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

The effectiveness of fallowing strategies in disease control in salmon aquaculture assessed with an SIS model

Salmon production is an important industry in Scotland, with an estimated retail value >£1 billion. However, this salmon industry can be threatened by the invasion and spread of diseases. To reduce this risk, the industry is divided into management areas that are physically separated from each other. Pathogens can spread between farms by local processes such as water movement or by long-distance processes such as live fish movements. Here, network modelling was used to investigate the importance of transmission routes at these two scales. We used different disease transmission rates (beta), where infected farms had the probability of 0.10, 0.25 or 0.50 per month to infect each contacted farm. Interacting farms were modelled in such a way that neighbours within a management area could infect each other, resulting in two contacts per farm per month. In addition, non-local transmission occurred at random. Salmon are input to marine sites where they are raised to harvest size, the site is then fallowed; in the model the effects of different fallowing strategies (synchronised, partial synchronised and unsynchronised fallowing at the management area level) on the emergence of diseases were investigated. Synchronised fallowing was highly effective at eradicating epidemics when transmission rate is low (beta = 0.10) even when long distance contacts were fairly common (up to 1.5 farm−1 month−1). However for higher transmission rates, long distance contacts have to be kept at much lower levels (0.15 contacts month−1 where beta = 0.25) when synchronised fallowing was applied. If fallowing was partially synchronised or unsynchronised then low rates of long-distance contact are required (0.75 or 0.15 farm−1 month−1) even if beta = 0.10. These results demonstrate the potential benefits of having epidemiologically isolated management areas and applying synchronised fallowing

Investigation of factors affecting skin penetration in vitro

When desirable retardation of skin penetration of toxic compounds such as pesticides and chemical warfare agents was evaluated using model permeants, retardation was observed under certain conditions, but was not predictable. It was concluded that generic penetration modulation was not a realistic goal. Investigations into skin surface sampling techniques highlighted the difficulties of minimising variability, and comparison of in vitro tape stripping with published in vivo data for a clobetasol propionate cream demonstrated the significance of formulation inhomogeneity. Determination of orally administered doxycycline in the stratum corneum using in vivo skin surface biopsies suggested that it was unlikely that this technique could be of value for most orally administered drugs. Evaporative loss of volatile permeants, such as fragrances, during skin penetration studies makes it impossible to achieve full mass balance. Direct capture of evaporating material was occlusive and significantly affected the amount that permeated through the skin membranes. A simple novel method was therefore developed to allow estimation of evaporative loss under the experimental conditions. Pre-study skin water permeability coefficient (Kp) is frequently used as a membrane integrity check and it is generally assumed that skin of higher water permeability will be of higher permeability for subsequently applied compounds, regardless of differing physiochemical properties. However, it was shown that Kp did not correlate with subsequent test compound permeation for twelve compounds of moderate to high lipophilicity

Physiological Response to Feeding in Little Penguins

© 2006 by The University of Chicago.Specific dynamic action (SDA), the increase in metabolic rate above resting levels that accompanies the processes of digestion and assimilation of food, can form a substantial part of the daily energy budget of free-ranging animals. We measured heart rate (fH) and rate of oxygen consumption ( ) in 12 little penguins while they digested a meal of sardines in order to determine whether they show specific dynamic action. In contrast to some studies of other penguin species, little penguins showed a substantial SDA, the magnitude of which was proportional to the size of the meal. The energy utilized in SDA was equivalent to 13.4% of the available energy content of the fish. Furthermore, animals such as penguins that forage in a cold environment will probably expend further energy in heating their food to body temperature to facilitate efficient digestion. It is estimated that this additional energy expenditure was equivalent to 1.6%-2.3% of the available energy content of the fish, depending on the time of year and therefore the temperature of the water. Changes in fH during digestion were qualitatively similar to those in , implying that there were no substantial circulatory adjustments during digestion and that the relationship between fH and in penguins is unaffected by digestive state

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

Seasonality and heterogeneity of live fish movements in Scottish fish farms

Movement of live animals is a key contributor to disease spread. Farmed Atlantic salmon Salmo salar, rainbow trout Onchorynchus mykiss and brown/sea trout Salmo trutta are initially raised in freshwater (FW) farms; all the salmon and some of the trout are subsequently moved to seawater (SW) farms. Frequently, fish are moved between farms during their FW stage and sometimes during their SW stage. Seasonality and differences in contact patterns across production phases have been shown to influence the course of an epidemic in livestock; however, these parameters have not been included in previous network models studying disease transmission in salmonids. In Scotland, farmers are required to register fish movements onto and off their farms; these records were used in the present study to investigate seasonality and heterogeneity of movements for each production phase separately for farmed salmon, rainbow trout and brown/sea trout. Salmon FW-FW and FW-SW movements showed a higher degree of heterogeneity in number of contacts and different seasonal patterns compared with SW-SW movements. FW-FW movements peaked from May to July and FW-SW movements peaked from March to April and from October to November. Salmon SW-SW movements occurred more consistently over the year and showed fewer connections and number of repeated connections between farms. Therefore, the salmon SW-SW network might be treated as homogeneous regarding the number of connections between farms and without seasonality. However, seasonality and production phase should be included in simulation models concerning FW-FW and FW-SW movements specifically. The number of rainbow trout FW-FW and brown/sea trout FW- FW movements were different from random. However, movements from other production phases were too low to discern a seasonal pattern or differences in contact pattern

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments

Sudden Cardiac Death in Dialysis: Arrhythmic Mechanisms and the Value of Non-invasive Electrophysiology

Sudden Cardiac Death (SCD) is the leading cause of cardiovascular death in dialysis patients. This review discusses potential underlying arrhythmic mechanisms of SCD in the dialysis population. It examines recent evidence from studies using implantable loop recorders and from electrophysiological studies in experimental animal models of chronic kidney disease. The review summarizes advances in the field of non-invasive electrophysiology for risk prediction in dialysis patients focusing on the predictive value of the QRS-T angle and of the assessments of autonomic imbalance by means of heart rate variability analysis. Future research directions in non-invasive electrophysiology are identified to advance the understanding of the arrhythmic mechanisms. A suggestion is made of incorporation of non-invasive electrophysiology procedures into clinical practice.Key Concepts:– Large prospective studies in dialysis patients with continuous ECG monitoring are required to clarify the underlying arrhythmic mechanisms of SCD in dialysis patients.– Obstructive sleep apnoea may be associated with brady-arrhythmias in dialysis patients. Studies are needed to elucidate the burden and impact of sleeping disorders on arrhythmic complications in dialysis patients.– The QRS-T angle has the potential to be used as a descriptor of uremic cardiomyopathy.– The QRS-T angle can be calculated from routine collected surface ECGs. Multicenter collaboration is required to establish best methodological approach and normal values.– Heart Rate Variability provides indirect assessment of cardiac modulation that may be relevant for cardiac risk prediction in dialysis patients. Short-term recordings with autonomic provocations are likely to overcome the limitations of out of hospital 24-h recordings and should be prospectively assessed