Relationship of trade patterns of the Danish swine industry animal movements network to potential disease spread.

The movements of animals were analysed under the conceptual framework of graph theory in mathematics. The swine production related premises of Denmark were considered to constitute the nodes of a network and the links were the animal movements. In this framework, each farm will have a network of other premises to which it will be linked. A premise was a farm (breeding, rearing or slaughter pig), an abattoir or a trade market. The overall network was divided in premise specific subnets that linked the other premises from and to which animals were moved. This approach allowed us to visualise and analyse the three levels of organization related to animal movements that existed in the Danish swine production registers: the movement of animals between two premises, the premise specific networks, and the industry network. The analyses of animal movements were done using these three levels of organisation. The movements of swine were studied for the period September 30, 2002 to May 22, 2003. For daily movements of swine between two slaughter pig premises, the median number of pigs moved was 130 pigs with a maximum of 3306. For movements between a slaughter pig premise and an abattoir, the median number of pigs was 24. The largest percentage of movements was from farm to abattoir (82.5%); the median number of pigs per movement was 24 and the maximum number was 2018. For the whole period the median and maximum Euclidean distances observed in farm-to-farm movements were 22 km and 289 km respectively, while in the farm-to-abattoir movements, they were 36.2 km and 285 km. The network related to one specific premise showed that the median number of premises was mainly away from slaughter pig farms (3) or breeder farms (26) and mainly to an abattoir (1535). The assumption that animal movements can be randomly generated on the basis of farm density of the surrounding area of any farm is not correct since the patterns of animal movements have the topology of a scale-free network with a large degree of heterogeneity. This supported the opinion that the disease spread software assuming homogeneity in farm-to-farm relationship should only be used for large-scale interpretation and for epidemic preparedness. The network approach, based on graph theory, can be used efficiently to express more precisely, on a local scale (premise), the heterogeneity of animal movements. This approach, by providing network knowledge to the local veterinarian in charge of controlling disease spread, should also be evaluated as a potential tool to manage epidemics during the crisis. Geographic information systems could also be linked in the approach to produce knowledge about local transmission of disease.

[1]  I. M. Sokolov,et al.  Epidemics, disorder, and percolation , 2003, cond-mat/0301394.

[2]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[3]  Stefan Bornholdt,et al.  Handbook of Graphs and Networks: From the Genome to the Internet , 2003 .

[4]  M. Bigras-Poulin,et al.  Network analysis of Danish cattle industry trade patterns as an evaluation of risk potential for disease spread. , 2006, Preventive veterinary medicine.

[5]  C. Webb,et al.  Farm animal networks: unraveling the contact structure of the British sheep population. , 2005, Preventive veterinary medicine.

[6]  J. W. Wilesmith,et al.  Predictive spatial modelling of alternative control strategies for the foot-and-mouth disease epidemic in Great Britain, 2001 , 2001, Veterinary Record.

[7]  Vladimir Batagelj,et al.  Pajek - Program for Large Network Analysis , 1999 .

[8]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[9]  Béla Bollobás,et al.  Mathematical results on scale‐free random graphs , 2005 .

[10]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Gregory Gutin,et al.  Digraphs - theory, algorithms and applications , 2002 .

[12]  L. Foulds,et al.  Graph Theory Applications , 1991 .

[13]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[14]  M. Kuperman,et al.  Small world effect in an epidemiological model. , 2000, Physical review letters.

[15]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[16]  S. Cornell,et al.  Dynamics of the 2001 UK Foot and Mouth Epidemic: Stochastic Dispersal in a Heterogeneous Landscape , 2001, Science.

[17]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[18]  M. Newman.  Random Graphs as Models of Networks , 2002, cond-mat/0202208.

[19]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[20]  Samuel R. Friedman,et al.  Social networks, risk-potential networks, health, and disease , 2001, Journal of Urban Health.

[21]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  M. Keeling.  The implications of network structure for epidemic dynamics. , 2005, Theoretical population biology.

[23]  M. Schoenbaum,et al.  Modeling alternative mitigation strategies for a hypothetical outbreak of foot-and-mouth disease in the United States. , 2003, Preventive veterinary medicine.

[24]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .

[25]  R. May,et al.  Infection dynamics on scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  C. Berge.  Graphes et hypergraphes , 1970 .