Högskolan i Skövde

Theoretical exploration of network structure significance requires a range of different networks for comparison. Here, we present a new method to construct networks in a spatial setting that uses spectral methods in combination with a probability distribu-tion function. Nearly all previous algorithms for network construction have assumed randomized distribution of links or a distribution dependent on the degree of the nodes.We relax those assumptions. Our algorithm is capable of creating spectral networks along a gradient from random to highly clustered or diverse networks. Number of nodes and link density are specified from start and the structure is tuned by three parameters (γ, σ, κ). The structure is measured by fragmentation, degree assortativity, clusteringand group betweenness of the networks. The parameter γ regulates the aggregation in the spatial node pattern and σ and κ regulates the probability of link forming.

Network measures are used to predict the behavior of different systems. To be able to investigate how various structures behave and interact we need a wide range of theoretical networks to explore. Both spatial and non-spatial methods exist for generating networks but they are limited in the ability of producing wide range of network structures. We extend an earlier version of a spatial spectral network algorithm to generate a large variety of networks across almost all the theoretical spectra of the following network measures: average clustering coefficient, degree assortativity, fragmentation index, and mean degree. We compare this extended spatial spectral network-generating algorithm with a non-spatial algorithm regarding their ability to create networks with different structures and network measures. The spatial spectral networkgenerating algorithm can generate networks over a much broader scale than the non-spatial and other known network algorithms. To exemplify the ability to regenerate real networks, we regenerate networks with structures similar to two real Swedish swine transport networks. Results show that the spatial algorithm is an appropriate model with correlation coefficients at 0.99. This novel algorithm can even create negative assortativity and managed to achieve assortativity values that spans over almost the entire theoretical range.

Background: Livestock movements can affect the spread and control of contagious diseases and new data recording systems enable analysis of these movements. The results can be used for contingency planning, modelling of disease spread and design of disease control programs.

Methods: Data on the Swedish cattle and pig populations during the period July 2005 until June 2006 were obtained from databases held by the Swedish Board of Agriculture. Movements of cattle and pigs were investigated from geographical and temporal perspectives, births and deaths of cattle were investigated from a temporal perspective and the geographical distribution of holdings was also investigated.

Results: Most movements of cattle and pigs were to holdings within 100 km, but movements up to 1200 km occurred. Consequently, the majority of movements occurred within the same county or to adjacent counties. Approximately 54% of the cattle holdings and 45% of the pig holdings did not purchase any live animals. Seasonal variations in births and deaths of cattle were identified, with peaks in spring. Cattle movements peaked in spring and autumn. The maximum number of holdings within a 3 km radius of one holding was 45 for cattle and 23 for pigs, with large variations among counties. Missing data and reporting bias (digit preference) were detected in the data.

Conclusion: The databases are valuable tools in contact tracing. However since movements can be reported up to a week after the event and some data are missing they cannot replace other methods in the acute phase of an outbreak. We identified long distance transports of cattle and pigs, and these findings support an implementation of a total standstill in the country in the case of an outbreak of foot-and-mouth disease. The databases contain valuable information and improvements in data quality would make them even more useful.

Registration ofcattle and pigmovements is mandatory in Sweden and all registered movements between farms in the years 2006–2008 were investigated using network analysis. The networks were analysed as monthly and yearly networks, separately per species and with the two species together. Measures that have been previously discussed in relation to outbreaks and disease control were calculated; moreover a measure of the ingoing infection chain was constructed.The ingoing infection chain captures in going contacts through other holdings, taking the temporal aspect and sequence of the movements into account. The distribution of the contacts among the holdings was skewed.Many farms had few or no contacts, while others had many, a pattern which has also been described from other countries. The cattle network and the combined network showed a recurring seasonal pattern, while this was not seen in the pig network.The in-degree was not equivalent to the ingoing infection chain; there were holdings with limited direct contacts, but a large number of indirect contacts.The ingoing infection chain could be a useful measure when setting up strategies for disease control and for risk based surveillance as it identifies holdings with many contacts through live animal movements and thus at potentially higher risk for introduction of contagious diseases.