The Bayesian Susceptible-Exposed-Infected-Recovered model for the outbreak of COVID-19 on the Diamond Princess Cruise Ship

Abstract

The outbreak of COVID-19 on the Diamond Princess Cruise Ship provides an unprecedented opportunity to estimate its original transmissibility with basic reproductive number (R0) and the effectiveness of containment measures. We developed an ordinary differential equation-based Susceptible-Exposed-Infected-Recovery (SEIR) model with Bayesian underpinning to estimate the main parameter of R0 determined by transmission coefficients, incubation period, and the recovery rate. Bayesian Markov Chain Monte Carlo (MCMC) estimation method was used to tackle the parameters of uncertainty resulting from the outbreak of COVID-19 given a small cohort of the cruise ship. The extended stratified SEIR model was also proposed to elucidate the heterogeneity of transmission route by the level of deck with passengers and crews. With the application of the overall model, R0 was estimated as high as 5.70 (95% credible interval: 4.23–7.79). The entire epidemic period without containment measurements was approximately 47 days and reached the peak one month later after the index case. The partial containment measure reduced 63% (95% credible interval: 60–66%) infected passengers. With the deck-specific SEIR model, the heterogeneity of R0 estimates by each deck was noted. The estimated R0 figures were 5.18 for passengers (5–14 deck), mainly from the within-deck transmission, and 2.46 for crews (2–4 deck), mainly from the between-deck transmission. Modelling the dynamic of COVID-19 on the cruise ship not only provides an insight into timely evacuation and early isolation and quarantine but also elucidates the relative contributions of different transmission modes on the cruise ship though the deck-stratified SEIR model.

Natural resistance against infections: focus on COVID-19

“…Specifically, Sweden reported a seroprevalence of 7.3% in the Stockholm area in April 2020 despite mathematical models predicting an infection rate of 20-25% [24]. An interesting case study is that of the Diamond Princess cruise ship that in February 2020 was confronted with a COVID-19 outbreak while in the western Pacific ocean, and reported half of the global COVID-19 cases at that time outside China [25,26]. The infection rates on the cruise ship were mathematically projected to be higher than those occurring in open spaces because complete isolation was not possible, and members of the crew were also exposed to the virus.…”

“…The infection rates on the cruise ship were mathematically projected to be higher than those occurring in open spaces because complete isolation was not possible, and members of the crew were also exposed to the virus. Different studies have estimated the basic reproduction number (R 0 ) during the outbreak period in the ship to be between 5.71 and 14.8 [25,26], which suggests that the number of exposed individuals was higher than the number of those who actually became infected. Subsequently, in contrast to the officially reported 712 individuals with PCR-positive results for COVID-19, one study reported a calculation in which this number should have been at least 1000 [26].…”

“…Different studies have estimated the basic reproduction number (R 0 ) during the outbreak period in the ship to be between 5.71 and 14.8 [25,26], which suggests that the number of exposed individuals was higher than the number of those who actually became infected. Subsequently, in contrast to the officially reported 712 individuals with PCR-positive results for COVID-19, one study reported a calculation in which this number should have been at least 1000 [26]. Although sensitivity issues with the diagnostic tests may explain some of the missing cases, the large difference is unlikely to be due to this sole cause.…”

Does the data tell the true story? A modelling assessment of early COVID-19 pandemic suppression and mitigation strategies in Ghana

“…., N T ) incident cases over consecutive time units, and a generation time distribution w, R 0 is estimated by these two methods: 2.2.2.1 Sequential Bayesian method (SB). This method relies on an approximation to the SIR model [39][40][41][42] whereby incidence at time t + 1, N(t + 1) is approximately Poisson distributed with mean…”

Bayesian Framework for Multi-Wave COVID-19 Epidemic Analysis Using Empirical Vaccination Data

“…Various Bayesian methods have been employed for the epidemiological and related models for studying COVID-19, including the Bayesian MCMC algorithm for the inference of statistical and epidemiological parameters [18][19][20][21], Naïve Bayes method for feature classification in the diagnosis of COVID-19 [22], Bayesian network for severity classification [23,24], spatial geo-referencing analysis [25,26], etc. A few studies have already presented remarkable attempts on methodologies that integrate Bayesian inference with SIR-based compartmental models.…”