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

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

Preventive Veterinary Medicine 80 (2007) 143–165 www.elsevier.com/locate/prevetmed Relationship of trade patterns of the Danish swine industry animal...

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Preventive Veterinary Medicine 80 (2007) 143–165 www.elsevier.com/locate/prevetmed

Relationship of trade patterns of the Danish swine industry animal movements network to potential disease spread Michel Bigras-Poulin a,b,*, Kristen Barfod c, Sten Mortensen d, Matthias Greiner b,e Groupe de Recherche en E´pide´miologie des Zoonoses et Sante´ Publique, Faculte´ de Me´decine Ve´te´rinaire, Universite´ de Montre´al, 3200 Sicotte, St-Hyacinthe, Canada, J2S 7C6 b International Epilab, Danish Institute for Food and Veterinary Research, MørkhøBygade 19, DK-2860 Søborg, Denmark c Danish Beacon and Meat, Axeltorv 3 – DK-1609 Copenhagen V, Denmark d Danish Institute for Food and Veterinary Research, MørkhøBygade 19, DK-2860 Søborg, Denmark e Federal Institute for Risk Assessment (BfR), Scientific Services Unit 33 - Epidemiology, Biostatistics and Mathematical Modelling, Alt-Marienfelde 17-21, D-12277 Berlin, Germany a

Received 20 April 2006; received in revised form 2 February 2007; accepted 8 February 2007

Abstract 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 * Corresponding author at: Faculte´ de Me´decine Ve´te´rinaire, Universite´ de Montre´al, 3200 Sicotte, St-Hyacinthe, Canada, J2S 7C6. Tel.: +450 773 8521x18471; fax: +450 778 8120. E-mail address: [email protected] (M. Bigras-Poulin). 0167-5877/$ – see front matter # 2007 Published by Elsevier B.V. doi:10.1016/j.prevetmed.2007.02.004

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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. # 2007 Published by Elsevier B.V. Keywords: Networks; Graphs; Swine movements; Epidemiology; Risk potential

1. Introduction The swine production industries of industrial countries are organised in a pyramidal structure with breeder production at the top and slaughter pig production at the bottom. Livestock industries, such as the swine industry, can have very complex networks or interrelationships among premises. One way to look at these interrelationships and the potential impact they might have on disease transmission is to summarize and describe the networks of transport of animals between premises. With the advent of data collection and electronic recording about movements of groups of swine, it is now possible to produce an individual farm level resolution representation of the industry’s complex trade patterns. The impact of these analyses is to better understand the trade patterns topology and the paths that can be followed by pathogens through direct animal contacts and, thus, to suggest new mechanisms to explain the occurrence of new diseases, to improve disease control and surveillance strategies. Networks provide a conceptual framework that can express relationships between elements such as the movement of swine between two premises. There are many examples of networks that are part of our day to day life: the electricity distribution network and water or sewage networks. Networks can be described at various scales. The network is defined largely by the elements at the junctions of the net (nodes) and by the nature of the relationships that link these elements (Bigras-Poulin et al., 2006). Networks can be studied using graph theory, which provides a rich analysis framework to study movements between parts of the system (Foulds, 1992). Many authors have defined networks with different topologies and have studied some of their characteristics as described in a handbook of

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graphs and networks (Bornhldt and Schuster, 2003). The great conceptual strength of networks is that they allow the epidemiologist to understand not only the impact of animal movements per se but also the relationship between these movements that produce paths. These paths can be followed by pathogens in a disease and/or infection transmission process, usually called the direct transmission route by epidemiologists. Webb (2005) and Webb and Sauter-Louis (2002) used the network conceptual framework to investigate the contact structure of the British sheep population, and BigrasPoulin et al. (2006) have described the network of cattle movements in Denmark. They expressed the view that contact structures have received little attention from epidemiologists, although they are very important to the understanding of disease transmission through animal contacts. The understanding of industry trade patterns and animal movements in the industry should provide essential knowledge concerning disease transmission by contact. Among others, Moore and Newman (2000), Pastor-Satorras and Vespignani (2001a), May and Lloyd (2001), Sander et al. (2003) and Keeling (2005) have studied the development of epidemics in networks. To apply the theoretical results produced by these authors and others, it was necessary to elucidate the characteristics of the Danish swine movements’ network. In the present epidemiological study, swine production premises are the nodes that were at the junctions in the net and the movements of animals constituted the basis for defining links. Few countries have the wealth of data needed to support the investigation of contact structure on a regular basis within the country. Denmark is such a country and the International EpiLab has supported a study of the animal movement data for cattle and swine. Trade patterns of animal movements for a specific industry are complex and difficult to study because there are many swine production related premises of different types that are heterogeneously spread over the country, and a highly dynamic flow of animals move among these premises. The paths followed by animals during movements and the dynamics of the flow of animals between premises are of special interest for predicting the outcome of an epidemic and for managing the epidemic during the crisis or disease spread in general. In the present study, the primary objective was to describe the network of trade patterns and animal movements in order to better understand the potential between herd transmissions of disease by animal contact. A secondary objective was to explore the degree of homogeneity within the industry since it is an important and general assumption of mathematical models of disease spread.

2. Materials and methods The present study was descriptive of Danish swine movements, the conceptual framework used was the network and the analytical framework was mathematical graph theory and descriptive statistics. The conceptual framework allowed for describing patterns of trade related to animal movements. A movement of animal consisted of a lot of swine that were moved within one recorded transport between two premises. A lot consisted of a group of one or more swine. Within the Danish swine industry the individual animal moved was not registered, only movements of a lot of swine were recorded.

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In a network or a graph there are two essential elements: the node and the link. The link is called an arc, when the joining of the two nodes has direction. The graph is then called a directed graph. In this work, directed graphs were used. A node was defined by a swine production premise which was a geographical site related to swine production where animals were kept on a permanent or a temporary basis. The existence of a link was defined by the movement of at least one lot of swine between two premises during the period of observation. A link involved a truck for the transportation of the animals. The network was used to show the pattern of animal movements between premises. The network linked many premises by one or many movements. The special case of premises with mixed species was not done in this study. A more thorough description of networks as applied to animal production can be found in Bigras-Poulin et al. (2006) or Webb and Sauter-Louis (2002). 2.1. Epidemiological units The conceptual framework used provided three levels for the analysis of swine movement data: the movement of animals between two premises, the premise specific networks, and the swine industry network.

3. Movements of animals Since all movements of animals have a date, a number of animals, a premise of origin, and a premise of arrival; they also have a corresponding arc that is defined by the premise of origin and the premise of arrival. The geographic location for most premises was available and recorded. The truck identification was also recorded. On one arc, there can be many animals transported and many shipments of animals and this is indicative of variation in the flow of movements of animals. 3.1. Premise specific network The premise specific network was defined as the set of premises and the set of links that were tied to a specific premise. This network was constituted of all premises and arcs that lead to this specific premise and of all premises and arcs, which moved away from the specific farm. In the present study, four arcs [i.e. all movements associated to link up to and including 4 arcs] moving from and leading to the specific farm, which occurred during the observation period, were used to construct the farm network for each specific farm. The premise specific network is a subset of the whole industry network.

4. Industry network The whole industry network was constituted by the set of all premises and the set of all arcs. The industry network is the union of all premise specific networks since networks are

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defined by a set constituted of a pair of set (nodes and links). Data analyses for the whole industry network were also repeated for one general subnet. This subnet was constituted by excluding abattoirs and slaughter related movements from the swine movement data. This was done because these movements were numerous and it can be assumed that they represented little or no risk for the transmission of many diseases of swine to other swine. 4.1. Data Danish Bacon and Meat (Dansk Slagterier) maintains registers of large quantity of specific data on the swine industry in Denmark. In the present study, the register of domestic swine movements was used as a source of data. All movements were recorded, thus the data set used for this study is a census of swine movements. The observation period extended from September 30, 2002 to May 22, 2003. The number of premises for which herd type was missing was 809 (5.6%). From this data source, an original data file was constructed using individual movements of lots transported between two premises on one truck as a record. Each record contained: truck identification, date, number of pigs moved, premise of origin and premise of arrival, location and herd type of each of the two premises. The premise geographical location was coded by X and Y coordinates using UTM zone 32N EUREF 89(WGS84) projection system. Premise types were: slaughter pig, breeding, semen production, rearing, trade, slaughter market, gathering stable, and abattoir or quarantine station. If a truck picks up many lots of animals on one route, this information could not be used in this study because truck routes were not available. Thus, contacts of swine from different lots in a single truck ride were not described. A truck ride was defined by the movement of a truck containing at least one pig between two premises. In order to describe the swine movements with focus on the trucks, the swine movements data file was aggregated for each individual truck recorded, then for each truckdate and finally for each truck-date-premise. Movement description was done by aggregating movements by type for premise of origin and by type for premise of arrival. The movements were aggregated on dates in order to describe the industry animal movements’ dynamic. A data file containing a record for each premise specific network was constructed. It consisted of: premise identification, premise type, premise location, number of premises adjacent to that specific premise in one arc, number of premises adjacent to that specific premise in 2 arcs, number of premises adjacent to that specific premise in 3 arcs, number of premises adjacent to that specific premise in 4 arcs, number of premises that could reach that specific premise in 1 to 4 arcs, number of premises adjacent from that specific premise in one arc, number of premises adjacent from that specific premise in 2 arcs, number of premises adjacent from that specific premise in 3 arcs, number of premises adjacent from that specific premise in 4 arcs, number of premises that could be reached from that specific premise in 1 to 4 arcs, number of movements of swine on the specific premise network, sum of distances covered by the premise specific network, average distance on a movement on the premise specific network, and total number of swine moved in the network. The method for constructing premise specific network characteristics is described later.

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4.2. Data analysis Data were described at each level of organisation: movement, premise specific network and industry network. Movements were described with focus on trucks, on movements ignoring the trucks and on daily premise to premise swine transport activity. Description was based on a stratification of premise according to type: slaughter pig, breeder, rearing, trade, gathering site, quarantine site, and abattoir. Geographic distances were calculated using the Euclidean distance. Descriptive statistics were calculated using SAS (version 8.2). The industry network possessed topological characteristics, which were important to classify the network. This, then, allowed us to make inferences about disease transmission using theorems and theoretical work done by network researchers. The analysis of the premise-specific-network epidemiological unit was done using mathematical graph theory (Foulds, 1992; Bang-Jensen and Gutin, 2002). The analysis produced knowledge and information about the relationships between premises and movements of animals within the Danish swine industry. A detailed description of graph theory applied to the Danish cattle movement network can be found in Bigras-Poulin et al. (2006). Graph theory was used to describe the graphs by using connectance, adjacency matrices and reachability matrices (Webb, 2005; Friedman and Aral, 2001), power of the power function distribution for degree of nodes, clustering coefficients (Watts and Strogatz, 1998), path lengths, and cycles (Foulds, 1992). Because the graph was directed, each of the characteristics had two values: one for the in side and one for the out side of the network. In a graph, walks are defined as the set of sequential movements linking a series of premises. They indicate the relationships among arcs or of the way in which a pathogen may travel from one premise to another and to another, and so on, even if it takes more than one movement (shipment) of animals. In a walk, a link between two premises is called a step. A path is a walk where no node occurs twice. Each path has a source node and an end node. The number of arcs of the shortest path, without cycle, needed to go from source to end node defines the length of the path. A cycle is defined as a path for which the source node and the end node are the same node. A walk containing a cycle has an infinite length. A network is weakly connected if each pair of vertices is connected by a path. A (weak in directed graph) component is a connected subset of a network (De Nooy et al., 2005). Network ‘‘connectance’’ was calculated as the ratio of number of arcs (movements between nodes involved in the movement of one animal) divided by the number of nodes (premises). The ‘‘degree’’ of a premise was defined as the number of direct connections between this premise and all other premises linked to it by the movements of animal. The estimation of the frequency distribution of the ‘‘in’’ and ‘‘out’’ degrees for the premises was achieved by using a power function and fitted as the slope of a log-log plot. The clustering coefficient was defined as the amount of interrelationship that exists between all the nodes that were directly connected to one specific node of interest (Bolloba´s and Riordan, 2003). It was calculated for all inward and outward movements by taking the average of all movements over all nodes. To investigate the shape of the graph, adjacency matrices were used (Foulds, 1992). The elements of this matrix were zero when no arc linked the nodes i and j, and were 1 when the arc existed. In the directed graph, the adjacency matrix may be asymmetrical because

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out-degree (from) for node (i) may not be equal to the in-degree (to). Adjacency matrices can be extended based on the choice of a path of length: l, 2, 3 or more (Bigras-Poulin et al., 2006). As an example, an adjacency matrix for path length two will consider only second neighbours. Reachability matrices were also used. They represented the cumulative number of linkages [for a given number (k) of arcs] present in a graph of n nodes or vertices. The reachability matrices indicated the number of nodes that could be joined to a specific node using a path of up to a specified number of steps. The specific premise network database was constructed using programs developed for that purpose in the M computer language (Cache´ Intersystems version 4.0). The premise specific networks were illustrated using the software Pajek (2003). Specific proprietary programs were developed in the M language to calculate the adjacency and reachability matrices. The networks of farm linkage via animal movements were built using computer programs developed specifically for this task using the M computer language from Cache´ Intersystems version 4.0. The program produced a three steps directed graph both from a specific premise or going to the specific premises. The illustration of premise specific networks included only representation of up to the 3 steps in or out to facilitate visual assessment. The resulting network was written in a format that could be read by the Pajek software for illustration purposes. The resulting graph of the network allowed the user to view the degree of complexity in the resulting specific premise network. The FruchtenbergReingold 3 D projection algorithm available in Pajek was used to make the visual assessment of the premise specific network easier. This algorithm reorganises the position of the nodes, which are originally positioned in a circle by Pajek into a more visually expressive format where the heavily connected nodes are separated from the other less connected ones.

5. Results The number of recorded slaughter pig farms was 13,259 with 299 breeder farms giving a ratio of 45.25 slaughter pig farms per breeder farm. 5.1. Truck movements During the observation period, 24.69% of trucks used to transport pigs were used only once, and 25% of the trucks made 14 rides or more. A total of 4584 different trucks were used during the observation period to transport the animals. The aggregation of movements between premises on a daily basis showed that out of the 399,921 truck movements transporting pigs and covering a total Euclidean distance of 13,427,141 km, 345,154 where done on different days. This indicated that 54,767 (13.7%) truck movements were recurrent between two premises on one day. On a daily basis, one specific truck will make only one movement transporting pigs between two specific premises in 20% of instances, two movements in 19.07% of instances, but in a few cases there could be more than 10 movements using one truck from one specific premise on one day. The median truck rides was 4 movements between any two premises on a daily basis.

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5.2. Movement of animals between premises There were 399,921 movements of pigs registered in the database for a total of 19,339,909 pigs moved in time period September 30, 2002 to May 22, 2003. 69.8% (13,252,000) of the pigs moved went to an abattoir, and 17,984,800 pigs came from a slaughter pig farm (Table 1). Pigs moving out of breeder farms went mostly to slaughter pig farms (46.75%) and to abattoirs (39.84%). For movements of swine, 94.44% of the movements originated from a slaughter pig farm; of those, approximately 6.79% ended in another slaughter pig farm and 90.69% went to the abattoir. The number of movement of pigs between a slaughter pig farm and an abattoir was 336,840 (Table 2). All premises had at least one movement of swine registered during the observation period but some premises had only movements in one direction; 418 premises had no movement from the premise and 9086 had no movements to the premise. Slaughter pig farms had no movements of swine to the farm in 60.76% (8220) of cases. For breeder farms, this number was 73.91% (221) and 52.5% (52) for rearing farms. 5.3. Movements between premises on a daily basis The distribution of number of pigs moved daily between two premises was asymmetric and varied greatly from premise to premise and from one type of premise to another (Table 3). Depending on premise type, the median number of pigs moved between two premises on one day varied from 8 to 600 and the maximum varied from 37 to 3306. This Table 1 Total number of swine moved (1000) in Denmark by type of premise of departure and arrival, during the period extending from November 1, 2002 to April 30, 2003 Type of herd of departure

Type of herd of arrival Abattoir

Slaughter pig

Gathering

Breeding

Rearing

Trade

Total

Slaughter pig Breeding Rearing Trades TOTAL

12917.3 280.3 52.7 1.7 13252.0

4249.2 328.9 183.0 2.6 4763.7

616.1 34.2 49.6 0 699.9

18.1 42.3 0.5 0 60.9

123.0 17.4 6.7 0 147.1

61.1 0.5 0 0 61.6

17984.8 703.6 292.5 4.3 18985.2

Table 2 Total number of movements of swine (transport) in Denmark by type of premise of departure and arrival, during the period extending from November 1, 2002 to April 30, 2003 Type of herd of departure

Type of herd of arrival Abattoir

Slaughter Pig

Gathering

Breeding

Rearing

Trade

Total

Slaughter pig Breeding Rearing Trades TOTAL

336840 11076 1153 74 349143

25211 7422 750 0 33383

8767 820 171 17 9775

79 360 28 0 467

427 64 13 0 504

109 2 0 0 111

371433 19744 2115 91 393383

(94.4%) (5%) (0.54%) (0.02%)

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Table 3 Median/maximum of number of pigs involved within one movement of animals between two Danish premises by type of premise, during the period extending from November 1, 2002 to April 30, 2003 Type of herd of departure

Type of herd of arrival Abattoir

Slaughter pig

Gathering

Breeding

Rearing

Trade

Slaughter pig Breeding Rearing

24/2018 14/213 30/210

130/3306 15/1154 219/1200

8/151 11/400 240/807

240/695 89/715 18/37

249/1262 306/562 570/694

600/1283 268/435

Fig. 1. Histogram of the Euclidian distances of movements of pig occurring in Denmark during the period extending from November 1, 2002 to April 30, 2003.

indicated a large heterogeneity between the premises and from time to time in numbers of pig moved. The median Euclidean distances separating the premises joined by one movement varied from premise to premise (Fig. 1) and from one type of premise to another with values between 4.3 km and 180.5 km (Table 4). The maximum Euclidean distances varied from 11.7 km to 351.5 km. The heterogeneity between premises and between types of premises was clearly observable when considering the number of pigs moved and the number of movements during the observation period (Tables 2 and 3). The harmonic nature of daily movements of swine can be seen from the time plot in Fig. 2. There was a clear weekly cycle related to the daily movements of pigs. During the Table 4 Median/maximum Euclidean distance (km) of movements of swine between two Danish premises by type of premise, during the period extending from November 1, 2002 to April 30, 2003 Type of herd of departure

Type of herd of arrival Abattoir

Slaughter Pig

Gathering

Breeding

Rearing

Trade

Slaughter pig Breeding Rearing

36.2/285.3 49.2/273.2 29.1/172.2

22/288.9 38.4/332.3 28.3/198.5

180.5/210.6 107.9/351.5 114.8/290.4

4.3/135.3 7.9/248.7 11.7/11.7

67.5/218.3 11.7/259.9 73.2/73.2

50.1/81.8

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Fig. 2. Time plot of the number of pigs moved and number of movement of pig by day, for movements occurring in Denmark during the period extending from November 1, 2002 to April 30, 2003.

Monday to Friday of the weeks, there were approximately 100,000 to 158,000 pigs moved within 2000–3000 movements between two premises. 5.4. Premise specific network Figs. 3–5 were examples illustrating premise specific networks. Slaughter pig farms, breeder farms, rearing farms and trades premises were mostly associated with movements away from the premise (Table 5). Gathering premises and abattoirs were mostly associated with movement going to the premise. A few abattoirs had movements of swine originating from them but they all went to another abattoir and were done for practical reasons. In general, slaughter pig farms showed a tendency to have small premise specific networks

Fig. 3. Premise specific network of a Danish slaughter pig farm (indicated by 1), with movements of animals that reached 4 premises (to) and 3 premises reached by the farm (from), in up to 3 steps, during the period extending from November 1, 2002 to April 30, 2003.

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Fig. 4. Premise specific network of a Danish slaughter pig farm (indicated by 24), with movements of animals that reached 19 premises (to) and 6 premises reached by the farm (from), in up to 3 steps, during the period extending from November 1, 2002 to April 30, 2003.

Fig. 5. Premise specific network of a Danish breeder farm (indicated by 80, center) with movements of animals that reached 0 premise (to) and 269 premises reached by the farm (from), in up to 3 steps, during the period extending from November 1, 2002 to April 30, 2003.

(Table 5). Breeder farms showed elaborate networks originating from them (Fig. 5). Breeder specific networks were more heterogeneous than those for slaughter pig or rearing farms. The reachability in path lengths up to 4 steps gave the same general information (Table 6)

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Table 5 Number of premises that were adjacent to a specific premise, in movement of swine of 1st to 4th path length, for movements occurring in Denmark during the period extending from November 1, 2002 to April 30, 2003 Premise type

Slaughter pig (N = 13259) Breeder (N = 299) Rearing (N = 99) Trade (N = 6) Gathering (N = 6) Abattoir (N = 28)

Median/95th percentile Path length 1

Path length 2

Path length 3

Path length 4

From

To

From

To

From

To

From

To

2/7

0/2

0/6

0/2

0/4

0/1

0/0

0/0

9/44

0/2

13/70

0/1

8/45

0/1

2/33

0/1

3/8

0/3

2/10

0/2

0/6

0/2

0/4

0/2

1/8

0/9

0/10

0/8

0/12

0/4

0/10

0/8

1/5

162/1392

0/6

107/659

0/4

46/226

0/0

20/100

0/5

1097/3137

0/0

450/2253

0/0

185/792

0/0

70/265

Table 6 Number of premises that were reached, in up to 4 movements of animals from and to a specific premise, for movements occurring in Denmark during the period extending from November 1, 2002 to April 30, 2003 Premise type

Slaughter pig Breeder Rearing Trade Gathering Abattoir

N

13259 299 99 6 6 28

Median/95th percentile From

To

3/12 26/130 5/20 1/22 1/12 0/5

0/5 0/2 0/7 1/12 398/1587 1535/4092

6. Industry network The number of premises that came in contact through animal movements during the observation period was 14,548. A total of 43,940 arcs connected these premises. This indicated a 3.02 level of connectance for the network. The median and 95th percentile for the total number of pigs and number of movements involved by type of premise can be found in Table 7. The average path length when cycles were excluded was 3.19 and the maximum path length was 8. There were 62 back and forth movements between two premises and two triangular cycles. The frequency distribution of degrees out of premise direction had approximately a power function with power 2.2966 while the distribution of the in-premise direction degrees showed a power of 0.566. The fit for the out degree showed a R2 of 0.89 and the in degree a R2 of 0.49. The clustering coefficient in the out direction was 0.005 and the

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Table 7 Median and 95th percentile of total number of pigs and total number of movements from and to in a Danish premise specific network over the period extending from November 1, 2002 to April 30, 2003 Premise type

N

Median/95th percentile From

Slaughter pig Breeder Rearing Trade Gathering Abattoir

13259 299 99 6 6 28

To

Number of pigs

Number of move

Number of pigs

Number of move

760/4634 2097/6979 1757/11875 328/2544 47/1580 0/1002

27/66 63/156 20/58 13/46 1/5 0/46

0/2302 0/1144 0/7528 201/60949 41718/374934 454877/1255877

0/14 0/11 0/30 4/96 692/4254 10154/42600

Table 8 Scale-free and clustering coefficients for Danish swine movements network including and excluding slaughter related movements and premises over the period extending from November 1, 2002 to April 30, 2003

Power coefficient (degree frequency) R2 Average cluster coefficient total Average cluster coeff. Breeder Average cluster coeff. Slaughter pig Number of connected premises Number of arcs

With slaughter sites

Without slaughter sites

In

Out

In

0.057 0.49 0.0641 0.056 0.0695 14,548 43,940

2.297 0.89 0.0053 0.0051 0.0055 6,666 11,217

2.303 0.91 0.0025 0.011 0.002

Out 1.689 0.89 0.0001 0 0.0001

coefficient of the in direction was 0.064. This indicated that clustering was mostly present for trade premises and for slaughter pigs, breeder, and rearing farms. The directionless clustering coefficient was 0.1. The subnet of the whole industry network without slaughter related nodes and movements was characterised by a slightly different topology when compared to the whole network (Table 8). The number of connected nodes became 6666 and they were linked by 11217 arcs giving a connectance of 1.68. A large number of nodes (7882) became disconnected when slaughter related movements were taken out of the network.

7. Discussion Trade patterns for animal movements of the swine industry were complex to study because they included many stakeholders, premises that were spread heterogeneously over the country, and the flows of animals between the premises were dynamic. The Danish swine industry had a pyramidal production structure that should appear in the flows of animals. Three aspects of this complex situation were of special interest for predicting the outcome of an epidemic and for controlling diseases. They were the topology of the

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network, the amount of heterogeneity in animal movement related to the specific premises and the dynamic of the flows of animals between premises. These three aspects were essential to understand the potential transmission of disease by animal contacts. Disease transmission, by animal contact, occurs at two known levels of organisation: within-farm and between-farm. These levels correspond to a geographic scale of distance related to the animal contacts. In the present study, the objective was to understand the between farm transmission of disease associated with industry trade patterns and the topology of the network of animal movements. This understanding would be essential when considering regionalisation within a country. The network framework allows the epidemiologist to recognise and illustrate the paths linking many pig production premises to one another. Pathogens can travel along these paths by contagion carried around by moving animals. This approach can be used to gain a larger space-time scale view of traffic in the study of disease transmission. When the network framework was applied to the Danish swine industry, there were three recognisable epidemiological units:  movement of animals between premises, involving one or more animals,  premise specific network of related sites linked by paths where pigs were sent or received,  swine industry network which was the union of all premise specific networks with or without slaughter related movements and nodes. 7.1. Movements of swine between premises The Danish swine industry was large compared to country size. The number of pigs sent to the abattoir during the six months observation period (12,917,300) was indicative of industry size since swine were produced as a meat commodity. The number of pigs moved was large (17,984,800) and the number of movements out of a slaughter pig farm was mostly to an abattoir (Table 2) as expected. The number of pigs involved (Table 1) was also a high proportion (71.8%) of all pigs moved. It is thus useful to consider the network that excludes slaughter movements. The total number of movements during the observation period (Table 2) indicated that animal movements were an important part of the activity of swine production. The numbers involved implied that animal movements were a potentially important mode of disease spread. The pyramidal production structure should be associated with more movements going from the top of the pyramid to the bottom than the number occurring between similar types of premises. This was observed in the animal movements’ data (Table 2). We can speculate that movements between two slaughter pig farms were more likely to involve piglets and the movements between slaughter pig farm and abattoir to involve slaughter pigs but no data was available to verify this. Adding the animal age information would permit a much better understanding of movements occurring between similar types of premises. These movements were likely to be more important for contagion. The comparison between median and maximum Euclidean distance, in general, indicated skewed distributions (Table 3). There were also large differences between the movements related to the different types of premises. These various differences indicated

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that there was a large degree of heterogeneity in the movements that were associated with specific premises. This heterogeneity could likely imply large differences in the risk potential for disease transmission associated with each of the various premises based on the characteristics of the movements related to them. The dynamics of the daily movements of animals between premises showed a highly harmonic shape, either when looking at number of animals or at number of movements. During the period of observation, the harmonic cycles were generally of similar amplitude except for the 3 weeks around Christmas time. The weekly harmonics assumed approximately an ‘‘M’’ shape as can be seen on visual assessment (Fig. 2). This indicated that there were two days with larger amounts of movements and pigs moved. This systematic behaviour again shows the highly structured activity along the production chain of the swine industry. The analysis of dynamics could be improved if a time-space continuum was used. It is likely that hyper graphs (Berge, 1973) and time series would provide an interesting analysis framework to realise this task. This would lead to a complicated analysis framework but it should be more representative of the integration of the various movement characteristics. Achieving this level of analysis of animal movement would be useful to manage the Danish swine industry on a daily basis and to help in disease spread control.

8. Trucks The number of different trucks (4584) used to move swine during the six months observation period could be seen as an extra number of premises where disease transmission can occur. The truck itself can be an epidemiological unit within which disease transmission can occur. Animals can be taken by the same truck during the travel route from different locations and then disembarked at different locations, but some animals will share the same crowded space for some time, thereby facilitating disease transmission. Furthermore, it could be hypothesised that the duration of transit could be part of a risk factor. A truck could be conceptualised as a moving premise where disease transmission can occur as long as the truck is not disinfected. The adequate cleaning process is expected to break the transmission potential of the truck environment. Thus, between disinfection a truck acts as a complicated moving premise. In this work truck rides between two premises were considered but not truck routes. Thus, the sharing of truck space by a group of swine, which made the truck a densely populated short time moving premise, was not done in this study. To analyse the risk potential of trucks for disease transmission, it would be necessary to construct truck routes. The median number of premises involved in truck routes was likely to be four plus one premises. This gave an approximation of the sharing potential. It should be remembered that 69.8% of the pigs go to the abattoir where the risk potential for animal disease transmission by direct contact was low or null because of the outcome for the pigs. 8.1. Premise specific network The premise specific network was a subnet of the whole swine industry network. It was constructed in such a way that all paths in the subnet contain the specific premise. The paths

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used for illustration purposes were at most three steps long going to the specific premise and similarly moving away from it. There were longer paths that existed for some premise specific networks. Visual assessment of the three premises shown in Figs. 3–5 illustrated the differences between these examples of specific premise networks through their trade patterns and the trade patterns of their business partners. The illustrative power of the figures should be noted and could provide interesting decision support to the decision maker working at disease control. Breeding and rearing premises generally showed more out going paths and a tendency for longer paths than other types of premises. This was especially true for breeding premises (73.9% had no incoming movements) and the others showed only a small amount of ingoing movements (Table 2). This indicated that these types of premises were mostly sources of pigs in terms of swine flows (60.8% of cases). They showed, in general, small networks with short paths and few premises involved as illustrated (Fig. 3 and Table 6). Abattoirs were path ends and sinks in swine flows (Table 6). As expected, abattoirs had large incoming networks. Gathering premises were few in numbers and they were not strict path ends but they acted mostly as sinks for swine flows (Table 6). These results indicated that slaughter pig farms (8220), breeder farms (221) and to a lesser degree rearing farms acted as sources of swine flows while abattoirs and gathering premises acted as sinks. Slaughter pig premises acted as amplifiers as seen by the comparison of number of pigs sent to number of pigs received (Table 1). It was likely that the swine movements between slaughter pig premises were associated with movements between maternity and grower farms but this could only be speculated because of the lack of age data. These premise specific network statistics were indicative of a structured industry with trade patterns corresponding to specialized premise activity, as seen from the comparison of premise type descriptive statistics. The comparison with the trade patterns of the Danish cattle industry (Bigras-Poulin et al., 2006) supported this conclusion since the cattle industry was less structured. An interesting corollary for the science of epidemiology was that it confirmed that graph theory could be used to measure the shape and amount of structure of an industry. Premise types were used as an indication of premise risk potential. This was in agreement with the previous paragraph. It could be pursued further by constructing a transit index for each premise using the reachability matrix. It would indicate if a premise was a source, a sink or the number of paths going through the premise as a measure of transit. The flows of swine in the Danish swine industry involved large number of animals moving along the paths (Table 1). A risk potential index for each premise could also be built by integrating reachability and flow information. This risk potential will vary from disease to disease and even from one strain of pathogen to another. Thus the characteristics of the networks should be weighted differently for the different situations. This idea is actually under study and the first results are promising. The walks linking premises contained few cycles. The existence of cycles would have a potential impact by acting as an amplifier for disease transmission over time if the cycle was not broken. During the observation period, the Danish swine industry network showed a small number of cycles (62) made of mostly back and forth movements between two premises. It was likely that over a longer period longer cycles would occur. They would be related to the movements of reproduction animals. If this was the case, it would imply the

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presence of slow turning cycles. These could maintain the endemic presence of some pathogens within the involved premises. The pathogens could then disappear from monitoring and reappear in a harmonic pattern. This seemed an interesting research avenue since some pathogens show this empirical behaviour. The concept of cycles that exists in networks is a good example of the richness of approaching the study of disease transmission in epidemiology using networks and graph theory. The visual comparison of those swine specific networks with those illustrating some premise specific networks of the Danish cattle industry (Bigras-Poulin et al., 2006) gave a quick impression of the differences between the trade patterns of the two industries. The presence of longer cycles was observed for the cattle industry. The heterogeneity between the trade patterns of premises can be seen in Tables 6 and 7 by comparing median and 95th percentile number of premises involved for the various in and out path lengths. The patterns of trade shown by the premise specific networks indicated an important amount of heterogeneity within and between premise types. When this was considered simultaneously with the structured behaviour of the network, it implied that some pathogens could take advantage of this regularity for disease transmission. The industry would then act as a complex disease transmission system. Understanding the risk potential of specific premises would need to evaluate the whole industry and evaluate riskpotential networks in the sense of Friedman and Aral (2001). 8.2. Swine industry network The Danish swine industry network is a large finite network corresponding to the union of all premise specific networks. For disease transmission, a metaphor can be used for the network. It could be compared to a river basin where some breeder farms and slaughter pig farms are springs and gathering premises and abattoirs are the delta. An important heterogeneity in trade patterns was observed among and between the slaughter pig and breeder farms, as well as for abattoirs. This heterogeneity was characteristic of the network topology that can be represented using a power function model of the node degree frequency distribution (Faloutsos et al., 1999). Since the swine industry network is a directed graph, there was a power for the inbound degrees ( 0.6) and one for the outbound degrees ( 2.3). This confirmed the scale free topology of the network and it indicated a network with at least one giant component as seen in scale free networks. From the observed values and theoretical work, it can be inferred that the network would show great robustness under attack and premise destruction because the power was less than 3 (Cohen et al., 2000; Callaway et al., 2000). Even if a large percentage of premises were rendered inactive, the network would maintain its structure. This is in agreement with what had been observed through history as agricultural premises had been subjected to catastrophic situations (wars, epidemics, etc) but the structure of the agricultural industry was maintained. It was an indication that the industry structure would be maintained even if the economic pressure caused a reduction in the number of premises. The maximum path length was eight arcs long with nine premises. The average path length was 3.19 and that was an indication that the network showed the small-world effect (Watts and Strogatz, 1998). Network topology was also characterized by the clustering measures. In this case, the clustering coefficient was 0.064 inbound while it was 0.005

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outbound. These results indicated a scale free network topology that also had the small world quality (Watts and Strogatz, 1998). The small world characteristic was related mostly to inbound movements and indicated complicated partnership trade patterns because it implied that when two business partners sent animals to a third premise they also were linked by an animal movement. The descriptive measures of the network topology can give the epidemiologist insight on disease transmission behaviour within the network (Moore and Newman, 2000; Abramson and Kuperman, 2001). 8.3. Swine industry network exclusive of slaughter movements For many animal diseases, movements to abattoir represent little or no risk because there are no movements of live animals out of the abattoir and back to the farms. The sanitary status of abattoirs is a public health issue rather than an animal disease issue. Because of this, it was appropriate to consider data from the subnet that excluded slaughter related nodes and movements. A large number of premises became disconnected in the subnet. The subnet was made of 1051 weak components but it still showed a large component including 10547 premises. Connectance was decreased nearly by half but the scale-free nature of the network was maintained in the subnet (Table 8). The in movements were more balanced to the out movements as seen by the power coefficients of the degree distribution. The clustering coefficients were also smaller than in the whole industry network. In the subnet, the clustering coefficients were of the magnitude of those of a random graph. The topology of the subnet was different and made it easier to understand disease persistence (Table 8). 8.4. Disease spread implications For network topology, a completely randomized graph corresponds to lack of structure while at the other end of the spectrum one finds the lattice network which is systematically and highly structured. Natural networks such as the Danish animal movement based swine industry network were in between these two extremes. The completely randomized network would have a disease transmission behaviour which corresponds to that of usual mathematical models of transmission based on the law of mass action and an assumption of homogeneous contact structure (Anderson and May, 1992). Our understanding and predictions about disease spread was usually based on these assumptions. The above results clearly indicated that the Danish swine movement network was not a completely randomized network. The Danish swine movement network was shown to have many intense flows as seen from the ratio of number of pigs moved over number of movements (48.3). The network size characteristics and intensity of movements should facilitate spread. Although the inbound clustering coefficient should decrease the risk of spread since it indicated that movements tend to originate from premises with correlated risks, their size was not sufficient for this effect to occur. This was especially true when slaughter activity were excluded. The power function topology of scale-free networks has been theoretically demonstrated to indicate that the reproductive ratio below which a disease disappeared was very low (Pastor-Satorras and Vespignani, 2001a,b; May and Lloyd, 2001; Keeling, 2005).

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It can then be inferred that a disease present in the Danish swine industry that can transmit through animal movements was likely to remain present because it can easily hide in the large component. A corollary to this was that if disease control is undertaken it will be very difficult to reduce prevalence to such a level that would insure that the disease will disappear. It can be speculated that this was true for the Danish swine industry salmonella program. The topology of the subnet excluding slaughter related movements indicated that the scale-free nature was even more present when considering the power coefficients of the degree distribution (Table 8). The clustering coefficients were of the order of a random network (Newman, 2003). This implied that the robustness and the capacity to maintain the presence of a pathogen could be more readily inferred from the characteristics of the subnet. 8.5. Disease control implications The large amount of between premises heterogeneity in the movements of animals indicated an important degree of asymmetric variation between farms in movements of animals. The premise specific networks showed a tendency to be large for approximately 5% of the specific premises. This indicated that heterogeneity had to be taken into account when managing an epidemic crisis. The period during which the index case or cases can transmit the agent and, thereby, cause disease through animal movement can be relatively long, up to 3 weeks in the case of the UK 2001 FMD epidemic (Keeling et al., 2002). Because of this detection problem at the onset of the epidemic, it is important to use the appropriate quantity of human resources to achieve rapid control of the epidemic. To accomplish effective control, it is essential to know the risk potential of the index farm or farms and the ability to trace animals at local scale is necessary. Existing mathematical models of disease spread such as interspread (Morris et al., 2001) and spread model (Schoenbaum and Disney, 2003) generate movements of animals based on farm size using a constant stochastic animal movement algorithm and a fixed area within which these movements can go. These are constraints, which correspond to a random network and assume a large degree of homogeneity in movements of animals for any farm. This will average out over the course of the epidemic because much iteration is done. Also, the simulation model is useful for the evaluation of various strategies, given that the model can be a priori calibrated and the characteristics of the viral strain are presumed known. It is an efficient preparedness tool. On the other hand, the fact that the assumption of homogeneity is not met makes the simulation model much less useful to control a crisis. The network approach proposed in this project has shown to be much more appropriate to support disease control activities because it can better handle heterogeneity. Disease control must be achieved at the premise scale, not at the whole industry scale as is the case for preparedness. At this local geographical scale the heterogeneity must be taken into account. The district veterinarian has access to a large amount of sociological knowledge at the local scale. The network approach can support the district veterinarian at the local scale and communicate the information to the industry scale head quarters.

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For disease control, the network approach is dependent on regularly valid and complete updated data. The update time is a crucial characteristic of a crisis management system based on the network approach. At the moment the update time for the movement of animal data in Denmark is 7–10 days. This is long and will reduce the efficiency. To be useful, the movements of the index case or cases need to be updated rapidly. For prolonged usage throughout management of the crisis, data on movements of animals must be updated in real time. The route of the trucks should also be registered. The network analysis used, especially if the knowledge is made available through a geographic information system, can provide a means to achieve the trace history and potential risk level of the premises involved as index case or cases. The graphs produced are premise specific and are at local scale for geographic location and farm information but are not limited to that geographic scale since many premises could be involved. 8.6. Limitations Individual identification is not necessarily useful for disease control when swine only move from farm to abattoir. But when an animal goes back up onto the production pyramid, then the individual identification becomes useful to track disease and attribute origin. When individual animal identification is available it should be registered with movement data. Data validation was often a problem because the analysis and description of trade patterns required the construction of many data files from data originating from various data sources. This construction added up missing values along the way, and, thus, for some constructed variables there can be a larger number of missing values. For example, missing the geographical latitude and longitude for a single premise will prevent the computation of distances for many paths of animal movements that go through that premise. Because missing data are generally independent between individuals, every merge will increase the impact of missing data approximately by adding the proportion of missing data at every step of the merge. This is especially true when networks and flows were studied. The data represented a census of animal movements during the six months observation period. Thus, there was no sampling error. There could be some biases: potential representation bias associated with exclusion caused by missing data, bias related to the observation period which is only 6 months long, and bias due to the lack of precision in animal categories used (missing age categories, farm specialization categories, and production site category). The potential impact on the presented results should not be large but these would be a problem if complicated hypotheses were tested. Routinely, it should have been possible to illustrate the premise specific networks using the location of the farms on a geographical projection of Denmark. The period under analysis was short (6 months) and few cycles were observed. It is likely that a longer observation period would find a larger number and longer cyclic movements. This longer period should cover the span of two average reproductive animal’s life. It can be speculated that these cycles would be important to understand disease transmission and/or development for disease such as post-weaning multisystemic wasting syndrome.

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8.7. Potential improvements Classification of premises can be done using crude or refined class definitions. In this first work on swine movements, a crude classification was used. The types of pig moved were unknown. Piglets, sows or slaughter pigs are not differentiated in the movement of pigs. This makes the interpretation of number of pigs moved difficult since the reason behind the movements is often zootechnical and related to age. It would be useful to add this information in order to better qualify movements and to stratify production using more precisely defined classes. The lack of precise variables that indicated premise type reduced the possibility of characterizing the premise specific networks. Vice-versa, premise specific network’s characteristics could be used to help define classes of movements and of premises. This information could be used to estimate pathogen specific disease transmission risk potential. It could also be merged with other data sources to do cross validation of the data. It must be understood that when using network analysis to study disease transmission and contagion, node characteristics of interest will likely vary with each specific pathogen and it will also be true for the definitions of risk potential links. Each specific pathogen will likely have its appropriate and optimal time scale for transmission. This scale will then be used to define risky movements and risky links and risk factors for potential pathogens. In the data, truck routes were not available since the order of the pick ups and beginning and end of truck routes were not present in the data files. Making data about truck movements available would allow us to consider the network of truck movements and construct a truck network where trucks would be nodes. A network containing premises and trucks as nodes could be considered. Flows of animals within networks using hyper graphs (Berge, 1973) should be undertaken. It would be of great scientific and practical interest to better understand disease transmission. The major knowledge to be gained by studying flows is the estimation of speed and change of speed of animal transit. Using simultaneously network analysis and geographic information systems (GIS) should be undertaken. Knowledge production by network analysis could be automated and integrated in a database of farming premises characteristics in order to create an estimate of the risk of disease transmission related to each of the premises. This new database could then be linked into a GIS system and be available for decision making during epidemic crises or for disease control in general (outside crisis situations).

9. Conclusions The Danish swine movement network was found to be a large finite scale-free directed graph with at least one large component and possessed the small-world characteristic. The network is robust to premise retrieval and change. Within such a network the reproduction ratio for disease spread is very low which implies that a pathogen can maintain itself and spread even when it is at a low prevalence. Under this situation it can be expected that many pathogens would be difficult to eradicate. The network approach and graph theory based analysis are an efficient conceptual framework to study movements of animals and trade patterns. It provides tools for analysis

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and illustrations of the relationships between movements of animals. Improved data quality should allow for the linking of animal movement networks and geographic information systems. The development of such an interface would be useful for the follow-up and management of animal movements. One important issue for disease management at the country level is to recognize the strata that exist within an animal production industry and which farming premises should be aggregated within these strata. The present study has only begun to identify some of the tools that can be used to find these strata. The trade patterns are specific by animal industry, specialized activity, time and space. A study of swine movements over a much longer period should be undertaken. There is a large degree of heterogeneity associated with movements of animals either at the movement level or at the premise specific network level. The heterogeneity of movements of animals is such that actual mathematical models are more useful for epidemic intelligence and preparedness but are likely to be lacking when it comes to actual crisis management. The network approach is potentially a more efficient way that could be used for epidemic crisis management and other disease control programs but the data quality issues have to be dealt with. The data quality issues are still important and need to be solved in order to do a more satisfactory epidemiological analysis of the Danish animal production situation. The potential improvements presented in this paper should be implemented especially the integration of network analysis into a GIS.

Acknowledgements ˚ 01The research was funded as a project of the International EpiLab (93S-2465-A 01269) and done at the International EpiLab in Denmark. The funding came from various sources within the government and animal industries of Denmark. The authors wish to thank Mette Marie Larsen for her work on the data, Anette Boklund of Danish Bacon and Meat Council, Bertel Strandbygaard of the Danish Veterinary Services.

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