The network of sheep movements within Great Britain: Network properties and their implications for infectious disease spread

Abstract

During the 2001 foot and mouth disease epidemic in the UK, initial dissemination of the disease to widespread geographical regions was attributed to livestock movement, especially of sheep. In response, recording schemes to provide accurate data describing the movement of large livestock in Great Britain (GB) were introduced. Using these data, we reconstruct directed contact networks within the sheep industry and identify key epidemiological properties of these networks. There is clear seasonality in sheep movements, with a peak of intense activity in August and September and an associated high risk of a large epidemic. The high correlation between the in and out degree of nodes favours disease transmission. However, the contact networks were largely dissasortative: highly connected nodes mostly connect to nodes with few contacts, effectively slowing the spread of disease. This is a result of bipartite-like network properties, with most links occurring between highly active markets and less active farms. When comparing sheep movement networks (SMNs) to randomly generated networks with the same number of nodes and node degrees, despite structural differences (such as disassortativity and higher frequency of even path lengths in the SMNs), the characteristic path lengths within the SMNs are close to values computed from the corresponding random networks, showing that SMNs have 'small-world'-like properties. Using the network properties, we show that targeted biosecurity or surveillance at highly connected nodes would be highly effective in preventing a large and widespread epidemic.

Figure 1

The average number of connections per node 〈k〉 and the size of the giant strongly connected component (GSCC) for networks built by considering consecutive four-week periods starting on 1 January 2003 until 30 November 2004. The continuous line (solid diamonds) represents the average considering only those nodes that were active during the considered four-week period. The dotted line (open diamonds) represents the average considering all the nodes that were involved in movements during the whole period of study. The continuous line (open circles) represents the GSCC size.

Figure 2

The in and out degree distribution of the sheep movement network starting on 8 September 2004.

Figure 3

The size distribution of the strongly connected components. (a) Below the percolation threshold, the network is fragmented in components of small sizes. (b) Above the percolation threshold, the GSCC becomes isolated from the remaining components. Distributions over the different time-periods considered are consistent. The isolated points on the right represent the GSCCs.

Figure 4

The average number of connections per node in the GSCCs (〈k〉_GSCC) is shown by the continuous line (left-hand axis). The proportion of edges that join two different nodes in both directions is shown by the dotted line (right-hand axis).

Figure 5

The distributions of path lengths for the SMNs starting on (a) 19 May 2004 and (b) 8 September 2004 (continuous lines). The dashed lines represent the path length distribution of random networks built by considering the same number of nodes and the same in and out degree for the nodes as in the SMNs. In the insets, the link length distributions for the SMNs (continuous lines) and for the equivalent random graphs (dashed lines) are plotted.

Figure 6

The average proportion of infectious nodes (I) at the end of a four-week epidemic for the SMN starting on 8 September 2004 (continuous line) and for the corresponding random graph (dashed line). The confidence intervals are smaller than the symbols.

Figure 7

The average in (continuous line) and out (dashed line) degree of the m (=50) most recent nodes to become infectious for the SMN starting on 8 September 2004 (black lines) and for the corresponding random graph (grey lines) for τ=0.5. Different values of m produce similar qualitative behaviour.

Figure 8

The effect of removing nodes according to their in times out degree (continuous line) on the GSCC size. For comparison, the dashed line represents the random removal of nodes. For both control methods, the starting network is the SMN starting on 8 September 2004.