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Transcript
Contact network structure and risk of infection
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Christley; R.M. , Pinchbeck; G.L. , Bowers; RG. , Clancy; D , French; N.P. , Bennett; R and Turner; J
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Epidemiology Group, Faculty of Veterinary Science, 2Department of Mathematics, Faculty of Science,
University of Liverpool, Liverpool, United Kingdom, 3IVABS, Massey University, New Zealand.
Abstract
This study investigates the effect of structural features of contact networks on transmission of infection
in populations. We examined measures of network centrality that may be useful to identify individuals
of high risk of infection during outbreaks using susceptible-infectious-recovered models. Centrality
describes an individual’s position in a population; numerous parameters are available to assess this
attribute. Here we use a number of centrality measures including degree, eigenvector centrality,
betweenness, closeness and information centrality. Each of the measures of centrality was associated
with risk of infection in the simulated outbreaks. Importantly, degree (which is the most readily
measured) was at least as good as other network parameters in predicting risk of infection.
Identification of more central individuals in populations may be used to inform surveillance and
infection control strategies.
Objective
The objective of this work was to investigate the utility of a range of network parameters to predict an
individual’s risk of infection during outbreaks.
Introduction
The role of networks of transmission routes has been highlighted by recent high-profile outbreaks,
including avian influenza and foot and mouth disease (FMD). In many cases, the contact network
connecting individuals in a population and through which disease may transmit is poorly defined.
However, there have been recent attempts to define such networks for certain diseases in particular
populations. For example, networks associated with cattle (Christley et al., 2005b) and sheep (Webb,
2005) movement in the UK has been described, and the network associated with livestock movement in
the early days of the 2001 FMD outbreak in the UK has been investigated (Ortiz-Pelaez et al., 2006).
Here we utilise a simplified network structure to investigate the relationship of several measures of
network centrality to the risk of infection after emergence of a novel infectious disease in a fully
susceptible population (Christley et al., 2005a).
Methods
An undirected network consisting of 100 nodes and 2000 links was generated (density = 0.2). Nodes
were selected with probability proportional to their degree+1. In order to generate a network with
clustering, each node was assigned to one of 24 groups. If the selected nodes were in the same group
they were connected with probability 1; else they were connected with probability 0.05. Network
characteristics of each node, including centrality measures and assignment to the core of periphery,
were performed using UCInet v6.16 for Windows (Analytic Technologies Inc).
Transmission of an infectious agent through the network was simulated using a susceptible-infectiousrecovered model. In each simulation, an outbreak was simulated by randomly selecting a node to
become infected. At each subsequent time step transmission to susceptible neighbours was tested.
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
Available at www.sciquest.org.nz
Infectious nodes recovered after 14 time steps to be permanently immune. For each of three
transmission probabilities (0.00375, 0.0075 & 0.015) 500 simulations were undertaken. Details of the
methods used have been published (Christley et al., 2005a).
Results
The network included a 43 node core. This core predicted well those individuals at greatest risk of
infection (Figure 1).All six centrality measures were associated with the probability of infection (Figure
2).
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0.02
0.06
0.08
0.10
0.0040
0.0055
Closeness
0 50
Random walk betweenness
0.0 0.2 0.4 0.6 0.8 1.0
Probability of infection
0.0 0.2 0.4 0.6 0.8 1.0
Degree
0.04
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Shortest path betweenness
0.0 0.2 0.4 0.6 0.8 1.0
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0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Probability of infection
0.0 0.2 0.4 0.6 0.8 1.0
Figure 1: Probability of infection when transmission probability=0.0075. (Red=0.601-0.7, blue=0.501-0.6,
black=0.401-0.5, yellow=0.201-0.4, green=0-0.2.) Square nodes belong to the core and circular nodes to
the periphery (adapted from Christley et al, 2005a)
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Information
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0.05
0.10
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Eigenvector
Figure 2: Relationship between node degree, random-walk betweenness, shortest-path betweenness,
closeness, information centrality and eigenvector centrality and the proportion of times infected during
500 simulations, where the transmission parameter =0.00375 (red), 0.0075 (blue) and 0.015 (green).
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
Available at www.sciquest.org.nz
Discussion
We have identified a number of network centrality measures that may be useful predictors of
individuals’ risk of infection during outbreaks of disease in naive populations. In the example
investigated here, the degree centrality performed as well as, or better than, other measures. This has
important practical implications, as degree can be measured at the node-level, whereas other measures
require assessment of the population network. However, the topology of the network examined was
relatively simple; each of the centrality measures were correlated with each other in this example. In
more complex networks this is often not the case and measures other than degree may perform better in
such networks. Furthermore, transmission of many diseases occurs via directed contacts (the pathogen
transmits in only one direction, or not equally in each direction). Whilst there is evidence that measures
of centrality that ignore such directionality still have predictive ability (Bell et al., 1999, Corner et al.,
2003), the effect of such simplifications requires further investigation.
In conclusion, network analysis of population contact structure provides a number of individual
measures that may correlate with risk of infection. Such measures could prove valuable for disease
surveillance and outbreak control purposes. Further investigation of context-specific population contact
structures and transmission parameters are required.
References
BELL, D. C., ATKINSON, J. S. & CARLSON, J. W. (1999) Centrality measures for disease
transmission networks. Social Networks, 21, 1-21.
CHRISTLEY, R. M., PINCHBECK, G. L., BOWERS, R. G., CLANCY, D., FRENCH, N. P.,
BENNETT, R. & TURNER, J. (2005a) Infection in social networks: Using network analysis to
identify high-risk individuals. American Journal Of Epidemiology, 162, 1024-1031.
CHRISTLEY, R. M., ROBINSON, S. E., LYSONS, R. & FRENCH, N. P. (2005b) Network analysis
of cattle movement in Great Britain. Proceedings of the Society for Veterinary Epidemiology
and Preventive Medicine, 234-244.
CORNER, L. A., PFEIFFER, D. & MORRIS, R. S. (2003) Social-network analysis of Mycobacterium
bovis transmission among captive brushtail possums (Trichosurus vulpecula). Preventive
Veterinary Medicine, 59, 147-167.
ORTIZ-PELAEZ, A., PFEIFFER, D., SOARES-MAGALHAES, R. J. & GUITIAN, F. J. (2006) Use
of social network analysis to characterize the pattern of animal movements in the initial phases
of the 2001 foot-and-mouth disease epidemic in the UK. Proceedings of the Society for
Veterinary Epidemiology and Preventive Medicine. Exeter.
WEBB, C. R. (2005) Farm animal networks: unraveling the contact structure of the British sheep
population. Preventive Veterinary Medicine, 68, 3-17.
Acknowledgements
This work was supported by a research grant VTRI VT0103 from the Higher Education Funding
Council for England (HEFCE) and the Department for Environment, Food and Rural Affairs (Defra).
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
Available at www.sciquest.org.nz