Date Published: September 12, 2013
Publisher: Public Library of Science
Author(s): Kathrin Büttner, Joachim Krieter, Arne Traulsen, Imke Traulsen, Yamir Moreno.
Centrality parameters in animal trade networks typically have right-skewed distributions, implying that these networks are highly resistant against the random removal of holdings, but vulnerable to the targeted removal of the most central holdings. In the present study, we analysed the structural changes of an animal trade network topology based on the targeted removal of holdings using specific centrality parameters in comparison to the random removal of holdings. Three different time periods were analysed: the three-year network, the yearly and the monthly networks. The aim of this study was to identify appropriate measures for the targeted removal, which lead to a rapid fragmentation of the network. Furthermore, the optimal combination of the removal of three holdings regardless of their centrality was identified. The results showed that centrality parameters based on ingoing trade contacts, e.g. in-degree, ingoing infection chain and ingoing closeness, were not suitable for a rapid fragmentation in all three time periods. More efficient was the removal based on parameters considering the outgoing trade contacts. In all networks, a maximum percentage of 7.0% (on average 5.2%) of the holdings had to be removed to reduce the size of the largest component by more than 75%. The smallest difference from the optimal combination for all three time periods was obtained by the removal based on out-degree with on average 1.4% removed holdings, followed by outgoing infection chain and outgoing closeness. The targeted removal using the betweenness centrality differed the most from the optimal combination in comparison to the other parameters which consider the outgoing trade contacts. Due to the pyramidal structure and the directed nature of the pork supply chain the most efficient interruption of the infection chain for all three time periods was obtained by using the targeted removal based on out-degree.
In the last decade, tremendous theoretical advances have been made in epidemiology on networks –. So far, such studies have implicitly focused mostly on the transmission of human diseases –. In more recent years, this kind of network analysis has also been increasingly applied to evaluate the risk of disease transmission through animal movements in the livestock industry. Most of these studies have focussed on analysing the structure of trade networks via animal movements and comparing trade networks of different time periods –. In order to utilise these insights, one has to infer how the spread of disease can be controlled by appropriately changing the network structure in the early phase of an epidemic. To understand the network resilience to the removal of parts of the network, percolation is an important concept –. The underlying idea is to remove a certain fraction of nodes until the network breaks apart , –. One practical example of a percolation process is the vaccination of animals. If an animal is vaccinated against a disease, it cannot transmit this disease to other animals. From an epidemiological perspective, this individual is removed from the network. This does not only prevent the animal from being infected, but it also can interrupt the chain of infection such that a further spread to other animals is prevented . Nodes can be removed in different ways: at random or successively regarding their rank of different centrality parameters, e.g. in-degree and out-degree, ingoing and outgoing infection chain, betweenness centrality or ingoing and outgoing closeness centrality. Typically, it makes sense to remove highly central nodes first.
Previous analyses of this network showed that it had a significant right-skewed distribution of the calculated centrality parameters for all observed time periods, which indicates a large heterogeneity , . Other trade networks of animal movements have revealed similar patterns , , , –, despite the fact the trade network strongly depends on the transported species. Such a distribution, with a majority of holdings having a very small centrality value and only few holdings with a very high centrality, has important implications for processes taking place in this kind of network, such as the spread of an epidemic. Due to the few highly central holdings, the network structure is very robust regarding the random removal of holdings. The probability of hitting the few highly central holdings is very low in this procedure; therefore, a lot of holdings have to be removed to destroy the network structure. But if these highly central holdings are removed in a targeted fashion, a rapid fragmentation of the network can be obtained , –. The prototypic example of such a phenomenon is the Internet, which has been shown to be very robust towards random removal of nodes, but highly vulnerable to targeted attacks –.
The centrality parameters of our trade network had a right-skewed distribution, which has important consequences for network resilience. The random removal of holdings in all three observed time periods did not lead to a rapid fragmentation of the network structure, even though the largest slope was obtained for multipliers. In contrast, by selective removal of the most central holdings, e.g. via selective vaccination or culling, the network structure decomposes and further disease spread can be prevented. Therefore, targeting highly central holdings is much more effective than the random removal of holdings. The targeted removal of holdings based on out-degree, outgoing infection chain, betweenness centrality and outgoing closeness centrality was a highly efficient method to interrupt the chain of infection during an epidemic. However, the removal by out-degree showed the most rapid fragmentation and did not differ substantially from the optimal removal of nodes. The reason for this is the pyramidal structure and the directed nature of the pork supply chain with the majority of the animal movements taking a directed path through the system. In contrast, the removal of holdings based on the rank of the centrality parameters in-degree, ingoing infection chain and ingoing closeness centrality is not an appropriate method to decompose the network structure. Knowledge of the structure of trade networks and their reaction to the removal of holdings or contacts can be used to optimise control strategies during an epidemic or to improve prevention measurements. We anticipate that control strategies which do not take the network structure into account are not as effective as the targeted removal of nodes, but more efficient than a random removal of nodes.