Samples are collected on an annual basis as part of the national disease surveillance programme, and consist of pooled organ homogenate supernatants which are then stored at −80◦C. In these samples, PMCV was first detected from broodstock fish on a marine site in July 2009, with infection in 100% of the pools . It was later detected in December of the same year in 100% of pools of broodstock fish at a second broodstock farm. These are subsequently referred to as the index cases, to be used as the starting point for simulation of the epidemic. The rationale behind setting these two farms as index cases is that they are the earliest detections , and do not seem to be epidemiologically connected. There were 9 parameters in the SIE compartment model . Following the approach used by Widgren et al. , and for model parsimony, the shed rate α was fixed at 1.0 per day, thereby defining the unit of the environmental infectious pressure variable ϕi. In the absence of more detailed data, it was assumed that the threshold for two seawater farms being connected by local spread was an euclidean distance of 10 km. It was further assumed that freshwater farms were not connected via local spread but only via fish movement. In the model, four event types were defined. “Enter” concerns hatchings and international imports. “Internal transfer” occurs on the day that individual fish change their age category, from egg-juvenile to smolt, or from smolt to growth-repro. “External transfer” occurs when fish move from one farm to another. “Exit” is linked with slaughter, cannabis grower supplies euthanasia or international export, and from this point these fish are no longer included in the simulation.
Each of the scheduled events was executed in the model once the simulation, in continuous time, reached the time for any of the events. 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, identifier 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. The following data processing steps were used to generate events for the simulation. 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 egg juvenile 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 . The disease spread model was implemented in SimInf , which is an R package for data-driven stochastic disease spread simulations. This package was adapted, in part, from the Unstructured Mesh Reaction–Diffusion Master Equation framework . It interfaces high performance compiled code and OpenMP, which allows work to be divided across multiple processors and computations to be performed in parallel. The disease spread simulations were performed using the SimInf package version 5.1.0 and R version 3.4.2. The simulation was initiated by first supplying the model with an initial state in every farm, together with all events.
At the outset, infection prevalence was assumed to be zero, since the earliest detection of the agent in the country, dry racks for weed on archived broodstock samples, was in July 2009 . The initial environmental infectious pressure, ϕi, was also set to zero, as it was assumed that PMCV was not present in the country at the time of initialization . Based on test results on archived broodstock samples , the introduction of the agent was assumed to have occurred in two separate occasions at two different farms: 1 month prior to the time of sampling of the first positive archived sample in the population of broodstock fish resident in the farm at the time of sampling, and a second time in November 2009, affecting broodstock fish in a broodstock farm where it was later detected in December of that year.With the final model, farm and fish PMCV prevalence were estimated on a daily basis following the simulated introduction of the agent. The spread of the agent was plotted as a time series and the modeled epidemic curves were described. The role of both local spread and fish movement was evaluated by setting either D to zero , or moving all fish shipped to the susceptible compartment at the time of shipment .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, outdegree, 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, outdegree 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, 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 .