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Construction of networks with intrinsic temporal structure from UK cattle movement data.

Heath MF, Vernon MC, Webb CR - BMC Vet. Res. (2008)

Bottom Line: However, this approach loses information on the time sequence of events thus reducing the accuracy of model predictions.The redefinition of what constitutes a node has provided a means to simulate disease spread using all the information available in the BCMS database whilst providing a network that can be described analytically.This will enable the construction of generic networks with similar properties with which to assess the impact of small changes in network structure on disease dynamics.

View Article: PubMed Central - HTML - PubMed

Affiliation: University of Cambridge, Department of Veterinary Medicine, Madingley Road, Cambridge, UK. mfh2@cam.ac.uk

ABSTRACT

Background: The implementation of national systems for recording the movements of cattle between agricultural holdings in the UK has enabled the development and parameterisation of network-based models for disease spread. These data can be used to form a network in which each cattle-holding location is represented by a single node and links between nodes are formed if there is a movement of cattle between them in the time period selected. However, this approach loses information on the time sequence of events thus reducing the accuracy of model predictions. In this paper, we propose an alternative way of structuring the data which retains information on the sequence of events but which still enables analysis of the structure of the network. The fundamental feature of this network is that nodes are not individual cattle-holding locations but are instead direct movements between pairs of locations. Links are made between nodes when the second node is a subsequent movement from the location that received the first movement.

Results: Two networks are constructed assuming (i) a 7-day and (ii) a 14-day infectious period using British Cattle Movement Service (BCMS) data from 2004 and 2005. During this time period there were 4,183,670 movements that could be derived from the database. In both networks over 98% of the connected nodes formed a single giant weak component. Degree distributions show scale-free behaviour over a limited range only, due to the heterogeneity of locations: farms, markets, shows, abattoirs. Simulation of the spread of disease across the networks demonstrates that this approach to restructuring the data enables efficient comparison of the impact of transmission rates on disease spread.

Conclusion: The redefinition of what constitutes a node has provided a means to simulate disease spread using all the information available in the BCMS database whilst providing a network that can be described analytically. This will enable the construction of generic networks with similar properties with which to assess the impact of small changes in network structure on disease dynamics.

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In- and out-degree frequency distributions for the 14-day infection network. Data for 2004 and 2005 for movements as nodes according to the 14-day infection network structure (see text).
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Figure 4: In- and out-degree frequency distributions for the 14-day infection network. Data for 2004 and 2005 for movements as nodes according to the 14-day infection network structure (see text).

Mentions: The maximum out-degree is the same for both networks (704), while the maximum in-degree is higher for the 14-day infection network (1,177 vs 804). The distributions of in-degree frequencies for both networks exhibit regions that correspond to scale-free networks, but the regions are small (Figs. 3 and 4). For low in-degrees (below 20) the plot shows a scale-free profile which then flattens out to a characteristic frequency of approximately 3000 up to in-degree 100. This is followed by an abrupt fall in frequency of nodes with high in-degree. Out-degree plots are similar, but more curvilinear in the first region (Figs. 3 and 4). Some of the anomalies are the result of the different behaviour of different types of locations. When in-degree is plotted only for movements from farms (so including only edges that link movements on and off the same farm), and out-degree for movements to farms (similarly), then more typically scale-free distributions are seen (7-day infection network, Fig. 5). Similar frequency plots for movements from and to markets only (for example) are very unlike scale-free distributions (7-day infection network, Fig. 6). Two-dimensional degree distributions reveal that very few nodes have both a high in- and out-degree, and that most have a low value for both (Table 1).


Construction of networks with intrinsic temporal structure from UK cattle movement data.

Heath MF, Vernon MC, Webb CR - BMC Vet. Res. (2008)

In- and out-degree frequency distributions for the 14-day infection network. Data for 2004 and 2005 for movements as nodes according to the 14-day infection network structure (see text).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2335102&req=5

Figure 4: In- and out-degree frequency distributions for the 14-day infection network. Data for 2004 and 2005 for movements as nodes according to the 14-day infection network structure (see text).
Mentions: The maximum out-degree is the same for both networks (704), while the maximum in-degree is higher for the 14-day infection network (1,177 vs 804). The distributions of in-degree frequencies for both networks exhibit regions that correspond to scale-free networks, but the regions are small (Figs. 3 and 4). For low in-degrees (below 20) the plot shows a scale-free profile which then flattens out to a characteristic frequency of approximately 3000 up to in-degree 100. This is followed by an abrupt fall in frequency of nodes with high in-degree. Out-degree plots are similar, but more curvilinear in the first region (Figs. 3 and 4). Some of the anomalies are the result of the different behaviour of different types of locations. When in-degree is plotted only for movements from farms (so including only edges that link movements on and off the same farm), and out-degree for movements to farms (similarly), then more typically scale-free distributions are seen (7-day infection network, Fig. 5). Similar frequency plots for movements from and to markets only (for example) are very unlike scale-free distributions (7-day infection network, Fig. 6). Two-dimensional degree distributions reveal that very few nodes have both a high in- and out-degree, and that most have a low value for both (Table 1).

Bottom Line: However, this approach loses information on the time sequence of events thus reducing the accuracy of model predictions.The redefinition of what constitutes a node has provided a means to simulate disease spread using all the information available in the BCMS database whilst providing a network that can be described analytically.This will enable the construction of generic networks with similar properties with which to assess the impact of small changes in network structure on disease dynamics.

View Article: PubMed Central - HTML - PubMed

Affiliation: University of Cambridge, Department of Veterinary Medicine, Madingley Road, Cambridge, UK. mfh2@cam.ac.uk

ABSTRACT

Background: The implementation of national systems for recording the movements of cattle between agricultural holdings in the UK has enabled the development and parameterisation of network-based models for disease spread. These data can be used to form a network in which each cattle-holding location is represented by a single node and links between nodes are formed if there is a movement of cattle between them in the time period selected. However, this approach loses information on the time sequence of events thus reducing the accuracy of model predictions. In this paper, we propose an alternative way of structuring the data which retains information on the sequence of events but which still enables analysis of the structure of the network. The fundamental feature of this network is that nodes are not individual cattle-holding locations but are instead direct movements between pairs of locations. Links are made between nodes when the second node is a subsequent movement from the location that received the first movement.

Results: Two networks are constructed assuming (i) a 7-day and (ii) a 14-day infectious period using British Cattle Movement Service (BCMS) data from 2004 and 2005. During this time period there were 4,183,670 movements that could be derived from the database. In both networks over 98% of the connected nodes formed a single giant weak component. Degree distributions show scale-free behaviour over a limited range only, due to the heterogeneity of locations: farms, markets, shows, abattoirs. Simulation of the spread of disease across the networks demonstrates that this approach to restructuring the data enables efficient comparison of the impact of transmission rates on disease spread.

Conclusion: The redefinition of what constitutes a node has provided a means to simulate disease spread using all the information available in the BCMS database whilst providing a network that can be described analytically. This will enable the construction of generic networks with similar properties with which to assess the impact of small changes in network structure on disease dynamics.

Show MeSH
Related in: MedlinePlus