Comment on ''Properties of highly clustered networks"

We consider a procedure for generating clustered networks previously reported by Newman [Phys. Rev. E 68, 026121 (2003)]. In the same study, clustered networks generated according to the proposed model have been reported to have a lower epidemic threshold under susceptible-infective-recovered-type network epidemic dynamics. By rewiring networks generated by this model, such that the degree distribution is conserved, we show that the lower epidemic threshold can be closely reproduced by rewired networks with close to zero clustering. The reported lower epidemic threshold can be explained by different degree distributions observed in the networks corresponding to different levels of clustering. Clustering results in networks with high levels of heterogeneity in node degree, a higher proportion of nodes with zero connectivity, and links concentrated within highly interconnected components of small size. Hence, networks generated by this model differ in both clustering and degree distribution, and the lower epidemic threshold is not explained by clustering alone

From Markovian to pairwise epidemic models and the performance of moment closure approximations

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness

Network structure and risk-based surveillance algorithms for live shrimp movements in Thailand

Live shrimp movements pose a potential route for site‐to‐site transmission of acute hepatopancreatic necrosis disease (AHPND) and other shrimp diseases. We present the first application of network theory to study shrimp epizootiology, providing quantitative information about the live shrimp movement network of Thailand (LSMN), and supporting practical and policy implementations of disease surveillance and control measures. We examined the LSMN over a 13‐month period from March 2013 to March 2014, with data obtained from the Thailand Department of Fisheries. The LSMN had a mixture of characteristics both limiting and facilitating disease spread. Importantly, the LSMN exhibited power‐law distributions of in and out degrees with exponents of 2.87 and 2.17, respectively. This characteristic indicates that the LSMN behaves like a scale‐free network and suggests that an effective strategy to control disease spread in the Thai shrimp farming sector can be achieved by removing a small number of targeted inter‐site connections (arcs between nodes). Specifically, a disease‐control algorithm based on betweenness centrality (defined as the number of shortest paths between node pairs that traverse a given arc) is proposed here to prioritize targets for disease surveillance and control measures

Estimates for local and movement-based transmission of bovine tuberculosis in British cattle

Both badgers and livestock movements have been implicated in contributing to the ongoing epidemic of bovine tuberculosis (BTB) in British cattle. However, the relative contributions of these and other causes are not well quantified. We used cattle movement data to construct an individual (premises)-based model of BTB spread within Great Britain, accounting for spread due to recorded cattle movements and other causes. Outbreak data for 2004 were best explained by a model attributing 16% of herd infections directly to cattle movements, and a further 9% unexplained, potentially including spread from unrecorded movements. The best-fit model assumed low levels of cattle-to-cattle transmission. The remaining 75% of infection was attributed to local effects within specific high-risk areas. Annual and biennial testing is mandatory for herds deemed at high risk of infection, as is pre-movement testing from such herds. The herds identified as high risk in 2004 by our model are in broad agreement with those officially designated as such at that time. However, border areas at the edges of high-risk regions are different, suggesting possible areas that should be targeted to prevent further geographical spread of disease. With these areas expanding rapidly over the last decade, their close surveillance is important to both identify infected herds quickly, and limit their further growth

The Impact of Escaped Farmed Atlantic Salmon (Salmo salar L.) on Catch Statistics in Scotland

In Scotland and elsewhere, there are concerns that escaped farmed Atlantic salmon (Salmo salar L.) may impact on wild salmon stocks. Potential detrimental effects could arise through disease spread, competition, or inter-breeding. We investigated whether there is evidence of a direct effect of recorded salmon escape events on wild stocks in Scotland using anglers' counts of caught salmon (classified as wild or farmed) and sea trout (Salmo trutta L.). This tests specifically whether documented escape events can be associated with reduced or elevated escapes detected in the catch over a five-year time window, after accounting for overall variation between areas and years. Alternate model frameworks were somewhat inconsistent, however no robust association was found between documented escape events and higher proportion of farm-origin salmon in anglers' catch, nor with overall catch size. A weak positive correlation was found between local escapes and subsequent sea trout catch. This is in the opposite direction to what would be expected if salmon escapes negatively affected wild fish numbers. Our approach specifically investigated documented escape events, contrasting with earlier studies examining potentially wider effects of salmon farming on wild catch size. This approach is more conservative, but alleviates some potential sources of confounding, which are always of concern in observational studies. Successful analysis of anglers' reports of escaped farmed salmon requires high data quality, particularly since reports of farmed salmon are a relatively rare event in the Scottish data. Therefore, as part of our analysis, we reviewed studies of potential sensitivity and specificity of determination of farmed origin. Specificity estimates are generally high in the literature, making an analysis of the form we have performed feasible

A strategic model for epidemic control in aquaculture

A stochastic metapopulation model of infectious disease was developed to model the spread of disease within and between sites of a region of an aquaculture industry. The study was a theoretical one examining the effect of transmission parameters through a sensitivity analysis. Production was modelled as either dispersed over many sites, or concentrated into small areas to provide 'firebreaks' between such areas as a disease control strategy. The effectiveness of such a control strategy could then be examined for different industry and disease parameters (for example, overall production, and rates of within- and between-site infection). At the within-site level, contact was modelled as either frequency or density dependent, either of these extreme formulations being potentially appropriate for different diseases. Under density dependence, the effect of high host density of increasing the basic reproduction number R0 dominates, in contrast to the frequency dependent model. However, for both model types, concentration of production into separate areas successfully slows the spread of simulated disease, particularly where long-distance transmission of the pathogen is weak due to fast attenuation of infectious agent over distance and time

Time-to-response toxicity analysis as a method for drug susceptibility assessment in salmon lice

The salmon louse Lepeophtheirus salmonis (Krøyer, 1837) is an ectoparasite causing infections ofwild and farmed Atlantic salmon (Salmo salar L.) in the Northern hemisphere.While L. salmonis control at commercial mariculture sites increasingly employs non-medicinal approaches, such as cage designs reducing infection rates and biological control through cleaner fish, anti-parasitic drugs are still a requirement for effective fish health care. With only a limited range of salmon delousing agents available, all of which have been in use for more than a decade, drug resistance formation has been reported for different products. Successful resistance management requires reliable susceptibility assessment, which is usually achieved through L. salmonis bioassays. These tests involve the exposure of parasites to different drug concentrations and require significant numbers of suitable L. salmonis stages. The present study reports an alternative bioassay that is based on time-to-response toxicity analyses and can be carried outwith limited parasite numbers. The assay determines the median effective time (ET50), i.e., the time required until impaired swimming and/or attachment behaviour becomes apparent in 50% of parasites, by conducting repeated examinations of test animals starting at the timepointwhere exposure to a set drug concentration commences. This experimental approach further allows the estimation of the apparent drug susceptibility of individual L. salmonis by determining their time to response, which may prove useful in experiments designed to elucidate associations between genetic factors and the drug susceptibility phenotype of parasites. Three laboratory strains of L. salmonis differing in susceptibility to emamectin benzoate were characterised using standard 24 h bioassays and time-to-response toxicity assays. While both the median effective concentration (EC50) and the ET50 showed variability between experimental repeats, both types of bioassay consistently discriminated susceptible and drug-resistant L. salmonis laboratory strains. Statement of relevance: Infections by sea lice cause significant costs to the global salmon farming industry, which have been estimated to exceed €300 million per year worldwide. Control of sea lice still relies to a significant extent on chemical delousing; however, chemical control is threatened by resistance formation. Resistance can be combated by rotation between different drugs and strategic implementation of non-medicinal strategies. However, resistance management requires reliable and feasible methods of susceptibility assessment. The present study is a technical note introducing a novel approach to susceptibility assessments in sea lice. The method can be applied in susceptibility assessments on farms,where it offers the advantage of a reduced requirement of parasites for testing. In addition, the novel method allows deriving the times of parasite require to showa response after drug treatment has started, thus providing a variable characterizing the drug susceptibility phenotype of individual parasites. Accordingly, the bioassay approach presented here will be useful for studies aiming at unravelling the genetic determinants of drug resistance

When and why direct transmission models can be used for environmentally persistent pathogens

Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen’s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models’ mean outputs diverge, with distinct predictions of outbreak size and duration

Investigating the involvement of a Midichloria -like organism (MLO) in red mark syndrome in rainbow trout Oncorhynchus mykiss

Red mark syndrome (RMS) is a skin condition in Rainbow trout Oncorhynchus mykiss that has been reported worldwide but was first seen in the United Kingdom (UK) in 2003. The current study was conducted to examine if there was an association between a Midichloria-like organism (MLO) and RMS using a statistically appropriate sample set, whilst determining if there is a lack of association with Flavobacterium psychrophilum implicated in disease in previous studies. Fish in this study were obtained from three sites positive for RMS in the UK and United States (US), and three sites in the UK and the Netherlands that had no previous history of this condition. Samples taken from RMS-affected sites were found to show typical RMS pathology. Analysis of the major organs of affected fish by quantitative polymerase chain reaction (qPCR) demonstrated a significantly higher presence of the MLO in the RMS-affected tissues. Although most of the tissues were positive for the MLO, the highest correlation was seen in the skin, whilst the tissues from the unaffected fish were all negative. Thus, a strong positive correlation was found between the MLO and RMS-affected fish, whilst no association was found between the RMS-affected fish and F. psychrophilum other than superficial presence in the skin. The use of immunohistochemistry showed positive staining of what was considered to be MLO-related antigens in the internal organs of most RMS-affected fish. Attempts were made to culture the MLO, but no MLO was isolated

The Contact Structure of Great Britain's Salmon and Trout Aquaculture Industry

We analyse the network structure of the British salmonid aquaculture industry from the perspective of infectious disease control. We combine for the first time live fish transport (or movement) data covering England and Wales with data covering Scotland and include network layers representing potential transmission by rivers, sea water and local transmission via human or animal vectors in the immediate vicinity of each farm or fishery site. We find that 7.2% of all live fish transports cross the England-Scotland border and network analysis shows that 87% of English and Welsh sites and 72% of Scottish sites are reachable from cross-border connections via live fish transports alone. Consequently, from a disease-control perspective, the contact structures of England and Wales and of Scotland should not be considered in isolation. We also show that large epidemics require the live fish movement network and so control strategies targeting movements can be very effective. While there is relatively low risk of widespread epidemics on the live fish transport network alone, the potential risk is substantially amplified by the combined interaction of multiple network layers