Unexpectedly Intriguing!
February 21, 2020

COVID-19 is the name the World Health Organization has given to the highly contagious and deadly new viral infection that has severely impacted China's economy as it threatens to become a pandemic.

The world recently ran an experiment on how potentially contagious the viral infection formerly known as Novel Coronavirus 2019 (or 2019-nCoV) on a cruise ship, which was quarantined in Japan from 3 February 2020 through 19 February 2020. During that period, some 3,711 passengers and crew on board the Diamond Princess were at an elevated risk of exposure to the new coronavirus, as the ship effectively became a 'super spreading' site. In those 16 days, the number of passengers and crew testing positive for the COVID-19 infection grew from 1 to 621. The following chart tracks the cumulative number of passengers testing positive for the COVID-19 infection on each day of the Diamond Princess' quarantine period.

Reported Cases of Diamond Princess Passengers and Crew Testing Positive for COVID-19 Virus Infection by Day

Cruise ships have earned notorious reputations for becoming incubators for contagious diseases given their design, where people are contained in close quarters that provide an environment that is conducive to the spread of diseases. In the case of the Diamond Princess, in addition to sharing these characteristics, the quarantine practices put into effect on the ship after the first passenger was confirmed to have been infected proved to be ineffective in slowing the spread of the COVID-19 viral infection. The measures taken have been described as "an improvisation", including the fiasco of having the wrong masks initially provided to passengers. After the correct face masks were finally provided, the passengers were not adequately trained to fit them properly, impairing their effectiveness.

All these problems combined are why a National Institute of Health official described the ship's attempted quarantine as "ineffective", as the Diamond Princess became the home of the largest cluster of coronavirus cases outside China in the epidemic's earliest phase.

The failed quarantine of the Diamond Princess then gives us an example of how fast the COVID-19 coronavirus might spread in a crowded city with little-to-no effective quarantine procedures in place to slow the spread of the viral infection. But can we really tell anything about how fast it might spread from just 16 days worth of data?

The answer to that question is yes, provided we have a growth model that can provide a good indication of how quickly the disease could spread through an entire susceptible population.

To that end, we can apply the mathematical growth models that have been developed to track the progression of diseases in plants. The following figure illustrates the various growth models that might be employed:

Figure 1. Examples of disease progress curves represented by monomolecular, exponential, logistic, and Gompertz models

The following slideshow gives more background into these models:

Based on what has been learned about the COVID-19 virus, it fits the profile of a polycyclic disease. An exponential model might be used to describe its early phases, but a logistic (or Richards) growth model or a Gompertz growth model will more closely match its full progression.

But which to use? A 2015 paper by Wendi Liu, Sanyi Tang, and Yanni Xiao gives the edge to the general logistic growth model, although a 2017 paper by C.R. Sebrango-Rodriguez, D.A. Martinez-Bello, L. Sanchez-Valdes, P.J. Thilakarathne, E. Del Fava, Patrick Van Der Stuyft (UGent), A. Lopez-Quilez and Z. Shkedy argues in favor of averaging the models' results together.

For our part, we built a tool to model the progression of the COVID-19 virus onboard the Diamond Princess using both the logistic and Gompertz growth models, where we've assumed that all those on the ship would be susceptible to becoming infected if they had remained on board. To use the tool, just select the growth model for which you would like to see the results and enter the number of days you would like to project results for. If you're accessing this article on a site that republishes our RSS news feed, please click through to our site to access a working version.

Growth Model and Number of Days
Input Data Values
Select Growth Model
Number of Days Since First Reported Case

Projected Spread of Infection
Estimated Results Values
Modeled Percentage of Population Infected

The tool's results are expressed in terms of the percentage of the population affected, which for the Diamond Princess, totals 3,711 individuals.

In playing with the tool with our basic assumptions, we find that virtually all of the passengers and crew would have been likely to have become infected with the COVID-19 coronavirus if they had remained on the ship for more than 60 days, regardless of which growth model we select. The following chart visualizes the growth models' projections, where we find the COVID-19 virus would have been likely to spread to 95% or more of the 3,711 passengers and crew quarantined on the Diamond Princess after 60 days.

Reported and Modeled Percentage of 3,711 Passengers and Crew Testing Positive for COVID-19 While In Quarantine Onboard the Diamond Princess Cruise Ship

In reality, it's more likely that not all passengers would have been susceptible to the COVID-19 virus, but that's the conservative assumption to make for any new virus until we learn more about it.

We should also note that the data for the cumulative number of infected passengers and crew may not be representative of the true rate of spread of COVID-19. Japan's national health laboratories only had the capacity to run 300 tests per day during most of the quarantine period, where the daily numbers reported may well have been understated.

Speaking of which, here are our sources for the cumulative daily numbers of infected passengers and crew on the Diamond Princess:

Reported Cases of Diamond Princess Passengers and Crew Testing Positive
for COVID-19 Virus Infection During Its Quarantine Period
Date Number Tested Positive Source of Figure
03 February 2020 1 Princess Cruise Ship Temporarily Delayed for Coronavirus Testing
04 February 2020 10 10 Test Positive for Coronavirus Aboard Carnival's Diamond Princess
05 February 2020 20 20 people test positive for coronavirus on board Carnival’s Diamond Princess cruise in Japan
06 February 2020 41 Coronavirus cases triple to 61 on cruise ship quarantined in Japan, with 41 more reported
07 February 2020 61 Oregon woman infected with coronavirus quarantined in Japan
08 February 2020 67 Diamond Princess cruise ship has 67 passengers who have tested positive for coronavirus onboard, Japan's Health Minister announced
09 February 2020 69 Inferred from 10 February 2020 report.
10 February 2020 135 Diamond Princess cruise ship coronavirus cases double to 135; Marysville woman still healthy
11 February 2020 174 Japan confirms 39 new virus cases, 174 total on cruise ship
12 February 2020 174 No reports indicating change in number of positive test results for COVID-19 infection.
13 February 2020 218 44 more on Diamond Princess cruise ship test positive for COVID-19
14 February 2020 218 No reports indicating change in number of positive test results for COVID-19 infection.
15 February 2020 285 Travis Air Force Base Prepares For Coronavirus Airlift Of Diamond Princess Passengers
16 February 2020 355 Virus spreads on ship in Japan, American passengers set to disembark
17 February 2020 454 99 more coronavirus cases reported on cruise ship docked in Japan
18 February 2020 542 Japan says 88 more virus cases confirmed on quarantined ship
19 February 2020 621 79 New Cases Of Coronavirus On Quarantined Japan Cruise Ship Take Toll To 621

Since Japan's official quarantine ended on 19 February 2020, two Diamond Princess passengers who became infected with the COVID-19 coronavirus have died.

References

Wendi Liu, Sanyi Tang, and Yanni Xiao. Model Selection and Evaluation on Emerging Infectious Disease Data Sets including A/H1N1 and Ebola. Computational and Mathematical Methods in Medicine. 2015; DOI: 10.1155/2015/2017105.

SEBRANGO-RODRÍGUEZ, C., MARTÍNEZ-BELLO, D., SÁNCHEZ-VALDÉS, L., THILAKARATHNE, P., DEL FAVA, E., VAN DER STUYFT, P., LOPEZ-QUILEZ, A., SHKEDY, Z. (2017). Real-time parameter estimation of Zika outbreaks using model averaging. [PDF Document]. Epidemiology and Infection. (2017), 145, 2313–2323. DOI: 10.1017/S0950268817001078.


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