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 (R 0 ) 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 R 0 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, R 0 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 R 0 estimates by each deck was noted. The estimated R 0 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.

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