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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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Diagram of the structure of a link in the network. An edge (link) will exist between a movement from Farm A to Market B (Node 1), and a movement from Market B to Farm C (Node 2), if Node 2 occurs on, or within a specified time limit after, the date of Node 1. Where the linking location is a Market, the time limit is 6 days.
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Figure 1: Diagram of the structure of a link in the network. An edge (link) will exist between a movement from Farm A to Market B (Node 1), and a movement from Market B to Farm C (Node 2), if Node 2 occurs on, or within a specified time limit after, the date of Node 1. Where the linking location is a Market, the time limit is 6 days.

Mentions: In the basic SIR model for infectious disease [1], a population is divided into susceptible (S), infected (I) and resistant (R) sub-populations, and the spread of infectious disease in that population is calculated on the assumption of homogeneous mixing of the individuals, so that there is a fixed probability of contact between any two individuals. This model cannot be applied to disease spread between cattle farms, since they do not mix homogeneously and it is therefore essential to allow for the spatial distribution of farms, for example by controlling the probability of disease transmission between two farms by a function of their geographical proximity [2]. However, geographical proximity is not the only factor that may influence disease spread. Trade between farms creates a new topology in mapping disease risk. A more precise control of the probability of transmission could use the actual (and potentially infective) contacts between farms to build a contact network. Contact networks have been used in simulations of human disease (see review [3]), with the contact between two individuals being taken as persistent. For UK cattle farms, contact data is available in the form of the cattle movement database provided by the British Cattle Movement Service (BCMS). Because trade links are sporadic, movements are not well modelled as persistent contacts [4], and the temporal pattern of movements has important implications for the spread of infectious diseases. For structural studies of the cattle contact networks, movements have been regarded as quasi-persistent by considering the contacts resulting from movements during a relatively short period (e.g. 4 weeks) to be persistent through that period ([4,5]). Such networks can yield information relevant to non-persistent networks if they are considered ergodic [5]. Disease simulations have been carried out with a true temporal component, using a replay of the actual movements over a defined period [5,6]. Here, we attempt to use the BCMS movement data to build a network that incorporates the temporal sequence of movements between cattle premises, so that the structural features of such a network can be determined, and so that disease simulations can be run with less computational effort. The fundamental feature of our networks is that the nodes are not cattle farms but are instead movements between cattle farms (in fact between any cattle-holding premises or "locations"). Thus nodes have three basic properties: the source location, the target location, and the date of the movement. For simplicity, the number of animals moved is not included in the node definition. Edges (links) between nodes only exist when the target in one node is the source, in another node, of a movement on the same or a later date (Fig. 1). A further refinement is to include the type of each location (farm, market, slaughterhouse, showground, other) and to limit the time that may elapse after the first movement before the second movement is no longer linked to it. The time limit depends on the type of the linking location. We used the BCMS data for the whole of 2004 and 2005. The time limits for links involving farms were 7 days ("7-day infection network") or 14 days ("14-day infection network") (Fig. 2).


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

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

Diagram of the structure of a link in the network. An edge (link) will exist between a movement from Farm A to Market B (Node 1), and a movement from Market B to Farm C (Node 2), if Node 2 occurs on, or within a specified time limit after, the date of Node 1. Where the linking location is a Market, the time limit is 6 days.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Diagram of the structure of a link in the network. An edge (link) will exist between a movement from Farm A to Market B (Node 1), and a movement from Market B to Farm C (Node 2), if Node 2 occurs on, or within a specified time limit after, the date of Node 1. Where the linking location is a Market, the time limit is 6 days.
Mentions: In the basic SIR model for infectious disease [1], a population is divided into susceptible (S), infected (I) and resistant (R) sub-populations, and the spread of infectious disease in that population is calculated on the assumption of homogeneous mixing of the individuals, so that there is a fixed probability of contact between any two individuals. This model cannot be applied to disease spread between cattle farms, since they do not mix homogeneously and it is therefore essential to allow for the spatial distribution of farms, for example by controlling the probability of disease transmission between two farms by a function of their geographical proximity [2]. However, geographical proximity is not the only factor that may influence disease spread. Trade between farms creates a new topology in mapping disease risk. A more precise control of the probability of transmission could use the actual (and potentially infective) contacts between farms to build a contact network. Contact networks have been used in simulations of human disease (see review [3]), with the contact between two individuals being taken as persistent. For UK cattle farms, contact data is available in the form of the cattle movement database provided by the British Cattle Movement Service (BCMS). Because trade links are sporadic, movements are not well modelled as persistent contacts [4], and the temporal pattern of movements has important implications for the spread of infectious diseases. For structural studies of the cattle contact networks, movements have been regarded as quasi-persistent by considering the contacts resulting from movements during a relatively short period (e.g. 4 weeks) to be persistent through that period ([4,5]). Such networks can yield information relevant to non-persistent networks if they are considered ergodic [5]. Disease simulations have been carried out with a true temporal component, using a replay of the actual movements over a defined period [5,6]. Here, we attempt to use the BCMS movement data to build a network that incorporates the temporal sequence of movements between cattle premises, so that the structural features of such a network can be determined, and so that disease simulations can be run with less computational effort. The fundamental feature of our networks is that the nodes are not cattle farms but are instead movements between cattle farms (in fact between any cattle-holding premises or "locations"). Thus nodes have three basic properties: the source location, the target location, and the date of the movement. For simplicity, the number of animals moved is not included in the node definition. Edges (links) between nodes only exist when the target in one node is the source, in another node, of a movement on the same or a later date (Fig. 1). A further refinement is to include the type of each location (farm, market, slaughterhouse, showground, other) and to limit the time that may elapse after the first movement before the second movement is no longer linked to it. The time limit depends on the type of the linking location. We used the BCMS data for the whole of 2004 and 2005. The time limits for links involving farms were 7 days ("7-day infection network") or 14 days ("14-day infection network") (Fig. 2).

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