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.
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.
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 article, the Sierpinsky gasket is described by a complex fractal dimension whose imaginary part is a simple function (inverse of the logarithm) of the discrete scaling factor, and a set of simple physical systems (spins and percolation) on hierarchical lattices is analyzed to exemplify the origin of different terms in the discrete renormalization group formalism introduced to tackle this problem.
Abstract: We discuss in detail the concept of discrete scale invariance and show how it leads to complex critical exponents and hence to the log-periodic corrections to scaling exhibited by various measures of seismic activity close to a large earthquake singularity. Discrete scale invariance is first illustrated on a geometrical fractal, the Sierpinsky gasket, which is shown to be fully described by a complex fractal dimension whose imaginary part is a simple function (inverse of the logarithm) of the discrete scaling factor. Then, a set of simple physical systems (spins and percolation) on hierarchical lattices is analyzed to exemplify the origin of the different terms in the discrete renormalization group formalism introduced to tackle this problem. As a more specific example of rupture relevant for earthquakes, we propose a solution of the hierarchical time-dependent fiber bundle of Newman et al. [1994] which exhibits explicitly a discrete renormalization group from which log-periodic corrections follow. We end by pointing out that discrete scale invariance does not necessarily require an underlying geometrical hierarchical structure. A hierarchy may appear “spontaneously” from the physics and/or the dynamics in a Euclidean (nonhierarchical) heterogeneous system. We briefly discuss a simple dynamical model of such mechanism, in terms of a random walk (or diffusion) of the seismic energy in a random heterogeneous system.
183 citations
Additional excerpts
...The six main models were analysed in terms of discrete scale invariance (DSI), a feature of many complex systems (Saleur et al. 1996; Johansen & Sornette 1998; Sornette 1998)....
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TL;DR: Measurements of the distribution of epidemic sizes and duration are used to show that regularities in the dynamics of such systems do become apparent and that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.
Abstract: TEMPORAL changes in the incidence of measles virus infection within large urban communities in the developed world have been the focus of much discussion in the context of the identification and analysis of nonlinear and chaotic patterns in biological time series1–11. In contrast, the measles records for small isolated island populations are highly irregular, because of frequent fade-outs of infection12–14, and traditional analysis15 does not yield useful insight. Here we use measurements of the distribution of epidemic sizes and duration to show that regularities in the dynamics of such systems do become apparent. Specifically, these biological systems are characterized by well-defined power laws in a manner reminiscent of other nonlinear, spatially extended dynamical systems in the physical sciences16–19. We further show that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.
179 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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...…The Royal Society networks, and stressed the bimodal outbreak response that typifies percolation (ca 5% of susceptibles infected below the threshold, and a giant component of infected sites appearing above it, analogous to a spreading forest fire) (Rhodes & Anderson 1996; Grenfell et al. 2002)....
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TL;DR: It is argued that, under appropriate conditions, a static network analysis can be an appropriate tool for gaining insights into disease dynamics even when the relevant time-scales are similar, as with FMD.
Abstract: We analyse the relationship between the network of livestock movements in the UK and the dynamics of two diseases: foot-and-mouth disease (FMD), which has an incubation period of days, and scrapie, which incubates over years. For FMD, the time-scale of expected epidemics is similar to the time-scale of the evolution of the network. We argue that, under appropriate conditions, a static network analysis can be an appropriate tool for gaining insights into disease dynamics even when the relevant time-scales are similar, as with FMD. We show that a subclass of ‘linkage moves’ maintains the network structure, and so removing these links has a dramatic effect on the number of potentially infected farms, an effect corroborated by simulations. In contrast, because scrapie has a low probability of transmission per contact and a long incubation period, a static network representation is probably appropriate; however, the signature of the network in the pattern of transmission is likely to be faint. Scrapie-notifying farms were more likely to be associated with each other via trading at markets than were control farms; however, network community structure proves to be less representative of prevalence patterns than geographical region. These contradictory indicators emphasize that appropriate observation time frames and good discrimination among types of potentially infectious contacts are vital in order for network analysis to be a valuable epidemiological tool.
170 citations
"Preventable H5N1 avian influenza ep..." refers background in this paper
...This report shows that almost imperceptibly small, but targeted changes in structure may radically alter observed network behaviour (Kao et al. 2007)....
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...This property of ‘connecting up the network’ has previously been identified by Kao et al. (2007), but in our interpretation, hotspots function as a single collective rather than as numerous individual bridges....
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TL;DR: A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules.
Abstract: Networks are ubiquitous in natural, technological and social systems. They are of increasing relevance for improved understanding and control of infectious diseases of plants, animals and humans, given the interconnectedness of today's world. Recent modelling work on disease development in complex networks shows: the relative rapidity of pathogen spread in scale-free compared with random networks, unless there is high local clustering; the theoretical absence of an epidemic threshold in scale-free networks of infinite size, which implies that diseases with low infection rates can spread in them, but the emergence of a threshold when realistic features are added to networks (e.g. finite size, household structure or deactivation of links); and the influence on epidemic dynamics of asymmetrical interactions. Models suggest that control of pathogens spreading in scale-free networks should focus on highly connected individuals rather than on mass random immunization. A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules. Potential consequences for the study and management of plant and tree diseases are discussed.
164 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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...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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TL;DR: It is shown that 'silent spread' can occur because of incomplete protection at the flock level, even if a vaccine is effective in individual birds, and the use of unvaccinated sentinels can mitigate, although not completely eliminate, the problem.
Abstract: A chink in the protection of a caged flock can dramatically increase the chances of a flu outbreak.
152 citations