Efficient Interruption of Infection Chains by Targeted Removal of Central Holdings in an Animal Trade Network

Abstract

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.

Characteristics of the spatio-temporal network of cattle movements in France over a 5-year period

“…This is directly related to the fact that networks with power law degree distributions, also called scale-free networks (Albert and Barabási, 2002) are robust against random failures, but, when the node removal is done according to nodes ranked by degree, a comparatively small number of removals can lead to break down of the network. This also corroborates up to some extent the results of previous studies Rautureau et al, 2012;Büttner et al, 2013;Iyer et al, 2013). We also investigated 3-month networks as this duration is close to the one allowing the maximum short-range similarity and because monthly networks were too sparse and hence less meaningful for the assessment of network vulnerability or, conversely, resilience.…”

“…This is especially as the dynamic nature of such networks has a substantial impact on pathogen spread. This was revealed using time stamped chain of contacts (Nöremark et al, 2011;Büttner et al, 2013;Dorjee et al, 2013;Konschake et al, 2013;Nöremark and Widgren, 2014). In the absence of time series of animal movements long enough to allow a comprehensive representation of exchanges between herds, statistical and mechanistic modelling studies may prove to be useful.…”

“…Different animal markets in several countries were explored: cattle in Denmark, Canada, France, Italy, Sweden and UK (Bigras-Poulin et al, 2006;Dubé et al, 2010;Rautureau et al, 2011;Bajardi et al, 2011;Nöremark et al, 2011;Vernon, 2011), sheep in UK Kao et al, 2006) and pigs in Sweden, France, Germany and Canada (Nöremark et al, 2011;Rautureau et al, 2012;Büttner et al, 2013;Dorjee et al, 2013). Specifically, to cite only a few examples, various characteristics relating, on the one hand, networks representing animal trade and, on the other hand, pathogen spread, such as vulnerability to and effects of infectious diseases, were investigated based on these data.…”

“…Concerning the temporal dynamical characteristics of animal trade data, there are at least two distinct primary approaches to address movement networks: (i) as static networks, by considering temporal aggregated variants of the initial datasets Kao et al, 2006;Rautureau et al, 2011) or (ii) as continuous increments of small width time windows (Vernon and Keeling, 2009;Büttner et al, 2013;Bajardi et al, 2011). Most of the recent studies use a mix of both approaches.…”

Burkholderia mallei : The dynamics of networks and disease transmission

“…The GAM regression model identified a positive significant increase in the cases of glanders when closeness centrality out and in degree were above 0.0002577 and 73, with OR 4.46 and 2.05 respectively. We consider the closeness centrality out as a proxy for the internalization of farms in the observed network, consequently our results suggest that the outgoing movements from farms very internalized would represent greater risk for disease spread, because on average these farms would require fewer steps (short paths) to connect to other farms (Kathrin Büttner, Krieter, Traulsen, & Traulsen, ). High in‐degree has already been reported as risk factor.…”