Individuals were sampled at random from the compartments affected by the event. For example, for an external transfer event of n smolt from farm 1 to farm 2, n smolt were randomly selected from all smolts in farm 1 and placed into the same compartments in farm 2. Fish that entered the model were assumed to be susceptible in their respective age category. Imported fish were assumed to be susceptible, noting the aim of the study to explore spread in Ireland without considering international importation of PMCV. On average, 2,176,111 eggs were imported per year during the study period, according to information from the Irish Marine Institute . Fish remained in the same infection state whilst changing age category, from egg-juvenile to smolt or smolt to growth-repro, or moving between farms. Figure 1 presents the conceptual SIE compartment model for PMCV spread in farmed Atlantic salmon, including indirect transmission via the environment and fish movements between holdings.There is an EU legal requirement for aquaculture production businesses to be registered, and to keep records of all movements of aquaculture animals and products, both into and out of the farm . In Ireland, the storage of these movement data is undertaken by the MI. This database contains several variables, including the date of fish movement, origin and destination sites with geographic coordinates, life stage, species and quantity of fish moved. The present study was based on all fish movement reports to the Fish Health Unit of the MI covering the period from 1 January 2009 to 23 October 2017. This included 648 reports, with information about the identifier of the origin farm, grow racks with lights idetifier of the destination farm, the number of fish and age group and the date of the movement. Each record was linked to the geographical coordinates of the farms provided by the aquaculture production business records, to allow for incorporation of local spread during the modeling phase of this study.

A farm was considered “active” if any fish were present on the farm, according to movement records. Enter events, i.e., hatchings or imports , were imputed as needed to ensure that farm-level fish numbers were sufficient to allow fish shipments between farms as recorded in the fish movement database . The date of the imputed hatching events was calculated based on the average residence time of fish prior to shipment in the farm. In total, 90 enter events were imputed, including approximately a third of these during the first year of the simulation . This represented on average 10 imputed enter events per year. Most of this imputed enter events corresponded to eggs or juvenile fish , but some fish were entered as smolts , growth , or broodstock fish . Internal transfer events, i.e., moving from eggjuvenile to smolt or from smolt to growth-repro, were imputed when the relevant time during the simulation had been reached. When moving from egg-juvenile to smolt, fish were aged a week prior to shipping to seawater farms, and for aging from smolt to growth-repro, smolts were allowed to remain on the farm for 180 days. Exit events, i.e., mortality, slaughter, or euthanasia, were generated either the day prior to the last shipment of a fish cohort, when it was evident, based on the records, that the fish destination of the whole cohort was another farm , or after a fixed amount of time if it was clear from the records that the farm was the final destination of the fish . The duration of this period was 300 days in freshwater farms and 600 days for seawater farms. Broodstock fish in freshwater farms were assumed to live until 1 week prior to an egg shipment. A total of 55 unique farms were used for the simulation, with the following event types: enter, including reported imports , internal transfer , external transfer , and exit .

A time-series was created to explore seasonality in the input data, focusing on the number of events, the number of farms with at least one fish and the number of fish per age category. A further time-series was produced to investigate the proportion of farms connected to at least one other farm, for each month of the year. A smoother was added to each of these time-series, using local polynomial regression fitting in order to describe the temporal trend .In addition, we evaluated the effectiveness of an improved bio-security in specific farms. For the purposes of the simulations, our definition of bio-security refers to measures that prevent infected fish from entering a farm, akin to a bio-security strategy that is 100% effective in preventing infected fish from entering or leaving a farm. As described above, this was done by moving all fish shipped to the susceptible compartment at the time of shipment. Six strategies were tested. In the first strategy, all farms were targeted for an increase in bio-security. This would be a very costly approach, but a good ideal for comparison. In the remaining strategies, we targeted the 8 most central farms in terms of a specific farm centrality measure, which were indegree, out degree, incloseness, outcloseness, and betweenness,using the same methodology described previously by Yatabe et al. . The sample size was chosen arbitrarily, representing ∼25% of farms in Ireland at that time. Briefly, indegree describes the number of different farms from which a farm receives fish, out degree describes the number of different farms to which a particular farm sends fish, incloseness is an estimate of how close all other farms reach to a respective farm, outcloseness is an estimate of how close a respective farm reaches to other farms, and betweenness is a measure of the degree to which a particular farm falls on the shortest path between all pairs of farms in the network .

For estimating these centrality measures, at the beginning of every year the movement records from the preceding 2 years were used for estimation. For example, on 1 January 2011 centrality measures of all farms were estimated based on fish movement data from 1 January 2009 to 31 December 2010, farms were ranked and the top 8 for each centrality measure were selected for an increased bio-security. There were two exceptions to this 2-year window for estimation of centrality measures: the year 2010, where only the data from 2009 was used to estimate centrality measures, and 2009, where no data from previous years were available. Therefore, during this latter year no control measures were applied. The former six strategies were evaluated using two approaches for preventing the spread of a newly introduced agent into the country: firstly, by applying the control measures 1 month after the agent was first detected , from now on the ‘reactive’ approach, and secondly by applying the control measures as a standard practice from before the first detection of the agent , from now on the “proactive” approach.Based on the data available for 2009, a rapid increase was observed that year in the number of active farms and fish . However, this is an artifact as many farms had not yet been involved in fish movement and thereby appeared inactive . As a consequence, our results are reported from the start of 2010. The number of active farms declined slightly during the period 2010–2017 with relatively stable numbers during the 2010-2014 period, and a decrease during the 2015–2017 period . The total farmed Atlantic salmon population in Ireland had an increasing trend from 2010, with a peak of more than 32 million fish in early 2015, to later decrease until the end of the simulation, although not dropping to previous levels, rolling benches for growing where it reached ∼13 million fish. This increase was related to a large increase in the number of juveniles during 2014 and 2015. The number of fish within each age category varied seasonally, with juvenile fish showing peaks during winter and dips during autumn , the former associated with spawning and the latter with the transition of juvenile fish to smolts prior to stocking in seawater farms in autumn and spring. For the smolts, the converse was true, with peaks during autumn and spring. This age group decreases roughly every 180 days, as this is the amount of time after which they were aged into the growth-repro age group. This in turn determines the peaks of this latter age group. The reduction in the numbers of fish in the growth-repro age group were mainly in spring-summer and autumn-winter, being a mixture of elimination of fish stocked in a farm as smolts after 600 days and elimination of fish stocked at older ages after spending the mean residence time in the farm . Based on reported fish movement data, the externally scheduled events showed a moderate increase during the study period, except for the enter events, and exhibited seasonal variation.

External transfers increased from autumn through to spring, decreasing during summer, showing the seasonality in the smolt stocking in autumn and spring, and the spawning season in winter, where fish and eggs are moved from broodstock sites to hatcheries. The enter events peaked from autumn to winter, this being associated with the entry of fertilized eggs by local broodstock fish and tended to drop during spring and summer. Overall, the enter events showed a moderate decrease during the study period. Internal transfers had a seasonal pattern in line with the external transfers, as it was often the case that fish will be aged before movement to other farm, specifically fish in the egg-juvenile age group were aged to smolt when moving from a freshwater to a seawater farm, and smolts were aged to growth-repro age group when moving smolt from a seawater to a seawater farm. Exit events also followed external transfers closely. This is because these events were scheduled to occur the day prior to a fish shipment, if the number of fish to be shipped was less than the number of fish initially stocked with the cohort . The proportion of farms connected with at least one other farm within a month through live fish movements also showed a cyclical pattern, with peaks in February through to April, June through to August, and October through to December .Following introduction of infection in mid and late 2009, i.e., the index cases, a between-farm prevalence of 50% was reached on early 2011 , and 90% of the fish farms were infected by early 2013 . By 5 years after the simulated introduction in late 2014, 100% of the farms were infected, oscillating around this value until the end of the simulation. The farms holding growth fish and broodstock and smolts had a faster modeled epidemic curve, the first group reaching a between-farm prevalence of 50% by early 2011 and 100% by mid 2012, stabilizing around that value in late 2013. For the farms holding smolts, a between-farm prevalence of 50% was reached in late 2010, and 100% between-farm prevalence was reached for the first time in late 2011, dropping to 50–75% during most of 2012, to finally oscillate around 100% from mid 2013 onward. The modeled epidemic curve for farms holding eggs and juvenile fish was slower, reaching a between-farm prevalence of 50% by late 2012, and a between farm prevalence around 90% since early 2013, oscillating around this value until the end of 2016, where it stabilized at 100% until the end of the simulation . Fish prevalence follows a similar dynamic, with total and juvenile fish prevalence lagging behind fish prevalence in the growth-broodstock and smolt age groups, but with the former two age groups never reaching a level of 100%. This is due to the constant input of newly hatched fish, which the model assumes are introduced into the susceptible compartment. This can be seen as a drop in the egg-juvenile and total fish prevalence around winter, when the fertilized eggs and juvenile fish are entered into the fish population. A similar cyclical trend can be seen with fish prevalence in smolt, which declines in autumn and spring as juvenile fish are transitioning into this stage prior to the stocking in seawater farms.