A Major Outbreak of COVID-19 in the Diamond Princess Cruise Ship


 The COVID-19 pandemic broke out in Wuhan, China, and declared an international public health emergency by the World Health Organization in 2019. It mainly manifests as symptoms of respiratory infections, and severe cases can cause pneumonia and death. The Diamond Princess cruise ship outbroke cluster infection outside China during the early pandemic. The incident occurred on February 1, 2020, and an 80-year-old Hong Kong man was diagnosed with COVID-19. The cruise docked in Yokohama, Japan, for 14 days on-board quarantine; however, cluster infection outbroke rapidly. The results show that after 14 days of quarantine, 634 (17.1%) cases were diagnosed with a total of 3,711 population, and 328 (51.7%) cases were asymptomatic. As of April 24, 2020, 712 cases have been diagnosed and 14 deaths have occurred. A cumulative mortality rate reaches 1.96%. Using a nonlinear least-squares curve fitting with Microsoft Excel Solver, we obtain the parameters of the SIR mathematical model of infectious disease and the reproduction number (R0) of the COVID-19 outbreak is 2.37±0.26. Without an emergency evacuation plan, the total infection rate will reach 88.47%. These data show “only one” COVID-19 case could still outbreak cluster infection on large cruise ships. The possible causes and countermeasures are discussed.

Introduction by the virus. R 0 less than 1 means the disease will gradually dissipate. WHO estimates that the R 0 of COVID-19 ranges from 1.4 to 2.5 11 . Other preliminary studies have estimated that R0 ranges from 2.24 to 3.58 12 . Large-scale epidemiological studies have estimated an average R 0 = 3.77 10 .
The severity of clinical manifestations ranges from asymptomatic infection or mild illness to severe or fatal illness. Most patients have a fever, dry cough, and asthma 8 . In a study of 425 patients with pneumonia confirmed COVID-19 infection, of which 57% were male 9 . About one-third to one-half of the reported patients have underlying comorbidities, including diabetes, hypertension, and cardiovascular disease.
In terms of mortality, the official data released by China on February 4, 2020: around 2.1% worldwide, Wuhan 4.9%, Hubei Province 3.1%, and other provinces 0.16% 13 . Large-scale epidemiological studies have calculated an overall mortality rate of 3.06% 10 . However, some studies have used Wuhan Jinyintan Hospital, which treats many patients with pneumonia confirmed COVID-19 infection and has calculated a mortality rate of 11% 14 . As of September 24, 2020, total of 32,110,901 confirmed cases (85,314 in China) have been reported and 982,196 deaths in worldwide (4,634 in China), the mortality rate is 3.06% 15 .
The Diamond Princess is a cruise ship owned by Princess Cruises with a displacement of 115,875 tons. Since 2014, the port of registry is London, England. The Diamond Princess sailed from Yokohama on January 20, 2020, to Kagoshima on the 22nd, arrived in Hong Kong on the 25th, and then passed through Vietnam, Taiwan, and Okinawa. The cruise voyage is shown in After the outbreak of the incident, the Diamond Princess was anchored at the port of Yokohama, Japan on the night of February 3, and a total of 3,711 people were quarantined on-board for 14 days in private cabins. However, outbreaks of cluster infections continued to occur during the quarantine period. As of Feb 26, 705 people have been diagnosed with COVID-19, and an average of one-fifth has been diagnosed. This is the most extensive cluster infection outside China in the early pandemic 15 . Thus, it is related to epidemiology and virus spread are worth studying and discussing.
The Diamond Princess cruise ship carried a total of 3,711 people, including 2,666 tourists (including 1,285 Japanese, 470 Hong  Kong people, 425 Americans, 215 Canadians, 40 British, 25 Russians, 20 Taiwanese, 15 Israelis, and 13 New Zealanders) and 1,045 staff members (including 2 Taiwanese). The average age of the crew was 36, as well as the passengers were 69. The passengers were 55% female, while the crew was 81% male. Since February 4, many newly confirmed patients have been reported. The exact confirmation number and date are shown in Table 2

Methods
This study uses the SIR epidemic model, which is composed of three parts: S denotes the susceptible population, I denotes the infectious population, and R denotes the recovered (or immune) population. It consists of the following differential equations.
Where N is the total population, β and γ are parameters which can be used to define the basic reproduction number as follows The SIR model satisfies the following equations Because the SIR model is a set of nonlinear differential equations, we use a nonlinear least-squares curve fitting with Microsoft Excel Solver 2019 to analyze the data of confirmed cases. This is a powerful tool widely available in spreadsheets providing a simple method of fitting experimental data to nonlinear functions. The procedure is so easy to use. However, it has never been used to solve the R 0 in previous literature. The operation mode is so obvious that it is an excellent way for researchers to learn the underlying principle of least squares curve fitting 17 .
Consider the problem of fitting the cumulative infection data in Fig 1. We let the "cumulative confirmed case" in Table 2 as the target function. The accuracy of minimizing the problem depends on the function model chosen 18 .
Where , can be calculated by difference series.
Where n means day 1 to day n, and we let ∆ = 1 day.

Least Squares
The vertical deviation from the th point of the "observed" curve to the "calculated" curve is The least squares method is to find values of , in equations (1)-(3) that minimize the sum of the squares of the vertical deviations of the points from the curve 19 : Where n is the total number of points (=32 in Fig. 1) Here are steps to find the best values of and that minimize the sum in equation (14)  4. In column L, compute the vertical deviation in equation (13) and then square the deviation. For example, L6=(D6-E6)^2. 5. In cell L4, compute the sum of the squares of vertical deviations in column L. The sum in cell L4 is the sum in equation (14).
6. The least squares method is to find values of and that minimize the sum in cell L4. Microsoft Excel Solver is a tool that handles the problem. When Solver finishes its task in a few seconds, the spreadsheet will appear as in    (14).

Estimating Uncertainties in the Least-Squares Parameters
Uncertainties in , , and R 0 are as important as the values of the parameters themselves. The amount of uncertainty represents the degree to which the parameter fits the curve. The smaller the uncertainty of the parameter, the better the curve fit.
Here are steps on estimating uncertainties in , , and R 0 of

Results
As of the end of the quarantine on February 20, 2020, a total of 3,063 people has been tested by the 3,371 on the Diamond Princess, with a cumulative test rate of 82.5%, and 634 cases have been diagnosed with COVID-19, accounting for 17.1% of the total. It contains remarkably high asymptomatic infection cases of 328, accounted for 51.7% of all confirmed cases. As of April 24, 2020, 712 confirmed cases with 14 deaths and a cumulative mortality rate reached 1.96%. We took the older man boarding the ship on January 20 as the first case of infection, with a total population of N = 3,711. Using the least-squares method, the parameters β, γ, and R 0 are as follows = 0.3847 ± 0.0039, = 0.1621 ± 0.0046, 0 = 2.37 ± 0.26.
Using the parameters β, γ, and R 0 of SIR model, it can be further estimated that if all passengers continue to stay on the cruises when the quarantine period expires, the actively infected people in the Diamond Princess will reach a peak as 839 cases on Mar 1. As shown in Fig 5. Further, assuming all passengers and crews continue to extend the on-board quarantine time, we can estimate that the SIR model will reach a dynamic equilibrium in about two months. At that time, a total of 3,283 (88.47%) people will be infected. As shown in Fig 6.

Discussion
Cruise ships isolate travelers from the world while offering ideal urban versions on land. However, problems ashore (such as large-scale coronavirus outbreaks) sometimes sneak into ships. Despite efforts to establish a strictly controlled environment on cruise ships, it is easy to spread when things like infectious diseases seep into the ship. The coronavirus outbreak on the Diamond Princess cruise ship also affected other ships: The World Dream was quarantined for four days. Royal Caribbean and Norwegian Cruise Line do not allow travelers with Chinese, Hong Kong, or Macau passports or those who have recently traveled to China. The Westerdam has been shut out of five countries before being allowed to dock in Cambodia. The outbreak of the COVID-19 epidemic broke the commitment and atmosphere of cruise ships sailing on the high seas independently. As the virus and fear of it spread, the problem developed rapidly, and the bubble burst. It shows how the environment reflects the medical, political, and cultural impact of the epidemic.
Several aspects of the COVID-19 cluster infection event on the Diamond Princess cruise ship worthy of discussion. First, is the cruise ship suitable for the isolation of infectious diseases? In the two weeks of port quarantine, the infection cases have become the largest number of people infected with the COVID-19 virus outside China. The first day that Diamond Princess was quarantined, 10 of the 3,711 passengers and crew members tested positive for the virus on February 4. People with symptoms left the ship and were taken to a Japanese hospital, and the remaining passengers stayed in their rooms during the quarantine. Patients without the virus allowed to disembark, and cumulative 634 cases were tested positive for the virus when quarantine was lifted on February 20. The increasing number of cases on board makes it look like it is "promoting transmission." Indeed, without evacuation, we estimated that the cumulated infection rate will reach 88.47%.
There is no literature regarding virus sampling on the Diamond Princess cruise ship environment, but we can indirectly understand how viruses pollute the environment from a recent study. A virus sample was taken from the hospital environment of a patient with mild upper respiratory tract infection COVID-19 in Singapore. The results showed that the ward was extensively polluted: toilet and sink samples were positive, air samples were negative, and swabs drawn from the exhaust port were tested positive. Patients cause severe pollution to the environment through respiratory droplets and fecal discharge. Thus, the environment is a potential medium of transmission 22 .
Secondly, quarantine is a public health crisis for the people on board, and it can also be used as a micro-experiment: despite accelerated artificial conditions, the ship is still a small-scale model of a large-scale outbreak; even patients diagnosed in followup actions deserve further research. In particular, COVID-19 in addition to data from Wuhan and Hubei, China, there is also a lack of knowledge of how viruses are transmitted outside of China. As we all know, the Chinese disease prevention and control department modified the diagnostic conditions on February 13, resulting in significant data changes. Data over time for patients with the new coronavirus on the Diamond Princess cruise ship and the disease progression of those who are positive for the virus but not sick are extremely valuable.
A similar cluster infection occurred in the US Navy aircraft carrier Theodore Roosevelt was deployed in the Pacific Ocean, and three sailors on the ship were tested positive for COVID-19 during the preparation of this manuscript on March 24, 2020. Within a few days, this number climbed to dozens. To prevent the spread of the disease, captain Brett Crozier wanted to evacuate most of the crew ashore, but he refused. A few days later, Crozier mailed several naval officers, requesting that the ship be largely evacuated. This letter leaked to the press. Theodore Roosevelt was ordered to sail to Guam and docked on March 27 23  1. Inside the large ship, it is like a small city, and there are many social activities of thousands of people, thus facilitate more intensive and close contacts.
2. Due to long-term close contact, the spread of infectious diseases can be extended to the second or even the fourth generation and spread widely. Even if some people only stay on the ship for 1 to 3 days.
3. Thousands of people disembark from ships; these activities included playing and purchasing, which promoted the spread of different viruses worldwide.
4. Once the crew is infected, it may become a "super spreader", spread to its countrymen, and new passengers coming up one after another.
5. "Air conditioning" equipment with the poor design is added to the "narrow space" in the large ship. When a person gets infected with such a respiratory tract virus, coughs or sneezes. Especially, droplets or aerosol will be easily inhaled by another passenger.
Finally, the cluster infection data of the Diamond Princess cruise ship is consistent with the SIR transmission model, and the R0 of COVID-19 on this cruise ship is 2.37. This value is similar to the R0 of SARS-CoV when it broke out in Hong Kong is 2-5 26 , and more significant than the R0 of Mers-CoV when it broke out in the Middle East is 0.3-0.8 27 . Due to the limitation of the detection speed and the absence of total inspection, this value may be underestimated. Besides, 51.7% of the asymptomatic patients were diagnosed on the Diamond Princess cruise ship. This data is precious because asymptomatic infected patients will not enter clinics or hospitals, or virus detection by PCR screening. This kind of data from other countries is not easily available. Besides, despite an outbreak in cruise, the mortality rate of 1.96% is far lower than the worldwide mortality rate of 3.06%. However, it is much higher than the 2009-2010 overall H1N1 influenza death rate of 0.03% 28 . Judging from the outbreak of the COVID-19 cluster infection by the Diamond Princess, it is unwise for the Japanese government to port-quarantine all tourists on the cruise ship for two weeks, and the inaction of the British shipowner should also be responsible for this incident. According to the results of this research, "only one" passenger diagnosed with COVID-19 on a large cruise ship or warship on the high seas, epidemics will outbreak in a short time. For mitigation, it is necessary to move to the isolation dock as soon as possible.
Then, evacuate all passengers and crew members to the designated isolation building on the shore, and perform the comprehensive test, and quarantine.
In conclusion, the large cruise ship travels on the high seas, and thousands of people live in densely enclosed, central airconditioned cabins. Once the pathogen penetrates, it will become a hotbed for infectious diseases and accelerate the spreading. This study firstly uses the nonlinear least-squares curve fitting with Microsoft Excel Solver to obtain the SIR model parameters of the COVID-19 cluster infection on the Diamond Princess cruise ship. Without an emergency evacuation plan, the model estimates that the total infection rate could be as high as 88.47%. All countries should learn from this incident and work out large-scale ship quarantine procedures