Mechanistic Transmission Modeling of COVID-19 on the Diamond Princess Cruise Ship Demonstrates the Importance of Aerosol Transmission

TL;DR: The results demonstrate that aerosol inhalation was likely the dominant contributor to COVID-19 transmission among passengers aboard the Diamond Princess Cruise Ship, and underscore the importance of implementing public health measures that target the control of inhalation of aerosols in addition to ongoing measures targeting control of large droplet and fomite transmission, not only aboard cruise ships but in other indoor environments as well.

Abstract: Background The current prevailing position is that coronavirus disease 2019 (COVID-19) is transmitted primarily through large respiratory droplets within close proximity (i.e., 1-2 m) of infected individuals. However, quantitative information on the relative importance of specific transmission pathways of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (i.e., droplets, aerosols, and fomites across short- and long-range distances) remains limited. Methods To evaluate the relative importance of multiple transmission routes for SARS-CoV-2, we leveraged detailed information available from the Diamond Princess Cruise Ship outbreak that occurred in early 2020. We developed a framework that combines stochastic Markov chain and negative exponential dose-response modeling with available empirical data on mechanisms of SARS-CoV-2 dynamics and human behaviors, which informs a modified version of the Reed-Frost epidemic model to predict daily and cumulative daily case counts on the ship. We modeled 21,600 scenarios to generate a matrix of solutions across a full range of assumptions for eight unknown or uncertain epidemic and mechanistic transmission factors, including the magnitude of droplet and aerosol emissions from infected individuals, the infectious dose for deposition of droplets and aerosols to the upper and lower respiratory tracts, and others. Findings A total of 132 model iterations met acceptability criteria (R2 > 0.95 for modeled vs. reported cumulative daily cases and R2 > 0 for daily cases). Analyzing only these successful model iterations yields insights into the likely values for uncertain parameters and quantifies the likely contributions of each defined mode of transmission. Mean estimates of the contributions of short-range, long-range, and fomite transmission modes to infected cases aboard the ship across the entire simulation time period were 35%, 35%, and 30%, respectively. Mean estimates of the contributions of large respiratory droplets and small respiratory aerosols were 41% and 59%. Short-range transmission was the dominant mode after passenger quarantine began, albeit due primarily to aerosol transmission, not droplets. Interpretation Our results demonstrate that aerosol inhalation was likely the dominant contributor to COVID-19 transmission among passengers aboard the Diamond Princess Cruise Ship. Moreover, close-range and long-range transmission likely contributed similarly to disease progression aboard the ship, with fomite transmission playing a smaller role. The passenger quarantine also affected the importance of each mode, demonstrating the impacts of the interventions. Although cruise ships represent unique built environments with high ventilation rates and no air recirculation, these findings underscore the importance of implementing public health measures that target the control of inhalation of aerosols in addition to ongoing measures targeting control of large droplet and fomite transmission, not only aboard cruise ships but in other indoor environments as well. Funding Funding information is not available.

Summary

Introduction

• Information on the relative importance of specific transmission pathways of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remains limited.
• 1 The World Health Organization’s (WHO) current position is that the COVID-19 virus is transmitted primarily through respiratory droplets and contact routes, while airborne transmission of the COVID-19 virus is likely not a major route of transmission other than in settings in which aerosol generating procedures are occurring.
• Conversely, numerous researchers4–12 and professional societies (e.g., ASHRAE13) have raised concerns that longer-range airborne transmission is likely occurring from both symptomatic and asymptomatic (or pre-symptomatic) individuals through a combination of larger respiratory droplets that are carried further than 1-2 m via airflow patterns and smaller inhalable aerosols (i.e., ‘droplet nuclei’) that can easily transport over longer distances.
• 21,22 Understanding the importance of each transmission pathway for COVID-19 is critical to informing public health guidelines for effectively managing the spread of the disease.
• In the absence of empirical studies using controlled exposures to elucidate transmission pathways,23 mathematical modeling approaches can offer insights into the likely importance of the different modes of disease transmission among human populations,24–28 provided that sufficiently accurate inputs are available.

Methods

• The Diamond Princess Cruise Ship presents a unique built environment case study, with a known number of passengers, crewmembers, and COVID-19 cases over time, discovered through high rates of testing, and a relatively high degree of knowledge of several important human and built environment factors.
• The Diamond Princess experienced a major outbreak of COVID-19 in early 2020, with 712 of 3711 passengers and crew members on board becoming infected (19% of the community)29 and at least 57 other passengers who tested positive in the days after they left the ship and returned to their home countries.
• As reported, the COVID-19 outbreak was traced to a single passenger from Hong Kong who boarded the ship in Yokohama on January 20 and then disembarked in Hong Kong on January 25.
• Full model details are described in the SI.
• The Markov chain model informs a doseresponse model, which in turn informs an epidemic model to generate estimates of daily and cumulative daily case counts aboard the ship from January 20 (when there was only one index case aboard the ship) to February 24 (when all passengers disembarked).

Dose-Response Model

• To estimate the infection probability of SARS-CoV-2 viruses deposited to different body sites of susceptible individuals, the authors used a negative exponential dose-response model, which implies that a single particle can start an infection and all single particles are independent of each other.
• The probability of infection for one susceptible individual in the cruise ship was calculated using Equation 1: = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑓𝑒𝑐𝑡𝑒𝑑 𝑐𝑎𝑠𝑒𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝑠 = 1 − exp[−(𝛼𝑈𝑅𝑇 × 𝑁𝑈𝑅𝑇 + 𝛼𝐿𝑅𝑇 × 𝑁𝐿𝑅𝑇)].
• The authors are not aware of any clinical studies to date that report these values for SARS-CoV-2 in humans or animals.
• This approach allows us to test scenarios with this uncertain parameters without knowing (or needing to know) the actual magnitude of ID50, which can then be used to infer the likely magnitude of this ratio based on successful model outcomes.

Transmission Mode Contribution to Infection

• This approach allows for summarizing estimates of infection contributions by transmission mode, contact range, micro-environment (i.e., public areas or passenger cabins), and/or simulation period independently, as needed.
• Short-range transmission occurs by direct deposition of respiratory droplets and inhalation of aerosols only when susceptible individuals were within a defined close-range contact area of infected individuals.
• The close-range contact area was defined assuming a conical area in front of an infector with the head angle of 60° and length of 3 meters (described in detail in the SI, Section 1.2.2)34,35.
• Fomite transmission occurs when susceptible individuals came in contact with contaminated surfaces, which could be contaminated by infected individuals through direct touching, direct deposition of respiratory droplets, and/or deposition of respiratory aerosols at any time point and location in the model framework.

Combining the Transmission Risk Model with a Developed Epidemic Model

• The mechanistic infection transmission model was combined with a modified version of the ReedFrost epidemic model to simulate the transmission of COVID-19 aboard the ship.
• The numbers of susceptible individuals who were not cabinmates with an infector (𝑁𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝑠−𝑐𝑜𝑚𝑚𝑜𝑛) and susceptible individuals inside the infected cabins (𝑁𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝑠−𝑐𝑎𝑏𝑖𝑛) at the beginning of each simulation day (𝑑) were estimated using the Equations 4-5 (except for the first period of infection transmission): 𝑁𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑙𝑒𝑠−𝑐𝑜𝑚𝑚𝑜𝑛(𝑑) = 𝑁𝑡𝑜𝑡𝑎𝑙−𝑜𝑛𝑏𝑜𝑎𝑟𝑑 − [𝑁𝑖𝑛𝑓𝑒𝑐𝑡𝑒𝑑−𝑐𝑎𝑏𝑖𝑛(𝑑) × 𝑁𝑎𝑣𝑒𝑟𝑎𝑔𝑒−𝑐𝑎𝑏𝑖𝑛].
• The authors assumed the infected cases could spread infectious particles only one day after the incubation period, when their clinical symptoms began.
• The authors divided the transmission patterns into four periods, each of which having different epidemic characteristics, as described in the SI (Section 1.1).
• Several checkpoint conditions were introduced to the epidemic model to ensure reasonable bounds (SI Section 2.3).

Analysis

• The model framework requires numerous assumptions or estimates for unknown or uncertain input parameters, which were culled from existing literature where possible and otherwise estimated or assumed using known information about the Diamond Princess Cruise Ship.
• Because there is high uncertainty around several critical model parameters, the authors utilized a scenario modeling approach in which values for unknown or uncertain epidemic and transmission modeling parameters were varied over a wide range of possibilities to generate a matrix of possible solutions.
• A total of 21,600 scenarios were modeled across a range of estimates or assumptions for eight critical unknown or uncertain input parameters (Table 1).
• Estimates and assumptions for these parameters are described in detail in the SI (Section 3).
• The authors ran the model with each possible combination of the eight unknown or uncertain input parameters shown in Table 1 (10×5×6×3×3×2×2×2=21,600) in order to search a wide range of possible parameter values and combinations of parameter values.

Results

• The cumulative number of infected cases reported in various outlets was 765 cases; the average (±SD) cumulative number of modeled infected cases among iterations meeting acceptability criteria was 736 (±64) .
• Table 2 shows the number of acceptable iterations that were associated with a specific assumption for each of the eight unknown or uncertain model input parameters, as well as the average R2 value for those iterations.
• The estimated contribution of short-range (droplet + aerosol) transmission did not exceed 44% in any of the model scenarios that met acceptability criteria, while individual model scenarios exceeded 61% and 73% for long-range aerosol and fomite transmission, respectively.
• Before the quarantine, only the differences between short- and long-range transmission (Mann-Whitney U-test p<0.0001) and between long-range and fomite transmission (Mann-Whitney U-test p=0.0004) were significant.
• Conversely, median (mean) estimates of the contribution of droplets and aerosols after the passenger quarantine began were 15% (27%) and 85% (73%) (p<0.0001), respectively, suggesting that even though short-range transmission likely dominated during this period , smaller aerosol transmission likely accounted for the vast majority of infected cases post-quarantine, rather than larger droplets.

Discussion

• The model approach is designed to identify the most likely values of several unknown or uncertain parameters by analyzing only those model results that met acceptability criteria, and thereby providing insight into the likely importance of the various modes of transmission included in the framework.
• Results show that the long-range transmission of aerosols containing SARS-CoV-2 was most likely the dominant mode of COVID-19 transmission aboard the ship even with a very high ventilation rate (9-12 air changes per hour) and no recirculated air.
• There are several limitations to this modeling approach.
• While the average contribution of fomite transmission among acceptable model iterations was estimated to be lower than other the other two pathways, under some specific assumptions (e.g., ID50,URT/ID50,LRT = 1, see SI Section 4.4) or transmission periods (e.g., before passenger quarantine started), fomite transmission could have been the dominant transmission mode.
• The authors also did not consider the impacts of potentially influential characteristics such as temperature, humidity, sunlight, or not-well-mixed conditions in the control volumes considered herein.

Contributors

• The model development was led by PA, who came up with the original idea and advanced the framework with help from BRS, ZK, JGCL, and JGA.
• PA, ZK, and BRS contributed to processing the model and analyzing the outcomes.
• PA, BRS, and JGA contributed to writing the manuscript.
• PA, BRS, and ZK generated the figures and tables.
• All authors interpreted the findings and approved the final version for publication.

Figures

Figure 3. Mean (SD) estimates of (a) the proportion of cases and (b) the effective reproduction number before and after passenger quarantine

Table 1. Summary of the ranges of 8 unknown or uncertain critical model input parameters that defined each model iteration

Figure 2. Estimates of the contributions of transmission modes and viral sources to infected cases aboard the Diamond Princess Cruise Ship over the entirety of the simulation period

Figure 5. Estimates of the contribution of droplets and aerosols to infected cases aboard the Diamond Princess Cruise Ship over the entirety of the simulation period as well as before and after quarantine measures

Figure 1. Reported (actual) and modeled (predicted) cumulative COVID-19 cases aboard the Diamond Princess Cruise Ship from January 20 – February 24, 2020. Modeled cases are from 132 model scenarios that met acceptable criteria (R2 >0.95 for cumulative daily cases and R2 > 0 for daily cases).

Figure 4. Estimates of the contribution of multiple transmission modes to infected cases aboard the Diamond Princess Cruise Ship over the entirety of the simulation period as well as before and after quarantine measures

Table 2. Distribution of acceptable model iterations (defined as R2 > 0.95 between reported and modeled daily cumulative case numbers and non-negative R2 for daily case numbers) that were associated with a specific assumption for eight unknown or uncertain model input parameters

Frequently asked questions

Q1. What are the contributions in "Mechanistic transmission modeling of covid-19 on the diamond princess cruise ship demonstrates the importance of aerosol transmission" ?

In this paper, the authors used a mechanistic modeling approach to investigate the relative importance of multiple transmission routes of SARS-CoV-2 among individuals aboard the Diamond Princess cruise ship, which experienced a major outbreak of COVID-19 in early 2020. 

Q2. How many iterations met the acceptability criteria for the model?

A total of 132 model iterations met the acceptability criteria of R2 > 0.95 for daily cumulative cases and R2 > 0 for daily cases (0.6% of the total number of model iterations). 

Q3. Why was short-range transmission the dominant mode after passenger quarantine began?

Short-range transmission was the dominant mode after passenger quarantine began, albeit due primarily to aerosol transmission, not droplets. 

Q4. What is the likely mode of transmission of COVID-19?

Results show that the long-range transmission of aerosols containing SARS-CoV-2 was most likely the dominant mode of COVID-19 transmission aboard the ship even with a very high ventilation rate (9-12 air changes per hour) and no recirculated air. 

Q5. how many iterations of the coronavirus model met acceptability criteria?

A total of 132 model iterations met acceptability criteria (R2 > 0.95 for modeled vs. reported cumulative daily cases and R2 > 0 for daily cases). 

Q6. What is the likely cause of COVID-19?

Their results demonstrate that aerosol inhalation was likely the dominant contributor to COVID-19 transmission among passengers aboard the Diamond Princess Cruise Ship. 

Q7. How many iterations of the model met acceptability criteria?

The estimated contribution of short-range (droplet + aerosol) transmission did not exceed 44% in any of the model scenarios that met acceptability criteria, while individual model scenarios exceeded 61% and 73% for long-range aerosol and fomite transmission, respectively. 

Q8. How did the researchers estimate the number of COVID-19 cases aboard the Diamond Princess?

31To estimate the likely contributions of specific infection transmission modes to the number of COVID-19 cases among individuals aboard the Diamond Princess Cruise Ship, a combination of epidemic, mechanistic transmission, and dose-response models was adopted. 

Q9. What is the shortest-range transmission of SARS-CoV-2?

Short-range transmission occurs by direct deposition of respiratory droplets and inhalation of aerosols only when susceptible individuals were within a defined close-range contact area of infected individuals. 

Q10. How did the authors evaluate the relative importance of multiple transmission routes for SARS-CoV-2?

To evaluate the relative importance of multiple transmission routes for SARS-CoV-2, the authors leveraged detailed information available from the Diamond Princess Cruise Ship outbreak that occurred in early 2020. 

Q11. What is the probability of a person developing a virus on a cruise ship?

The authors assumed that (i) the infection is spread from infected individuals to others by four main transmission pathways (long-range inhalation, short-range inhalation, direct deposition within close-range, and fomite), (ii) a portion of susceptible individuals in the group will develop the infection and will be infectious to others (the portion of ‘susceptibles’ who will develop the infection is estimated by the transmission risk model), (iii) the probability of coming into adequate contact with any other specified individual in the group within one time interval depends on the interaction behavior of the individual and is estimated using the Markov chain method, (iv) the susceptible individuals in the cruise ship were isolated from others outside the cruise ship, and (v) these conditions remain constant during one whole day of the outbreak. 

Q12. What was the average estimate of the contribution of aerosols to passenger quarantine?

Median (mean) estimates of the contribution of droplets and aerosols prior to the passenger quarantine were 40% (50%) and 60% (50%) (p=0.32), respectively, suggesting that both larger respiratory droplets and smaller respiratory aerosols contributed approximately equally to infected cases aboard the ship during this time period. 

Q13. How many scenarios were modeled across a range of estimates or assumptions?

A total of 21,600 scenarios were modeled across a range of estimates or assumptions for eight critical unknown or uncertain input parameters (Table 1).