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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., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Alahakoon et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

As most disease causing pathogens require transmission from an infectious individual to a susceptible individual, continued persistence of the pathogen within the population requires the replenishment of susceptibles through births, immigration, or waning immunity. Consider the introduction of an unknown infectious disease into a fully susceptible population where it is not known how long immunity is conferred once an individual recovers from infection. If, initially, the prevalence of disease increases (that is, the infection takes off), the number of infectives will usually decrease to a low level after the first major outbreak. During this post-outbreak period, the disease dynamics may be influenced by stochastic effects and there is a non-zero probability that the epidemic will die out. Die out in this period following the first major outbreak is known as an epidemic fade-out. If the disease does not die out, the susceptible population may be replenished by the waning of immunity, and a second wave may start. In this study, we investigate if the rate of waning immunity (and other epidemiological parameters) can be reliably estimated from multiple outbreak data, in which some outbreaks display epidemic fade-out and others do not. We generated synthetic outbreak data from independent simulations of stochastic SIRS models in multiple communities. Some outbreaks faded-out and some did not. We conducted Bayesian parameter estimation under two alternative approaches: independently on each outbreak and under a hierarchical framework. When conducting independent estimation, the waning immunity rate was poorly estimated and biased towards zero when an epidemic fade-out was observed. However, under a hierarchical approach, we obtained more accurate and precise posterior estimates for the rate of waning immunity and other epidemiological parameters. The greatest improvement in estimates was obtained for those communities in which epidemic fade-out was observed. Our findings demonstrate the feasibility and value of adopting a Bayesian hierarchical approach for parameter inference for stochastic epidemic models., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors.)

Deterministic epidemic models that allow for replenishment of susceptibles typically display damped oscillatory behaviour. If the population is initially fully susceptible, once an epidemic takes off a distinct trough will exist between the first and second waves of infection. Epidemic dynamics are, however, influenced by stochastic effects, particularly when the prevalence is low. At the beginning of an epidemic, stochastic die-out is possible and well characterised through use of a branching process approximation. Conditional on an epidemic taking off, stochastic extinction is highly unlikely during the first epidemic wave, but the probability of extinction increases again as the wave declines. Extinction during this period, prior to a potential second wave of infection, is defined as 'epidemic fade-out'. We consider a set of observed epidemics, each distinct and having evolved independently, in which some display fade-out and some do not. While fade-out is necessarily a stochastic phenomenon, the probability of fade-out will depend on the model parameters associated with each epidemic. Accordingly, we ask whether time-series data for the epidemics contain sufficient information to identify the key driver(s) of different outcomes-fade-out or otherwise-across the sub-populations supporting each epidemic. We apply a Bayesian hierarchical modelling framework to synthetic data from an SIRS model of epidemic dynamics and demonstrate that we can (1) identify when the sub-population specific model parameters supporting each epidemic have significant variability and (2) estimate the probability of epidemic fade-out for each sub-population. We demonstrate that a hierarchical analysis can provide precise estimates of the probability of fade-out than is possible if considering each epidemic in isolation. Our methods may be applied to both epidemiological and other biological data to identify where differences in outcome-fade-out or recurrent infection/waves are purely due to chance or driven by underlying changes in the parameters driving the dynamics., (Copyright © 2022 The Authors. Published by Elsevier B.V. All rights reserved.)