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

Chao-Chih Lai; Chen-Yang Hsu; Hsiao-Hsuan Jen; Amy Ming-Fang Yen; Chang-Chuan Chan; Hsiu-Hsi Chen

doi:10.1007/s00477-020-01968-w

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

Stoch Environ Res Risk Assess. 2021;35(7):1319-1333. doi: 10.1007/s00477-020-01968-w. Epub 2021 Jan 26.

Authors

Chao-Chih Lai^{1

2

3}, Chen-Yang Hsu^{2

3}, Hsiao-Hsuan Jen², Amy Ming-Fang Yen⁴, Chang-Chuan Chan^{5

6}, Hsiu-Hsi Chen^{2

6}

Affiliations

¹ Emergency Department of Taipei City Hospital, Ren-Ai Branch, Taipei, 106 Taiwan.
² Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, Room 533, No. 17, Xu-Zhou Road, Taipei, 100 Taiwan.
³ Master of Public Health Program, National Taiwan University, Taipei, 100 Taiwan.
⁴ School of Oral Hygiene, College of Oral Medicine, Taipei Medical University, Taipei, 110 Taiwan.
⁵ Institute of Environmental and Occupational Health Science, College of Public Health, National Taiwan University, Taipei, 100 Taiwan.
⁶ Innovation and Policy Center for Population Health and Sustainable Environment, College of Public Health, National Taiwan University, Taipei, 100 Taiwan.

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.

Supplementary information: The online version contains supplementary material available at (10.1007/s00477-020-01968-w).

Keywords: Bayesian SEIR model; COVID-19 outbreak; Diamond princess cruise ship; Prediction.