BACKGROUND: Cruise ships carry a large number of people in confined spaces with relative homogeneous mixing. On 3 February, 2020, an outbreak of COVID-19 on cruise ship Diamond Princess was reported with 10 initial cases, following an index case on board around 21-25th January. By 4th February, public health measures such as removal and isolation of ill passengers and quarantine of non-ill passengers were implemented. By 20th February, 619 of 3700 passengers and crew (17%) were tested positive. METHODS: We estimated the basic reproduction number from the initial period of the outbreak using SEIR models. We calibrated the models with transient functions of countermeasures to incidence data. We additionally estimated a counterfactual scenario in absence of countermeasures, and established a model stratified by crew and guests to study the impact of differential contact rates among the groups. We also compared scenarios of an earlier versus later evacuation of the ship. RESULTS: The basic reproduction rate was initially 4 times higher on-board compared to the ${R}_0$ in the epicentre in Wuhan, but the countermeasures lowered it substantially. Based on the modeled initial ${R}_0$ of 14.8, we estimated that without any interventions within the time period of 21 January to 19 February, 2920 out of the 3700 (79%) would have been infected. Isolation and quarantine therefore prevented 2307 cases, and lowered the ${R}_0$ to 1.78. We showed that an early evacuation of all passengers on 3 February would have been associated with 76 infected persons in their incubation time. CONCLUSIONS: The cruise ship conditions clearly amplified an already highly transmissible disease. The public health measures prevented more than 2000 additional cases compared to no interventions. However, evacuating all passengers and crew early on in the outbreak would have prevented many more passengers and crew from infection.