/5/2020 A lab-confirmed case of COVID-19 was detected.
Quarantine for 14 days begins at 7am.
Passengers requested to stay in their cabins.
30 Feb/18/2020 End of quarantine
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Table 2– Summary of test positive COVID-19 cases by age group and symptom status
onboard the Princess Cruises Ship.
Age
group
Symptomatic
cases
Asymptomatic
cases*
Total Crude asymptomatic ratio‡ Persons aboard§
0-9 0 1 1 100%
(95%CI: 2.5%, 100%)
16
10- 1 1 2 50.0%
(95%CI: 1.3%, 98.7%)
23
20- 18 2 20 10.0%
(95%CI: 1.2, 31.7%)
347
30- 18 5 23 21.7%
(95%CI: 7.5%, 43.7%)
429
40- 18 7 25 28.0%
(95%CI: 12%, 49.4%)
333
50- 27 22 49 44.9%
(95%CI: 30.1%, 59.8%)
398
60- 73 56 129 43.4%
(95%CI: 2.5, 100%)
924
70- 92 136 228 59.6%
(95%CI: 53.0%, 66.1%)
1015
80- 27 25 52 48.1%
(95%CI: 34.0%, 62.3%)
215
90- 2 0 2 0%
(95%CI: 2.5%, 84.2%)
11
§ As of February 5, 2020
‡ Proportion of asymptomatic cases among all the cases. CI: Confidence Interval (CI) is
based on binomial distribution
* Symptom status is based on the information at the time of specimen collection. There
is a possibility that a fraction of asymptomatic cases develop symptom.
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19
Table 3 – The latest estimate of median effective reproduction number and fraction of
the density of R above the threshold of 1.0, February 18, 2020.
Range Percentage over 1.0
All 0.35 (95%CrI§:0.02, 2.19) 2%
Passenger Total‡ 0.19 (95%CrI: 0.00, 1.26) 0%
Within¶ (Passenger to
Passenger)
0.06 (95%CrI: 0.00, 0.73) 0%
Inter (Passenger to Crew) 0.10 (95%CrI: 0.00, 1.04) 0%
Crew Total 0.30 (95%CrI: 0.00, 3.84) 9%
Within (Crew to Crew) 0.15 (95%CrI: 0.00, 1.92) 1%
Inter (Crew to Passenger) 0.24 (95%CrI: 0.00, 2.17) 2%
§CrI: 95% credibility intervals (CrI)
‡ Total transmission includes within-type and inter-type transmission
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is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
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. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted February 28, 2020. ; https://doi.org/10.1101/2020.02.24.20027649doi: medRxiv preprint
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
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