Figure 1.
Changes in Network and Node Properties Associated with Increasing Vulnerability.
Network Properties – properties of the entire network which impact vulnerability (a) Density (ratio of edges to nodes) – As this ratio increases, there is an increase in connections between nodes, increasing the potential paths for disease spread. (b) Number of components (number of independent/isolated sub groups) – A decrease in the number of isolated groups increases the reachability of any random node (c) Giant Component (largest independent/isolated sub group) – if the largest component contracts infection, this infection can spread further through the Giant Component compared to smaller, more isolated components which will make the whole network more vulnerable. (d) Link Weight (strength of relationship/number of units moved or frequency of movement) – As more units are moved or units are moved more frequently, there is an increase in the chance of moving infected individuals. Node Properties – properties of each node which make the node more vulnerable or impact the vulnerability of the rest of the network. Black node = focal node (e) Degree (number of edges) – increases in the number of edges any node has increases the vulnerability of that node to potential transmission (must have contact/connection to transfer infection) (f) Betweenness (how often a node lies on the shortest path between two other nodes) – with low vulnerability the focal node has low betweenness and for the highest vulnerability the focal node has maximum betweeness, where every node must go through the focal node to reach any other node. (g) Infection chain (the number of nodes that can be reached by the focal node, accounting for timing of movements) – the focal node has a single edge (*), and those edges in the network which are formed before this edge (i.e. those animal transfers which happen before the focal node formed) cannot contribute to the infection chain, and are depicted with a dashed line. Edges which form after this edge are depicted with a solid line. With the lowest vulnerability, the focal node can only form a chain of one, because the outgoing edge from the next node has already formed. With medium vulnerability, the subsequent edge is formed after the focal node’s edge, thus stock could move from the focal node to 3 other nodes, giving it an infection chain of 3. In the final figure all movements occur subsequent to the formation of the focal node and thus the infection chain for this node increases to 5.
Figure 2.
Full ostrich movement network visualization with the least connected nodes (degree <20) not shown.
The farm ID numbers for the 10 most connected nodes are displayed, and all farms which tested positive for HPAI are shaded red and the farm ID number displayed for the ten farms with the highest degree.
Figure 3.
The monthly number of nodes (farms) and edges (ostrich movement events) occurring in the Western Cape, between September 2005 and March 2011.
The vertical lines occur mark December of every year.
Figure 4.
The results of a Bfast analysis of the (a) network density and the (b) Max outgoing infection chain.
The top frame of each panel displays the network index at each time step, while the second panel depicts seasonal variation detected in the measure over time. This variation is then removed and the resulting trend is displayed in panel three. The fourth panel depicts residual variation which cannot be accounted for in the seasonal variation or trend.
Figure 5.
The results of a Bfast analysis of (a) the number of birds moved, (b) average ingoing infection chain length, (c) number of components and (d) Giant Weak Component size.
The first frame of each panel displays the network index at each time step, while the second panel depicts seasonal variation detected in the measure over time. This variation is then removed and the resulting trend is displayed in panel three. The fourth panel depicts residual variation which cannot be accounted for in the seasonal variation or trend. The vertical lines in the second panel of image c indicate shifts in the season trends, while the vertical lines in the 3rd panel signify an abrupt change in the trend component of the time series. The corresponding confidence interval of each shift or change is depicted by horizontal lines below each.
Figure 6.
The distribution of logged betweenness (nInfected = 23, nNon_Infected = 324) and degree (nInfected = 42, nNon_Infected = 1575 scores for all farms (white) as well as the farms which tested positive for HPAI (black).
A Wilcoxon signed rank test revealed that the infected farms are significantly different from infected farms in the network in both betweenness (p<0.001) and degree (p<0.001).
Figure 7.
The log of the proportion of infected farms at increasing ingoing (top) and outgoing (bottom) infection chain lengths during 01/09/2010 - 01/04/2011.
Figure 8.
Ostrich production in South Africa.
This process incorporates the movement of birds between a number of different types of farms before they are sent to the abattoir to be slaughtered. The process begins at hatcheries where eggs are incubated and, once hatched, chicks are moved to chick rearing farms within 72 hours. This most frequently occurs between September and February each year. The birds remain at these rearing farms for 2–3 months, when they are moved to adult rearing farms. They remain at these locations until they reach 70–90 kg (for approx. 12–14 months) when they are moved to quarantine farms. They remain at these farms for ∼30 days, and once deemed disease free they are transferred to an abattoir for slaughter. These last two steps of the production cycle occur primarily between September and February.