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The influenza pandemic of 1918-19 was the most devastating pandemic of the 20th century. It killed an estimated 50–100 million people worldwide. In late 1918, when the severity of the disease was apparent, the Australian Quarantine Service was established. Vessels returning from overseas and inter-state were intercepted, and people were examined for signs of illness and quarantined. Some of these vessels carried the infection throughout their voyage and cases were prevalent by the time the ship arrived at a Quarantine Station. We study four outbreaks that took place on board the Medic, Boonah, Devon, and Manuka in late 1918. These ships had returned from overseas and some of them were carrying troops that served in the First World War. By analysing these outbreaks under a stochastic Bayesian hierarchical modeling framework, we estimate the transmission rates among crew and passengers aboard these ships. Furthermore, we ask whether the removal of infectious, convalescent, and healthy individuals after arriving at a Quarantine Station in Australia was an effective public health response. Author summary: The influenza pandemic of 1918–19 was one of the deadliest pandemics in history. In Australia, when it was apparent that the virus was severe, a quarantine service was established to intercept and quarantine ships that returned from overseas and travelled interstate. In this study, we look at the records of outbreaks on board the Medic, Boonah, Devon, and Manuka. Some of the ships carried surviving troops from the First World War, and infections were prevalent when they arrived at a quarantine station. Infectious, convalescent, and healthy individuals on board were moved to the quarantine station for treatment or isolation. We model the outbreaks on the four ships using stochastic epidemic models and estimate the model parameters within a hierarchical framework. Furthermore, we investigate whether the removal of individuals with various disease states was an effective intervention measure from a public health perspective. [ABSTRACT FROM AUTHOR]