For growth and broodstock, fish prevalence stabilizes around 100% from late 2013 until the end of the simulation .When the effect of local spread was removed from the simulation , a model that includes spread between farms is only possible via fish movement . In this scenario, the spread of PMCV slows down, but the overall pattern remains of an increasing trend reaching a between-farm prevalence of 100%. This level of prevalence was reached for the first time in late 2015, compared to the full model where 100% prevalence was reached 1 year earlier in 2014. For the model where transmission was only possible via local spread , between-farm prevalence never reached a 20% level until mid 2017, and oscillated most of the time around 10%. Under this scenario, the only time that between-farm prevalence is higher than in the scenario with spread only via fish movement is at the beginning of the epidemic , indicating that local spread was the main driver of the transmission between farms at this early time .Of the evaluated centrality based interventions, the most effective were the ones based on out degree and outcloseness, for both the reactive and proactive approaches . For the former, after all spread via fish movement from the targeted nodes is stopped in July 2012, the increasing trend in between-farm prevalence immediately stops, stabilizing around 60% until the end of the simulation for both out degree and outcloseness based interventions. The between-farm prevalence obtained with these interventions was slightly higher than the prevalence obtained when pathogen spread via fish movements from all fish farms was stopped, the difference being clearer from 2016 until the end of the simulation . In terms of the time required to reach set prevalence benchmarks, vertical farming system both out degree and outcloseness based targeted interventions are virtually indistinguishable, with the former being slightly better .
Regarding the targeted interventions based on the other centrality measures, the one based on incloseness was the one that performed worst, with virtually the same result as when no intervention is applied, followed by the ones based on indegree and betweenness, with the latter being similar to the ones based on out degree and outcloseness until early 2014, after which it produces a higher between-farm prevalence. Similarly, when targeted interventions are applied from early on in the proactive approach , the most effective targeting strategies are those based on out degree and outcloseness, which are virtually indistinguishable from the one based in removing spread via fish movement from all nodes. The strategies based on these centrality measures produced between-farm prevalences around 10% from their implementation through the end of the simulation. Similar to the reactive approach, the worst performing strategy here is the one based on incloseness, which produces virtually the same result as if no intervention was applied, although with a slight delay in the increase of between-farm prevalence from 2010 through mid 2014. The strategy based on indegree was second to last, reaching a between-farm prevalence of around 90% in early 2016 and stabilizing around that value until the end of the simulation. A betweenness-based strategy did not show a clear difference with the best performing strategies based on out degree and outcloseness until late 2012, where between-farm prevalence increased slightly above the value for the other two strategies, andthis difference remained until the end of the simulation .In this paper, we describe the use of data-driven network modeling as a framework to evaluate the transmission of PMCV in the Irish farmed Atlantic salmon population, and the impact of targeted intervention strategies.
To do this, we have simulated the introduction and spread of PMCV in the Irish Atlantic salmon farming industry using real data of live fish movements, compulsorily reported to local authorities during 1 January 2009 to 23 October 2017, and data from a prevalence study conducted from 30 May 2016 to 19 December 2017. Additionally, using the fish movement data set, we have imputed population dynamics events at the farms by using a set of rules based on domain knowledge of the fish production cycle. We were able to reproduce population dynamics and the observed PMCV prevalence in the observational study that was used to estimate model parameters, evaluate the importance of infection spread via fish movement and local spread, and evaluate the effects of different farm centrality based control strategies. Parameter estimation showed that the best fitting model was the one with increasing transmission rates as fish aged and with a rate of decay of the environmental infectious pressure that varied each quarter . In common with other viral infections of farmed Atlantic salmon, studies have shown that fish have increased PMCV prevalence and higher concentration of the virus in fish tissues as they age during the production cycle. Further, the probability of developing CMS increases with the length of time at sea . In the freshwater phase, viral particles are detected in low quantities, and CMS outbreaks and CMS-related pathological lesions have not been described . In a study to evaluate vertical transmission of the agent, PMCV was found in 128 of 132 broodfish, and later detected in all stages of progeny, but only at prevalences of < 25% and with concentrations close to the detection limit of the method .In the observational study used for estimating the parameters in our model, PMCV was found at higher concentrations in broodstock fish and lower concentrations in younger age groups . Although pathogen concentration was not part of our model, a possible extension would be to allow α, the rate of viral shedding, to vary by age group. In our modeling, simulation was initialized at two broodstock farms.
Within these farms, transmission was horizontal . As highlighted in the model, horizontal transmission between farms is important, but only via fish transfer and not via local spread. Our results indicate that the introduction of the agent in two specific farms during the second half of 2009, coupled with the structure of the network of live fish movements in the country, is enough to account for the widespread occurrence of PMCV currently observed in the country. These findings are in agreement with the recent work of Tighe et al. , who found that PMCV strains in Ireland are largely homogenous, without evidence of geographically linked clustering, consistent with a hypothesis of agent spread through fish movement . If local spread were the main driver, several locally distinct viral strains would be more likely. In addition, Tighe et al. suggests that the Irish strains from cluster I could have arrived in Ireland between 2010 and 2012, while the strains from cluster IV could have arrived between 2007 and 2009. This is very close to our simulated introduction during 2009 based on the results of archived samples. This study also suggests that these dates are supported by the testing of archived heart samples from Irish Atlantic salmon broodstock which showed that all samples collected prior to 2009 were PMCV negative, whereas those tested from 2009 onwards were positive. It is these data, from Morrissey et al. that form the basis for the current simulation study. PMCV is observed at low levels during the freshwater phase. Further, it is unclear whether persistent virus in these fish is a substantial contributor to mortality at sea compared to the infection pressure that is exerted from neighboring farms and other factors, external to the farm, that are associated with infection and disease . In recent work, Jensen et al. have highlighted a possible pathway of transmission from broodstock to smolt, a pathway that is not explicitly modeled in the current study. We consider that our modeling approach would be well-suited to evaluate the plausibility of alternative transmission routes. Although current parameter estimates appear to reproduce age-varying fish susceptibility, it was not possible to reproduce the observed drop in prevalence during the May-July period. There are reports of slight seasonal variations of clinical CMS in seawater farms, with an increase in cases in autumn and spring , but no reports on seasonal patterns in the detection of PMCV via RT-PCR or other diagnostic tests, let alone seasonality of detection in freshwater. The fact that all model parameterizations used were not able to reproduce the observed drop during the month of June leads us to think that further observational data is required, possibly with a study with sampling conducted evenly throughout the year, so it can include the months where no samples were taken and a more homogeneous number of farms and fish sampled at each time. Nonetheless, we believe that our model is valuable, and that important lessons could be learned from it, like the major importance of spread via fish movement and the best intervention strategies in order to prevent extensive infection spread. These lessons would apply not only to PMCV, vertical farming racks but also to infectious diseases whose spread is predominantly via fish movement . The decision to use a susceptible-infected over a susceptible-infected-susceptible model for within-farm spread was based on the fact that different experimental studies have found the viral genome present in tissues of challenged fish throughout the whole duration of the study, indicating that the salmon immune response may be unable to eliminate the virus .
This, together with studies where PMCV has been consistently found in cohorts of fish sampled through long periods of time, indicating that PMCV can be present in fish for some months , provides further support for the modeling approach used here. Nevertheless, more research is required to further validate or refute this modeling choice, as it is possible that fish clear the infection beyond the time frames used in both experimental and observational studies. The model was sensitive to changes in the values of the indirect transmission rate, rate of decay in environmental infectious pressure, and the rate of viral shedding from infected individuals, but not to changes in the level of spatial coupling . Model outputs were also not substantially influenced by different parameter assumptions regarding either distance or seasonality , noting that information about distance thresholds was derived from other viral infections such as infectious salmon anemia , where estimates have varied from 5 to 20 km or more . Collectively, these results suggest that local spread may play a secondary role in the spread of PMCV across the Atlantic salmon farms in the country. When local spread was removed completely from the model , it was even clearer that this transmission pathway under current model assumptions was not the most important. On the basis of these results, we hypothesize that the widespread presence of PMCV in Ireland is most likely a product of the shipments of infected but subclinical fish through the network of live fish movements that occur in Ireland. This is consistent with fish being infected but subclinical for months prior to manifesting signs of disease , and by the structure of the network of live fish movements in the country . There is limited knowledge of agent survival of PMCV in the aquatic environment. Infection risk is higher on farms with a history of CMS outbreaks , which could suggest survival of the causal agent in the local environment. Further, infection pressure from farms within 100 km of seaway distance was found to be one of the most important risk factors for clinical CMS diagnosis , although this study did not evaluate spread via fish movement. It is noted that the distance over which infection can be transmitted via water is determined by an interaction between hydrodynamics, viral shedding and decay rates . Further research on PMCV survival in the environment is needed to guide parameterization of future models. The most effective intervention strategies are based on out degree and outcloseness , with the highest impact being observed when using these intervention strategies with a proactive approach . Note that all outgoing shipments from selected farms are assumed to include only susceptible fish , which can be equated with high levels of bio-security. The out degree and outcloseness based strategies are comparable, most likely because both strategies refer to outgoing shipments from a farm , the former with the number of farms receiving fish from a given source, and the latter inversely related to the number of intermediaries between the source and the rest of the farms in the network. Both centrality measures were moderately correlated with each other, with a Pearson correlation of 0.53 for the proactive approach when including all farms for each time window used.