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 onboard 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.
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, where the measures taken have been described as “an improvisation“, where the wrong masks were provided to passengers, who were not adequately trained to fit them properly. That’s a major reason 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.
The 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 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. This figure illustrates the various growth models that might be employed.
This 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. Please click through to our site to access a working version.
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.
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
Since Japan’s official quarantine ended on 19 February 2020, two Diamond Princess passengers who became infected with the COVID-19 coronavirus have died.