Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales.
TL;DR: H5N1 avian influenza transmission probabilities and containment strategies, here modelled on the British poultry industry network, show that infection dynamics can additionally express characteristic scales, and hotspots can make more effective inoculation targets.
Abstract: Epidemics are frequently simulated on redundantly wired contact networks, which have many more links between sites than are minimally required to connect all. Consequently, the modelled pathogen can travel numerous alternative routes, complicating effective containment strategies. These networks have moreover been found to exhibit ‘scale-free’ properties and percolation, suggesting resilience to damage. However, realistic H5N1 avian influenza transmission probabilities and containment strategies, here modelled on the British poultry industry network, show that infection dynamics can additionally express characteristic scales. These system-preferred scales constitute small areas within an observed power law distribution that exhibit a lesser slope than the power law itself, indicating a slightly increased relative likelihood. These characteristic scales are here produced by a network-pervading intranet of so-called hotspot sites that propagate large epidemics below the percolation threshold. This intranet is, however, extremely vulnerable; targeted inoculation of a mere 3–6% (depending on incorporated biosecurity measures) of the British poultry industry network prevents large and moderate H5N1 outbreaks completely, offering an order of magnitude improvement over previously advocated strategies affecting the most highly connected ‘hub’ sites. In other words, hotspots and hubs are separate functional entities that do not necessarily coincide, and hotspots can make more effective inoculation targets. Given the ubiquity and relevance of networks (epidemics, Internet, power grids, protein interaction), recognition of this spreading regime elsewhere would suggest a similar disproportionate sensitivity to such surgical interventions.
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TL;DR: A new approach to design effective targeted intervention strategies to mitigate and control the propagation of infections across heterogeneous contact networks is introduced, using a newly developed individual-level deterministic Susceptible-Infectious-Susceptible (SIS) epidemiological model.
Abstract: In cases where there are limited resources for the eradication of an epidemic, or where we seek to minimise possible adverse impacts of interventions, it is essential to optimise the efficacy of control measures. We introduce a new approach, Epidemic Control Analysis (ECA), to design effective targeted intervention strategies to mitigate and control the propagation of infections across heterogeneous contact networks. We exemplify this methodology in the context of a newly developed individual-level deterministic Susceptible-Infectious-Susceptible (SIS) epidemiological model (we also briefly consider applications to Susceptible-Infectious-Removed (SIR) dynamics). This provides a flexible way to systematically determine the impact of interventions on endemic infections in the population. Individuals are ranked based on their influence on the level of infectivity. The highest-ranked individuals are prioritised for targeted intervention. Many previous intervention strategies have determined prioritisation based mainly on the position of individuals in the network, described by various local and global network centrality measures, and their chance of being infectious. Comparisons of the predictions of the proposed strategy with those of widely used targeted intervention programmes on various model and real-world networks reveal its efficiency and accuracy. It is demonstrated that targeting central individuals or individuals that have high infection probability is not always the best strategy. The importance of individuals is not determined by network structure alone, but can be highly dependent on the infection dynamics. This interplay between network structure and infection dynamics is effectively captured by ECA.
24 citations
TL;DR: The hypothesis that increasing economic efficiency in the domestic ostrich industry in South Africa made the system more vulnerable to outbreak of Highly Pathogenic Avian Influenza (H5N2), and the results indicated that as time progressed, the network became increasingly vulnerable to pathogen outbreaks.
Abstract: Background: The focus of management in many complex systems is shifting towards facilitation, adaptation, building resilience, and reducing vulnerability. Resilience management requires the development and application of general heuristics and methods for tracking changes in both resilience and vulnerability. We explored the emergence of vulnerability in the South African domestic ostrich industry, an animal production system which typically involves 3-4 movements of each bird during its lifetime. This system has experienced several disease outbreaks, and the aim of this study was to investigate whether these movements have contributed to the vulnerability of this system to large disease outbreaks.
Methodology/Principal Findings: The ostrich production system requires numerous movements of birds between different farm types associated with growth (i.e. Hatchery to juvenile rearing farm to adult rearing farm). We used 5 years of movement records between 2005 and 2011 prior to an outbreak of Highly Pathogenic Avian Influenza (H5N2). These data were analyzed using a network analysis in which the farms were represented as nodes and the movements of birds as links. We tested the hypothesis that increasing economic efficiency in the domestic ostrich industry in South Africa made the system more vulnerable to outbreak of Highly Pathogenic Avian Influenza (H5N2). Our results indicated that as time progressed, the network became increasingly vulnerable to pathogen outbreaks. The farms that became infected during the outbreak displayed network qualities, such as significantly higher connectivity and centrality, which predisposed them to be more vulnerable to disease outbreak.
Conclusions/ Significance: Taken in the context of previous research, our results provide strong support for the application of network analysis to track vulnerability, while also providing useful practical implications for system monitoring and management.
22 citations
Cites background from "Preventable H5N1 avian influenza ep..."
...Seasonal variation is not uncommon in domestic production systems, with comparable fluctuations observed in the British livestock [22,23] and poultry [25,26] industries....
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TL;DR: In this chapter, some concepts in disease modelling will be introduced, the relevance of selected network phenomena discussed, and results from real data and their relationship to network analyses summarised are summarised.
Abstract: Heterogeneous population structure can have a profound effect on infectious disease dynamics, and is particularly important when investigating “tactical” disease control questions. At times, the nature of the network involved in the transmission of the pathogen (bacteria, virus, macro-parasite, etc.) appears to be clear; however, the nature of the network involved is dependent on the scale (e.g. within-host, between-host, or between-population), the nature of the contact, which ranges from the highly specific (e.g. sexual acts or needle sharing at the person-to-person level) to almost completely non-specific (e.g. aerosol transmission, often over long distances as can occur with the highly infectious livestock pathogen foot-and-mouth disease virus—FMDv—at the farm-to-farm level, e.g. Schley et al. in J. R. Soc. Interface 6:455–462, 2008), and the timescale of interest (e.g. at the scale of the individual, the typical infectious period of the host). Theoretical approaches to examining the implications of particular network structures on disease transmission have provided critical insight; however, a greater challenge is the integration of network approaches with data on real population structures. In this chapter, some concepts in disease modelling will be introduced, the relevance of selected network phenomena discussed, and then results from real data and their relationship to network analyses summarised. These include examinations of the patterns of air traffic and its relation to the spread of SARS in 2003 (Colizza et al. in BMC Med., 2007; Hufnagel et al. in Proc. Natl. Acad. Sci. USA 101:15124–15129, 2004), the use of the extensively documented Great Britain livestock movements network (Green et al. in J. Theor. Biol. 239:289–297, 2008; Robinson et al. in J. R. Soc. Interface 4:669–674, 2007; Vernon and Keeling in Proc. R. Soc. Lond. B, Biol. Sci. 276:469–476, 2009) and the growing interest in combining contact structure data with phylogenetics to identify real contact patterns as they directly relate to diseases of interest (Cottam et al. in PLoS Pathogens 4:1000050, 2007; Hughes et al. in PLoS Pathogens 5:1000590, 2009).
16 citations
Cites background from "Preventable H5N1 avian influenza ep..."
...Multi-scale percolation as described here has also been analysed in several real networks [39, 41]....
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TL;DR: The susceptibility of the English and Welsh fish farming and fisheries industry to emergent diseases is assessed using a stochastic simulation model that considers reactive, proactive, and hybrid methods of control which correspond to a mixture of policy and the ease of disease detection.
Abstract: The susceptibility of the English and Welsh fish farming and fisheries industry to emergent diseases is assessed using a stochastic simulation model. The model dynamics operate on a network comprising directed transport and river contacts, as well as undirected local and fomite transmissions. The directed connections cause outward transmission risk to be geographically more confined than inward risk. We consider reactive, proactive, and hybrid methods of control which correspond to a mixture of policy and the ease of disease detection. An explicit investigation of the impact of laboratory capacity is made. General quantified guidelines are derived to mitigate future epidemics.
15 citations
Cites background from "Preventable H5N1 avian influenza ep..."
...…and undirected links, the effects of long-range connections (e.g., small-world networks), and emergent properties due to clustering, community association, or fragmentation of network parts (Keeling, 1999; Sharkey et al., 2006; Green et al., 2009; Munro and Gregory, 2009; Jonkers et al., 2010)....
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..., small-world networks), and emergent properties due to clustering, community association, or fragmentation of network parts (Keeling, 1999; Sharkey et al., 2006; Green et al., 2009; Munro and Gregory, 2009; Jonkers et al., 2010)....
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TL;DR: Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks is considered, applicable to several sexually transmitted diseases and computer viruses, and it is shown that the probability of invasion from any given individual is equal to the (probabilistic) endemic prevalence, following successful invasion, at the individual.
Abstract: Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD). By representing the model as a percolation process and utilising the property of duality, we also provide a theoretical definition of invasion probability. We then show that, for undirected networks, the probability of invasion from any given individual is equal to the (probabilistic) endemic prevalence, following successful invasion, at the individual (we also provide a relationship for the directed case). The total (fractional) endemic prevalence in the population is thus equal to the average invasion probability (across all individuals). Consequently, for such systems, the regions or individuals already supporting a high level of infection are likely to be the source of a successful invasion by another infectious agent. This could be used to inform targeted interventions when there is a threat from an emerging infectious disease.
15 citations
References
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TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them.
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other.
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.
18,415 citations
TL;DR: It is found that scale-free networks, which include the World-Wide Web, the Internet, social networks and cells, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates.
Abstract: Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network1. Complex communication networks2 display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web3,4,5, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.
7,697 citations
"Preventable H5N1 avian influenza ep..." refers background in this paper
...…heterogeneous, redundantly wired networks that feature many possible routes between most network nodes, e.g. Internet, social and ecological systems, protein interaction networks, and which exhibit power law statistics (Rhodes & Anderson 1996; Albert et al. 2000; Albert & Barabasi 2002; May 2006)....
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...Others offer hope in identifying the most highly connected sites (hubs) as the most vulnerable part of such systems (Albert et al. 2000; Callaway et al. 2000; May & Lloyd 2001; Song et al. 2005; Jeger et al. 2007)....
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...Following existing advice (Albert et al. 2000; Song et al. 2005; Jeger et al. 2007; Dent et al. 2008), we focused first on hubs; all other sites we call peripherals....
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...Internet, social and ecological systems, protein interaction networks, and which exhibit power law statistics (Rhodes & Anderson 1996; Albert et al. 2000; Albert & Barabasi 2002; May 2006)....
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TL;DR: After defining a set of new characteristic quantities for the statistics of communities, this work applies an efficient technique for exploring overlapping communities on a large scale and finds that overlaps are significant, and the distributions introduced reveal universal features of networks.
Abstract: A network is a network — be it between words (those associated with ‘bright’ in this case) or protein structures. Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of1,2,3,4. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins5,6, industrial sectors7 and groups of people8,9) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.
5,217 citations
"Preventable H5N1 avian influenza ep..." refers background in this paper
...Instead, hotspots tend to associate spatially (over short distances) to span large areas in thin strands, and, crucially, share many mutual contacts with other hotspots that extend this overlap network-wide (Newman 2003; Palla et al. 2005)....
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TL;DR: This paper studies percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolators, bond percolations, and models in which occupation probabilities depend on vertex degree.
Abstract: Recent work on the Internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes or links. Such deletions include, for example, the failure of Internet routers or power transmission lines. Percolation models on random graphs provide a simple representation of this process but have typically been limited to graphs with Poisson degree distribution at their vertices. Such graphs are quite unlike real-world networks, which often possess power-law or other highly skewed degree distributions. In this paper we study percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolation, bond percolation, and models in which occupation probabilities depend on vertex degree. We discuss the application of our theory to the understanding of network resilience.
2,298 citations
"Preventable H5N1 avian influenza ep..." refers background in this paper
...Others offer hope in identifying the most highly connected sites (hubs) as the most vulnerable part of such systems (Albert et al. 2000; Callaway et al. 2000; May & Lloyd 2001; Song et al. 2005; Jeger et al. 2007)....
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TL;DR: A power-law relation is identified between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent to explain the scale-free nature of complex networks and suggest a common self-organization dynamics.
Abstract: Complex networks have been studied extensively owing to their relevance to many real systems such as the world-wide web, the Internet, energy landscapes and biological and social networks. A large number of real networks are referred to as 'scale-free' because they show a power-law distribution of the number of links per node. However, it is widely believed that complex networks are not invariant or self-similar under a length-scale transformation. This conclusion originates from the 'small-world' property of these networks, which implies that the number of nodes increases exponentially with the 'diameter' of the network, rather than the power-law relation expected for a self-similar structure. Here we analyse a variety of real complex networks and find that, on the contrary, they consist of self-repeating patterns on all length scales. This result is achieved by the application of a renormalization procedure that coarse-grains the system into boxes containing nodes within a given 'size'. We identify a power-law relation between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent. These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics.
1,303 citations
"Preventable H5N1 avian influenza ep..." refers background in this paper
...Others offer hope in identifying the most highly connected sites (hubs) as the most vulnerable part of such systems (Albert et al. 2000; Callaway et al. 2000; May & Lloyd 2001; Song et al. 2005; Jeger et al. 2007)....
[...]
...Following existing advice (Albert et al. 2000; Song et al. 2005; Jeger et al. 2007; Dent et al. 2008), we focused first on hubs; all other sites we call peripherals....
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