Network analysis of swine movements in a multi-site pig production system in Iowa, USA

Preventive Veterinary Medicine 174 (2020) 104856

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Network analysis of swine movements in a multi-site pig production system in Iowa, USA

T

Tiago L. Passafaroa, Arthur F.A. Fernandesa, Bruno D. Valenteb, Noel H. Williamsc, Guilherme J.M. Rosaa,d,* a

Department of Animal Sciences, University of Wisconsin, 1675 Observatory Drive, Madison, WI 53706, United States PIC North America, 100 Bluegrass Common Blvd, Suite 2200, Hendersonville, TN 37075, United States c Iowa Select Farms, 811 South Oak Street, Iowa Falls, IA 50126, United States d Department of Biostatistics & Medical Informatics, University of Wisconsin, 610 Walnut Street, Madison, WI 53726, United States b

A R T I C LE I N FO

A B S T R A C T

Keywords: Basic reproduction number Infectious diseases Percolation analysis Swine movements Time series network analysis

Pig production in the United States is based on multi-site systems in which pigs are transported between farms after the conclusion of each particular production phase. Although ground transportation is a critical component of the pork supply chain, it might constitute a potential route of infectious disease dissemination. Here, we used a time series network analysis to: (1) describe pig movement flow in a multi-site production system in Iowa, USA, (2) conduct percolation analysis to investigate network robustness to interventions for diseases with different transmissibility, and (3) assess the potential impact of each farm type on disease dissemination across the system. Movement reports from 2014–2016 were provided by Iowa Select Farms, Iowa Fall, IA. A total of 76,566 shipments across sites was analyzed, and time series network analyses with temporal resolution of 1, 3, 6, 12, and 36 months were considered. The general topological properties of networks with resolution of 1, 3, 6, and 12 months were compared with the whole period static network (36 months) and included the following features: number of nodes and edges, degree assortativity, density, average path length, diameter, clustering coefficients, giant strongly connected component, giant weakly connected component, giant in component, and giant out component. Small-world and scale-free topologies, centrality parameters, and percolation analysis were investigated for the networks with 1-month window. Networks’ robustness to interventions was assessed by using the Basic Reproduction Number (R0). Centrality parameters indicate that gilt development units (GDU), nursery, and sow farms have more central role in the pig production hierarchical structure. Therefore, they are potentially major factors of introduction and spread of diseases over the system. Wean-to-finishing and finishing sites displayed high in-degree values, indicating that they are more susceptible to be infected. Percolation analysis combined with general properties (i.e. heavy-tailed distributions and degree disassortative) suggested that networks with 1-month time resolution were highly responsive to interventions. Furthermore, the characteristics of a disease should have strong implications in the biosecurity practices across production sites. For instance, biosecurity practices should be focused on sow farms for highly contagious disease (e.g., foot and mouth disease), while it should target nursery sites in the case of a less contagious diseases (i.e. mycobacterial infections). Understanding the patterns of swine movements is crucial for the swine industry decision-making in the case of an epidemic, as well as to design cost-effective approaches to monitor, prevent, control and eradicate infectious diseases in multi-site systems.

1. Introduction The structure of pig production in the United States heavily relies on intensive farming systems comprised of multiple sites (Tokach et al., 2016). In these multi-site systems, farms are highly specialized in one of the stages of the production (e.g., farrowing, growing or fattening) and

⁎

pigs are transferred to a new location after the conclusion of a specific phase. Although ground transportation becomes a critical tool for the pork supply chain in such a system, it also constitutes a potential factor of introduction and dissemination of infectious diseases across farms. For instance, Fritzemeier et al. (2000) stated that 28 % of the secondary outbreaks of swine fever in Germany between 1993 and 1998 were

Corresponding author at: 1675 Observatory Drive, Madison, WI 53706, United States. E-mail address: [email protected] (G.J.M. Rosa).

https://doi.org/10.1016/j.prevetmed.2019.104856 Received 12 June 2019; Received in revised form 23 October 2019; Accepted 19 November 2019 0167-5877/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Geographical distribution of the different types of farms in Iowa Select Farms. This figure excludes one observation from a GDU farm located in Nebraska, USA.

(PRRSV) outbreaks in sow farms in the United States. In another study, Valdes-Donoso et al. (2017) used a random forest algorithm to predict swine movements within a regional pig production system in the United States. From the best of the authors knowledge, no studies in the United States have investigated which farms in a multi-site system work as super-spreaders or super-receivers for simulated diseases with different transmissibility. Such information could be used to prevent the introduction of emerging and exotic diseases in the country (e.g. African swine fever), as well as to develop contingency plans to control disease outbreaks at local or national levels. A way to assess which farms in a pig production system are working as super-spreaders or super-receivers is to use Percolation Analysis (PA). Such an approach is often used to assess the robustness of a network due to changes in its structure by removing part of the nodes until the whole network is fragmented. A practical consequence of the use of PA is the vaccination of animals. According to Büttner et al. (2013), pigs vaccinated against a specific disease cannot transmit it or be infected, assuming that the vaccination is 100 % effective in stablishing sterile immunity for each pig in the farm. Therefore, these pigs have no impact in spreading the disease, and consequently the farm node can be “excluded” from the network. Typically, in PA, nodes are removed randomly or sequentially based on a ranking defined by centrality measures (Büttner et al., 2013; Büttner and Krieter, 2018) or by the Basic Reproduction Number (R0) (Woolhouse et al., 2005; Volkova et al., 2010). The main goal of such analysis is to identify nodes that have more impact on the fragmentation of the network. This information is essential to develop cost-effective surveillance approaches. For example, sites with a high risk to spread infectious diseases could be monitored more closely, and biosecurity practices might be improved or additionally implemented in these farms. Therefore, the objectives of this study were: (1) to describe pig movement networks in a multi-site production system in Iowa, USA, (2) to conduct percolation analysis to investigate network robustness to interventions for diseases with different transmission rates, and (3) to assess the potential impact of each farm type on disease dissemination across the system.

caused by ground transportation. Moreover, foot and mouth disease (FMD) was spread over Europe in 2001 reaching France, Ireland, and the Netherlands due to the transport of infected animals from the United Kingdom (Pluimers et al., 2002). Even before these episodes, the European Union (EU) was aware of the importance of monitoring the movement of livestock species, and stipulated that its member countries were required to collect and store transport of live pig records into national databases (EUR-Lex, 2000). Conversely, in the United States the shipment of pigs is partially regulated, and no source provides complete information of such movements (Valdes-Donoso et al., 2017). According to these authors, the United States Department of Agriculture through the animal disease traceability program collects only movement data when pigs are moved across states, or when pigs are transported to the market. Therefore, most of the available shipment records are disconnected and held by individual producers and meat packing plants. The lack of consistent information on pig movement data in the United States makes it more challenging for the country to unravel many epidemiologic questions, to design contingency plans, and to monitor the risk of introduction of exotic diseases. However, local databases of pig movement are of a great value for producers since they can be used by single companies to help design and improve their surveillance, control, and eradication plans for infectious diseases. Pig transportation data can be analyzed as a network structure in which sites and shipments correspond to nodes and edges of the network, respectively. Such type of analysis has been applied to study pig movements to assess the risk of disease introduction and dissemination (Nöremark et al., 2011; Rautureau et al., 2012; Guinat et al., 2016), to identify farms working as super-spreaders or super-receivers (Büttner et al., 2013; Büttner and Krieter, 2018), to develop strategies to mitigate and prevent disease outbreaks (Thakur et al., 2016; Salines et al., 2017), and to generate network parameters to simulate disease transmission (Dorjee et al., 2013; Kukielka et al., 2017; Relun et al., 2017). However, most of these research was conducted in Europe, with very few investigating typical pig movement in the United States. For instance, Lee et al. (2017) investigated the association of the network structures with Porcine Reproductive and Respiratory Syndrome Virus 2

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Table 1 Description of the terminology of network general topological properties and centrality parameters. Term

Range

Definition

General network properties Nodes Edges

0 to ∞ 0 to ∞

Average path length

0 to ∞

Diameter

0 to ∞

Density Degree assortativity Clustering coefficient

0 to 1 −1 to 1 0 to 1

Giant weakly connected component

0 to ∞

Giant strongly connected component

0 to ∞

Giant in component Giant out component Small-world topology

0 to ∞ 0 to ∞ –

Scale-free topology Node centrality parameters Degree In-degree Out-degree Betweenness

–

The elements of the network (Wasserman and Faust, 1994) and represent the sites of our study The elements of the network that connect nodes (Wasserman and Faust, 1994), and represent the movement of pigs among farms. The average number of links to transverse along the shortest path between all possible pairs of nodes (Watts and Strogatz, 1998). The length of the shortest path between the most distanced nodes in the network, given that the shortest path actually exists (Wasserman and Faust, 1994). The number of edges observed in the network divided by all possible connections in the network (Wasserman and Faust, 1994). The tendency of the nodes to connect with nodes of similar (> 0) or dissimilar (< 0) degree (Newman, 2002). The undirected metric that measures the probability of two nodes connected to a third one be linked to each other (Watts and Strogatz, 1998). The largest subset of the directed network which nodes are connected and mutually reachable disregarding the directionality of the edges (Kao et al., 2007). The largest subset of the directed network which nodes are connected and mutually reachable considering the directionality of the edges (Kao et al., 2007). A subset of the network that has direct access to the giant strong component (Lentz et al., 2016). A subset of the network that is accessed from the giant strong component (Lentz et al., 2016). A network with high cluster coefficient and short average path length compared with randomly generated networks of equivalent size (Watts and Strogatz, 1998). A network that the distribution of in-degree and out-degree follow a power law distribution (Barabási and Réka, 1999).

0 0 0 0

to to to to

∞ ∞ ∞ ∞

The The The The

number of contacts of a node (Wasserman and Faust, 1994). number of incoming contacts of a node (Wasserman and Faust, 1994). number of outgoing contacts of a node (Wasserman and Faust, 1994). frequency that a node lies in the shortest path of all possible pairs of nodes (Freeman, 1977)

2. Material and methods

2.2. Swine movements network analysis as a time series

2.1. Swine movement data

Time series networks of swine movements were constructed to assess the temporal development of the network for the whole period of 3 years including all shipments between production sites. The initial temporal resolution considered monthly snapshots (≈30 days) of the whole period that was later aggregated by 3, 6, 12, and 36 months, similarly to the method employed by Lentz et al. (2016). In this approach, the time series of the whole period static network is assumed to be a sequence of adjacency matrices, as follows:

Reports of swine shipments between production sites from 2014–2016 were provided by Iowa Select Farms (ISF), Iowa Falls, IA. The ISF is a large integrator pig producer, managing over 600 farms distributed across 50 counties in Iowa (Fig. 1). In our study, a total of 618 farms have moved pigs across different locations at least once during the whole period of three years. Only one farm in ISF was located in Nebraska, USA and the vast majority of the farms were weanto-finishing (59 %) followed by finishing (24 %), GDU (8 %), sows (6 %), and nurseries (3 %). The raw data comprised 296,220 shipments and included the information on the date of the movement, suppliers, receivers, number of pigs in each shipment, geographical location, and type of each farm (nursery, gilt development unit (GDU), sow farm, wean-to-finishing farm, and finishing farm). Information on shipments delivered to abattoirs and cull stations were removed from the data since they represented ending points or external movements in the production system. Boar studs were also excluded from the analysis because shipments assigned to such farms are typically of low volume and restricted within studs. These characteristics alleviate risks of introduction and dissemination of diseases into the production system via ground transportation. Movements from external pig producer companies were also excluded from the analysis, as no additional information of the farms was provided besides the number of pigs and shipments. Furthermore, observations of movement directions opposite to the expected standard flow (e.g. nursery to sow), and/or with no information regarding either the site of origin, or the farm of destination, or the number of pigs in the shipment were also removed from the analysis. After the data curating process, 192,654 observations (72 % of the raw data) were removed from the analysis with the vast majority of shipments related to the market process (56 % of the raw data). The remained data included a total of 76,566 shipments. Data editing and graphical visualization were conducted in R (R Development Core Team, 2015) with the dplyr (Wickham et al., 2017) and the ggplot2 (Wickham, 2016) packages, respectively.

T

A=

∑ At t=1

(1)

where A is the adjacency matrix for the whole 3-year period, At is the adjacency matrix for the month t (t = 1, 2, …,T; T= 36). The adjacency matrices were constructed considering the production sites as the network nodes, and the shipments between them as the network edges. In the adjacency matrix, edges are represented as Aij = 1 if during the covered period at least one shipment from node i to node j has occurred, otherwise Aij = 0 . Such edges are directed reflecting the known status of origin/destination and also could be weighted by the number of shipments or pigs. General network properties were investigated and compared between each aggregated period of 1, 3, 6, 12, and 36 months, considering the following features: number of active nodes and edges, average path length (APL), diameter, density, degree assortativity, clustering coefficient, giant strongly connected component (GSCC), giant weakly connected component (GWCC), giant in component (GIC), and giant out component (GOC). Descriptions of these features are presented in Table 1. 2.3. Network topologies and centrality parameters The small-world and scale free topologies, the centrality parameters and the percolation analysis were performed by assuming snapshots of 1-month resolution for the whole period of 3 years. Monthly intervals were considered to reflect the typical time span to detect most of the swine diseases outbreaks, which is commonly referred to as the high risk period (Horst et al., 1997). For instance, foot-and-mouth disease in 3

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virulence, βin and βout are the average of the unweighted or weighted (i.e. shipments or pigs) in and out degrees, respectively; σin and σout are the standard deviations of the unweighted or weighted in and out degrees, respectively; and rin,out is the Pearson correlation coefficient between in and out degrees considering unweighted or weighted versions. In the case of a homogeneous-mixing population, the in-degree and outdegree standard deviations are zero, reducing the Eq. (2) to:

Europe (Gibbens et al., 2001) and Asia (Nishiura and Omori, 2010; Yoon et al., 2015), and classical swine fever in Netherlands (Elbers et al., 1999) have been diagnosed up to 30 days after the initial outbreak. Therefore, splitting the whole static network in monthly intervals is a reasonable period to develop and plan strategies to control and mitigate infectious diseases outbreaks in a multi-site system. Furthermore, previous studies have used the same time frame to evaluate swine movements facilitating any kind of comparisons (Nöremark et al., 2011; Rautureau et al., 2012; Lee et al., 2017). The small-world topology was assessed by constructing 1,000 random Erdos-Renyi networks (Erdos and Rényi, 1960) containing the same number of nodes and edges of each monthly network snapshots. The APL and clustering coefficient were compared with the corresponding simulated and observed networks. Networks are considered to have a small-world topology if they show smaller or similar average path length and six times greater cluster coefficient than the average estimates obtained from the equivalent random networks (Watts and Strogatz, 1998). Scale-free topology was investigated by fitting the unweighted degree distribution x as a power law distribution defined as p(x ) ∼ x α , where α is the scale parameter. The standard Kolmogorov–Smirnov (KS) statistics was used to obtain the xmin cut-off value of the empirical power law distribution, and the scale parameter α was estimated by using the maximum likelihood estimation given xmin . Parameters uncertainty was assessed with a non-parametric bootstrap procedure. Similarly to Broido and Clauset (2019), the power-law distribution was also compared to three non-scale free alternative distributions (i.e., exponential, log-normal, and Poisson) by using a Voung normalized likelihood ratio test (LRT). In this approach, to make the model likelihoods directly comparable the xmin cut-off value is required to be the same for the different distributions. Here, we chose the xmin obtained from the power law distribution. Therefore, results are slighlty biased towards the power law distribution since the optimum value of xmin may be different for the non-scale free distributions. Production sites were described according to the centrality parameters including the unweighted degree, the weighted degree based on the number of animals or shipments, and betweenness (Table 1). Statistical differences in the distribution of the centrality parameters between the different types of farms were assessed with the Wilcoxon parwise test.

R 0Homogeneous = ρ0 βin βout

It is important to notice though that the absolute value of R0 was not specific for a given pathogen. In fact, the method explores the relative change in R0 due to the heterogeneous contact rates of the network. Hence, ρ0 was assumed to be constant and the relative value of R0 was calculated as R 0(Network ) R 0(Homogeneous) , representing the multiplicative effect of the first and second moments of the network on the R0 estimates (Volkova et al., 2010; Marquetoux et al., 2016). A percolation analysis was performed to identify those farms that are key in the dissemination of an infectious disease through the multisite system. The R0 was used to quantify network fragmentation. To make the analysis more relevant to diseases with different transmission rates, we simulated three scenarios based on the approach proposed by Volkova et al. (2010). In this context, the unweighted and weighted (based on shipments or pigs) degree were treated as the contact rates for each network with 1-month temporal resolution. In the first scenario, the unweighted degree was used to represent highly contagious diseases such as foot-and-mouth disease, porcine epidemic diarrhea virus, classical swine fever and African swine fever. The third scenario reflects lowly contagious diseases (e.g. mycobacterial infections) and considered the weighted degree on the number of pigs. The second scenario is intermediate and used the weighted degree on the number of shipments. The percolation analysis was conducted for each scenario and networks with time resolution of 1-month by calculating the relative magnitude of the basic reproduction number (R 0(reduced network ) R 0(full network ) ), which was computed based on the Eq. (2) and considering two intervention strategies. The first approach consists in quantifying the magnitude of R0 after randomly removing nodes from the network. This procedure was repeated 100 times for each 1month temporal resolution network and the average magnitude of the R0 was reported as a function of the fraction of removed vertices. The second strategy involves the consecutive exclusion of nodes ranked according to the magnitude of the R0. This procedure was performed by the following steps: 1) Calculate R0 including all nodes in the network, 2) Compute the contribution of each node on R0 as the difference between the R0 calculated with all nodes in the network and after removing the specific node, 3) Rank nodes based on the contribution on the R0, and 4) Remove each node from the network following the order defined in 3). During nodes removal their direct contact rates were treated as absent (βin = βout = 0) and re-calculations were performed to quantify the relative magnitude of R0. Furthermore, an additional PA was conducted to quantify the contribution of the type of production sites in the reduction of R0. Hence, nodes were sequentially removed from the network by considering a particular type of farm, and the magnitude of the R0 was quantified after excluding all sites of the same kind from each movement network. All tasks related to the implementation of the network analysis including construction, estimation of topological and centrality parameters, and the percolation analysis were carried out with the igraph R package (Csárdi and Nepusz, 2006). The network scale free-topology and the comparison of power law with non-scale free distributions were performed with the poweRlaw R package (Gillespie, 2015). In addition, all statistical tests were conducted at a 5 % significance level.

2.4. The multiplicative effect on the Basic Reproduction Number (R0) and percolation analysis The heterogeneity in the contact rate of a network structure was considered to assess its multiplicative effect on the Basic Reproduction Number (R0). Such a measure represents the expected average number of secondary cases generated from a single case introduced into a nonexposed and homogeneous population at equilibrium (Diekmann et al., 1990). A R0 > 1 indicates that an infectious disease outbreak will spread in the population, while for R0 < 0 indicates that the disease outbreak will naturally disappear (Diekmann et al., 1990). The heterogeneity in the contact rates of network structures might enhance the transmissibility of infectious disease throughout their systems (Woolhouse et al., 2005; Kiss et al., 2006). Furthermore, the presence of a positive correlation between the in-degree and out-degree structures of a network contributes to a relative increase in R0, whereas a negative or null correlation leads to a decrease or no impact on R0, respectively (Woolhouse et al., 2005). Therefore, to compute R0 such network features must be taken into consideration. As such, we have used the method defined in Volkova et al. (2010) and Marquetoux et al. (2016), where R0 accounts for the first and second moments of the contact rates, being estimated by the following formula:

R 0Network = ρ0 βin βout + σinσout rin,out

(3)

(2)

where: ρ0 is an unknown constant depending on the pathogen specific 4

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Fig. 2. Summary diagram of pig shipment reports for each month between farms in a multisite (Iowa Select Farms) from January 2014 to December 2016. Numbers in parenthesis within boxes (sites belonging to the cyclic component) and ellipses (sites belonging to the acyclic component) represent the percentage of sites which were active in a month. The thickness of an arrow and the numbers close to it represent the average amount of shipments and pigs (in parenthesis) transported per month during 3 years. This figure was based on the diagram depicted by Lee et al. (2017).

3. Results

series networks increased with the time resolution, ranging on average from 0.0009 (1-month window) to 0.0064 (12-month windows). The clustering coefficients were on average 0.017, remaining roughly steady irrespectively of the time resolution of 1, 3, 6, or 12 months. The size of GSCC (GWCC) was on average 0.5 % (37.5 %), 1.1 % (70.8 %), 1.6 % (91.4 %), 23.7 % (93.7 %) of the size of the whole network for the time series networks with temporal resolutions of 1, 3, 6, and 12 months, respectively. Similarly, the size of GIC (GOC) was on average 0.2 % (5.3 %), 2.2 % (32.7 %), 2.83 % (70.6 %), and 24.7 % (82.2 %) of the size of the whole static network for the time series networks with temporal resolutions of 1, 3, 6, and 12 months, respectively.

3.1. Descriptive statistics of the movement data From January 2014 to December 2016, ISF transported more than 23 million pigs delivered by 76,566 shipments across different production sites. This corresponds to an average of approximately 643 thousand pigs transported monthly through 2,128 shipments (Fig. 2). In the same period of three years, ISF delivered 99,809 shipments to the market, harvesting about 12.2 million pigs. This corresponds to more than 4 million pigs delivered annually to the market and a production of approximately 453 million tons of pork year−1. The number of shipments and pigs purchased annually by ISF from external companies from 2014–2016 were 460 and 338,678, respectively. The vast majority of the purchases was to replace the breeding stock (71 %) and all external movements to ISF was originated from 11 companies. Sow farms sent the largest monthly amount of shipments (1,013) and pigs (331,984) to other production sites, whereas finishing farms sent the lowest quantity of shipments (67) and pigs (6,588). GDU farms received the lowest average number of shipments (216) and pigs (35,811) per month. Interestingly, sow farms received the greatest quantity of shipments (641) but with the lowest amount of pigs (10,215). Wean-to-finishing farms received the largest amount of pigs (276,132), followed by finishing sites (216,702). The most active sites in terms of monthly shipments received or sent were sow (97.65 %), nursery (83.73 %), and GDU (68.41 %) farms.

3.3. Network topologies and centrality parameters of 1-month temporal resolution networks Small-world topology was not observed for any of the monthly networks, with an APL smaller than 2 nodes, and clustering coefficient estimates lower than 0.05. The unweighted degree distribution of 1month temporal resolution networks was in agreement with a power law distribution (KS, p < 0.05). However, after comparing the power law with a non-scale free distribution for each 1-month temporal resolution networks the results were inconclusive (LRT, p > 0.05). The LRT statistics favored the power law against exponential (except in one month) and Poisson distributions for all networks with 1-month time window, while 28 out of 36 monthly networks displayed better LRT statistics for the log-normal distribution compared to the power-law distribution. Centrality parameters of the different production sites obtained for each snapshot of the 1-month temporal resolution networks are summarized in Fig. 3. Hence, each entry in the boxplot represents the centrality parameters observed for a site in a specific month. Statistical differences in the distribution of all centrality parameters were observed among the different types of farms (Wilcoxon pairwise test, p < 0.05). Overall, finishing and wean-to-finishing sites showed the second and third largest median estimates for all in-degree measures (Fig. 3A, B, and C), and finishing farms also displayed many outliers for the unweighted in-degree. Finishing and wean-to-finishing farms had the lowest median values for all sources of out-degree (Fig. 3A, B, and C). Moreover, nursery farms displayed the largest median values for all in-degree metrics, especially for the weighted in-degree based on the number of pigs. Nursery sites also exhibited the second largest median values with large variability for all out-degree measures. Meanwhile, sow farms showed the largest median estimates for all sources of outdegree. Sow sites had also the greatest betweenness coefficient,

3.2. General network properties for the time series networks The static network for the whole period of 36 months presented 618 nodes and 5,405 edges, with an APL of 6.56 and a diameter including 24 farms (Table 2). This static network also showed a density of 0.014, a clustering coefficient of 0.044, and a disassortative degree of -0.45. The whole period static network included 314, 618, 3, and 297 farms in the GSCC, GWCC, GIC, and GOC, respectively, corresponding to approximately 51 %, 100 %, 0.5 %, and 48 % of the network size. The networks constructed based on a temporal resolution of 1, 3, 6, and 12 months had on average 267 (358), 457 (858), 565 (1,477), and 579 (2,471) active farms (edges), respectively. On average the APL (diameter) were 2.5 (7.0), 3.5 (9.8), 3.9 (11.0), and 3.7 (12.0) for networks snapshots of 1, 3, 6, and 12 months, respectively. Regardless of the temporal resolution, all different snapshot networks showed a disassortative degree with values varying on average from -0.54 (6 month snapshots) to -0.37 (1 month snapshots). The density of the time 5

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Table 2 The average (minimum; maximum) estimates of the general topological properties including the number of active nodes and edges, average path length (APL), diameter, assortative degree, density, clustering coefficients, giant strongly connected component (GSCC), giant weakly connected component (GWCC), giant in component (GIC), and giant out component (GOC) of the time series networks with a time resolution of 1, 3, 6, 12, and 36 months observed at Iowa Select Farms data from January 2014 to December 2016. Time series resolution in months Metrics

1

3

6

12

36

Nodes

267.1 (225;306) 358.1 (247;432) 2.5 (1.5;3.3) 7.3 (4;11) −0.37 (-0.54;-0.28) 9 (6;11) 14 (1;43) 2.8 (0;6) 0.45 (0.00;0.97) 230.5 (148;277) 37.3 (23.9;44.8) 1.5 (0;11) 0.23 (0.00;1.78) 32.8 (0;109) 5.3 (0.00;17.6)

456.9 (392;514) 858.1 (696;997) 3.5 (2.8;4.4) 9.8 (7;12) −0.50 (-0.59;-0.43) 23 (18;26) 13 (2;38) 6.7 (0;9) 1.07 (0.00;1.46) 437.58 (381;498) 70.81 (61.65;80.58) 2.17 (0;9) 0.35 (0.00;1.46) 202.3 (0;358) 32.74 (0.00;57.93)

565 (549;595) 1447.2 (1253;1719) 3.9 (3.5;4.4) 11 (8;14) −0.54 (-0.62;-0.47) 39 (33;45) 15 (8;24) 10.2 (2;20) 1.64 (0.32;3.24) 564.67 (547;595) 91.37 (88.51;96.28) 3.83 (0;11) 0.62 (0.00;1.78) 436.5 (322;519) 70.63 (52.10;83.98)

579 (562;604) 2471.3 (2181;2755) 3.7 (3.3;4.4) 12 (9;15) −0.52 (-0.59;-0.49) 64 (57;72) 19 (16;24) 23.7 (14;34) 3.83 (2.27;5.50) 579 (562;604) 93.69 (94.94;97.73) 24.7 (1;60) 3.99 (0.16;9.71) 507.7 (462;543) 82.15 (74.76;87.86)

618

Edges APL Diameter AD Density (× 104) 3

CC (× 10 ) GSCC GSCC (%) GWCC GWCC (%) GIC GIC (%) GOC GOC (%)

5405 6.56 24 −0.45 140 44 314 50.81 618 100 3 0.49 297 48.06

Fig. 3. Production sites centrality parameters on the logarithmic scale for the time series networks with 1-month temporal resolution observed in the Iowa Select Farms data from January 2014 to December 2016. Plots describe the centrality parameters of A) unweighted in-degree and out-degree, B) weighted in-degree and out-degree based on the number of shipments, C) weighted in-degree and out-degree according to the number of pigs, and D) betweenness. Different letters above centrality parameters values indicate statistical difference at 5 % significance using the Wilcoxon pairwise test.

6

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Fig. 4. Percolation analysis of the time series networks with 1-month temporal resolution observed in the Iowa Select Farms data from January 2014 to December 2016, under three simulated scenarios, A) unweighted degree (highly contagious diseases), B) weighted degree by shipments (intermediate scenario between a high and low contagious diseases), and C) weighted degree by pigs (low contagious disease); and two approaches to remove nodes: random [dark blue (average), and light blue (95 % quantile interval)] and sequential [red]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

important due to the risk to introduce infectious diseases in the system, in our study such movements were not considered because of the lack of information regarding the provider sources. However, ISF only trades with an exclusive group of external providers and also implemented restrict biosecurity practices on the receiver farms, alleviating the risk of disease introduction through external sources. Furthermore, it is worth mentioning that the results of the network analysis employed in our study are representative for a multi-site system in Iowa, and could be slightly extrapolate to similar systems in the Midwestern of the United States. However, caution should be taken when extrapolating these findings to any multi-site systems in the United States, since production conditions including logistics, transportation, and biosecurity practices are different across the country. The investigation of temporal networks is fundamental to understand cyclic patterns and pinpoint overall changes in a pig production system, which may result in a higher risk to introduce infectious diseases. The main challenge of a temporal time series approach is to define an ideal time window that roughly preserves the main features of the whole period static network. In our study, a time series network analysis considering snapshots of 1, 3, 6, and 12 months was employed to assess changes in the trade system over time compared to a static network for the whole period of 3 years. As expected, the number of active nodes and edges, and the density of the networks decreased with shorter snapshot windows. These results suggest that few farms will play a role for disease spread in the system when shorter time windows are considered compared to the whole period of 3 years, facilitating the monitoring and control of diseases outbreaks. Overall, the APL, diameter, and clustering coefficient were roughly the same between the networks considering a time resolution of 1, 3, 6, and 12 months, corresponding to half the value of these features estimates in the whole period static network. These results indicate that independently of the temporal resolution, such network properties tend to be roughly constant over the snapshot time windows considered in our study. Regardless of the employed temporal resolution, all networks have disassortitative degree as observed in the whole period static network,

followed by GDU (Fig. 3D). 3.4. Multiplicative effect on R0 and the percolation analysis of the monthly networks The heterogeneity in the contact rates of the networks with temporal resolution of 1-month resulted in an average multiplicative effect on R0 of 1.33 (range: 1.18–1.50), 1.45 (range: 1.23–1.66), and 1.05 (range: 0.76–1.25) for the scenarios considering high, intermediate, and low contagious diseases, respectively. The percolation analysis of the time series networks for 1-month temporal resolution indicated that removing nodes sequentially according to the R0 were more efficient than at random for each simulated scenario (Fig. 4). Overall, the magnitude of the Ro decreased 75 % after sequentially removing 25 % of the sites from the network, while the same reduction was reached in the random approach only after excluding approximately 90 % of the farms. Sow farms had the largest impact in the magnitude of R0 when a highly contagious disease were simulated, contributing on average with 43 % of the R0 (Fig. 5A). Nursery farms had the largest contribution on the R0 when a low contagious disease was simulated. These farms accounted on average for more than 60 % of the R0 in each month (Fig. 5C). In the second simulated scenario, sow sites had a critical impact on the dissemination of the disease, contributing on average for 62 % of the R0 in each network (Fig. 5B). Finishing and wean-to-finishing sites displayed the lowest contribution on the R0 for each pig movement network, across the different simulated scenarios. 4. Discussion The ISF moved millions of pigs between 2014–2016 in which the vast majority of the shipments was restricted within the company, followed by shipments to cull stations and abattoirs, indicating that ISF is one of the most important companies for the pig industry in Iowa. Only a few shipments to ISF were originated from external sources. Although the inclusion of such shipments in the network analysis is

Fig. 5. Contribution on the relative magnitude of R0 described by types of farms observed on the time series networks with 1-month temporal resolution, under three different scenarios: A) unweighted degree (high contagious disease), B) weighted degree by shipments (intermediate scenario between a high and low contagious disease), and C) weighted degree by pigs (low contagious disease).

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the number of PRRSV cases in a multi-site system in the United States during a period of 3 years, with higher incidence of PRRSV in the winter compared to the summer. In their study, the vast majority of PRRSV cases were observed in sow farms followed by GDU and nursery sites. Therefore, additional care must be considered when transporting pigs in the cyclic component, for example, ensuring that shipments to a specific farm should always come from a site with better or similar health conditions. On the other hand, wean-to-finishing and finishing sites are at the end of the pork supply chain, integrating the acyclic component of the multi-site system where pigs are transported to the market. Both type of sites have high unweighted in-degree, as they typically receive pigs from multiple sources. Hence, these sites are more susceptible to be infected from incoming pigs, especially if some of these farms perform “lite farming” (i.e. receiving the remaining pigs from other sites and raising them until the market weight is reached). From an epidemiological perspective, lite sites have less impact in spreading diseases in multi-site production systems through ground transportation because such pigs are shipped out to abattoirs only. However, lite farms are still an important source to disseminate infectious diseases in a multi-site system via indirect contacts such as airborne and vector-borne transmissions, and pathogens carried by staff. For instance, Dee et al. (2009) and Otake et al. (2010) reported that aerosols of PRRSV and Micoplasma hyopneumonia could reach out distances of 4.7 and 9.1 km, respectively. The heterogeneity in the contact rates of the networks with temporal resolution of 1-month leads to an average increase of 33 %, 45 %, and 5 % in the initial spread size for infectious diseases with high, intermediate and low transmission rates, respectively, compared to similar networks with homogeneous mixing population and degree structure. These results suggest that the presence of highly connected nodes is likely to magnify the dissemination of infectious diseases in production systems (Marquetoux et al., 2016), which is more pronounced for diseases with high and intermediate transmission rates. Different from our study, Volkova et al. (2010) reported a higher multiplicative effect on R0 for disease with lower transmission rates. On the other hand, Marquetoux et al. (2016) found similar results to our study with infectious disease with higher transmission rates leading to a 18 % increase in the dissemination of the infectious disease compared to a homogeneous mixing population, and no significant impact of the contact rate on R0 for diseases with lower transmission rate. The percolation analysis showed that interventions based on R0 are more efficient to fragment each network across different scenarios compared to the random approach. This result combined with the general properties of the networks (heavy-tailed distribution and degree disassortative) suggest that the structure of such networks can be easily fragmented by targeting farms with several connections. These aspects of the networks are critical in developing cost-effective surveillance and control measures because interventions (i.e. vaccinations, quarantine, and improved hygiene) on approximate 25 % of the most critical farms can mitigate in 75 % the potential size of disease outbreaks. Similar results were reported in cattle (Woolhouse et al., 2005) and sheep (Volkova et al., 2010) movement networks in Scotland. In the current work, the transmission of the pathogens was simulated under three scenarios based on the unweighted and weighted degree of each network. In this context, interventions in different types of farms have a different contribution in mitigating the transmission of infectious diseases. For instance, sow farms were more influent in high and intermediate contagious disease scenarios. On the other hand, nursery sites had a greater impact in the low contagious disease scenario. These results suggest that the pattern of spread of different infectious diseases depends on its transmission rate and some production sites have more influence in its dissemination. Therefore, biosecurity and control practices can be designed specifically for each type of production sites to mitigate and prevent outbreaks. For example, medium to high contagious diseases require biosecurity practices to be implemented on sow farms including procedures such as the

indicating that nodes with dissimilar degree tend to connect to each other. The size of the GSCC, GWCC, GIC, and GOC substantially decreased with a shorter temporal resolution compared to the whole period static network. The GSCC and GWCC represented the lower and upper bounds of a potential disease outbreak in a trade system (Kiss et al., 2006), and the GIC and GOC are the components that can increase the overall size of the disease outbreak, since they can reach or be reached by the GSCC, respectively. Therefore, these results indicate that the size of a potential disease outbreak is overestimated in the whole period static network. Even for the time series networks the size of the disease outbreak may be overestimated, because neither GSCC nor GWCC takes into consideration the chronological sequence of the shipments. Furthermore, the GWCC disregards the direction of the movements. Such aspects of the size of a potential disease outbreak have been investigated in other studies. For instance, Lebl et al. (2016) accounted for the temporal aspect of the movements using simulations of the spread of a disease within a network with compartmental disease models, and reported that the final epidemic size was approximate 60 % of GSCC size. Lentz et al. (2016) compared static with temporal networks using pig transport data from Germany. These authors reported a causal fidelity of 0.74 and a causal error of 1.35, indicating that 24 % of the observed paths in the whole period static network were absent in the temporal network and that the disease outbreak size was overestimated by a factor of 1.35. Small-world topology was absent for each 1-month temporal resolution network, while scale-free topology was inconclusive for such networks, suggesting that the un-weighted degree may follow a powerlaw distribution, or as well as a log-normal distribution. According to Broido and Clauset (2019), strongly scale-free structure is rare, and for the vast majority of network systems a log-normal distribution provides similar or better fit compared to a power law distribution. Nevertheless, this result suggests that such networks have a heavy-tailed distribution in which few sites have many connections and most sites have a small number of edges, indicating the presence of hubs. Differently from our study, Lee et al. (2017) reported networks with scale-free and the absence of small-world topologies in the United States, while European studies found both scale-free and small-world topologies in pig trade networks (Rautureau et al., 2012; Büttner et al., 2013; Salines et al., 2017). The characterization of the network topology has different implications regarding disease dissemination, as well as surveillance and control measures (Thakur et al., 2016). In small-world topology, disease outbreaks can quickly spread within clusters and reach distant sites by traversing a few edges, but the size of the disease outbreak is expected to be smaller compared to random networks (Newman, 2003). Alternatively, the epidemics is expected to be larger in scale-free topology compared to random networks due to the presence of hubs. Disease outbreaks would spread faster at the initial stages when neighbor farms are affected, slowing down after reaching secondary contacts (Kiss et al., 2006). Additionally, networks displaying heavy-tailed distributions are sensitive to interventions in the hub nodes, resulting in a quick network fragmentation (Nair and Vidal, 2011; Thakur et al., 2016). The centrality parameters of the different production sites indicated that the GDU, nursery, and sow farms had a central role in each of the 36 swine movement networks. This result is consistent with other studies (Büttner et al., 2013; Thakur et al., 2016; Lee et al., 2017) and reflects the hierarchical structure of the pig production in the multi-site system. These three categories of sites are at the beginning of the pork supply chain and are also components of the two multi-site system cycles observed in Fig. 2: sow → GDU → sow and sow → nursery → GDU → sow. In this cyclic component, farms are constantly receiving and sending pigs to other types of sites, being critical sources to introduce and disseminate diseases through multiple-site systems. Furthermore, such farms are a critical source to maintain endemic diseases in the system since there is a real possibility of re-infection via ground transportation, especially for sow farms in which approximately 97 % of them are active in a month. For instance, Lee et al. (2017) reported 8

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infectious diseases has implications on the implementation of biosecurity practices across different types of production sites. For instance, biosecurity practices should be focused on sow farms to mitigate highly contagious disease, while nursery sites should be targeted in the case of a low contagious diseases.

vaccination of sows and gilts, increasing the quarantine period, pretesting animals for any disease of concern, enhancing the acclimatization procedure for replacement females, and banning all movements of pigs in the case of a disease outbreak. On the other hand, for diseases with low prevalence, biosecurity practices should focus on nursery farms including practices such as vaccination of piglets, increasing the period of empty days between nursery groups, enhancing hygiene protocols (i.e. third party inspection, power wash with hot water, and monitor the efficacy of different disinfectants), and restricting all movement of pigs in the case of a disease outbreak. Nevertheless, it is also important to consider additionally to the main results retrieved from the percolation analyses, each type of farm has specific factors that could contribute to the disease dissemination and detection through a multi-site system. For instance, piglets are more susceptible to infectious diseases and often have higher mortality rate compared to finisher pigs. Therefore, the clinical signs of a disease could be observed earlier in nursery than finishing farms, reducing the overall period to detect, report, treat, and mitigate a disease outbreak. In this manuscript, we focused on the transmission of infectious diseases via the ground transportation of pigs across sites. However, other sources of infection including indirect contacts such as airborne transmissions and fomites should also be considered to develop more consistent programs to monitor and prevent diseases in multi-site systems. Furthermore, the network analysis performed in our study was based on retrospective data, but it might be more valuable to monitor the transportation of pigs in real time. For instance, when a disease outbreak is reported in a farm, networks metrics such as the ingoing and outgoing infection chains (Nöremark et al., 2011) could be immediately used to back and forward trace sites that received or sent pigs to infected farms. This information would be important to send alerts to all involved sites, as well as to test pigs for specific pathogens and to temporary ban all movements towards these farms. Therefore, a pig producer company could take advantage of this approach by fasttracking shipments of pigs in an autonomous manner, without relying on a manual search of these shipments records spread over different spreadsheets. In addition, the ingoing and outgoing infection chains have the benefit to account for the chronological order of the shipments. Ultimately, preventing disease outbreaks with 100 % efficacy is virtually impossible in any pig production system due to multiple unpredictable factors such as the individual flaws in biosecurity practices. Nevertheless, understanding the pattern of pig movements in a multisite system is critical to identify sites with an important role in the transmission of infectious diseases, as well as to monitor and implement control measures in such farms, making it possible to mitigate the risk of disease outbreaks in a multi-site production system.

Acknowledgements The authors would like to acknowledge the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for providing the financial support of the first author. The authors were also grateful to two anonymous reviewers whose comments have greatly improved this manuscript. References Barabási, A., Réka, A., 1999. Emergence of Scaling in Random Networks 286. pp. 509–513. https://doi.org/10.1126/science.286.5439.509. Broido, A.D., Clauset, A., 2019. Scale-free networks are rare. Nat. Commun. 10, 1–10. https://doi.org/10.1038/s41467-019-08746-5. Büttner, K., Krieter, J., Traulsen, A., Traulsen, I., 2013. Efficient interruption of infection chains by targeted removal of central holdings in an animal trade network. PLoS One 8, 1–12. https://doi.org/10.1371/journal.pone.0074292. Büttner, K., Krieter, J., 2018. Comparison of weighted and unweighted network analysis in the case of a pig trade network in Northern Germany. Prev. Vet. 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5. Conclusions Network analysis is a powerful tool to describe and understand the patterns of pig movements, providing insights about the impact of disease transmissions. In our study, network analysis was used to characterize the transportation of pigs in a multi-site production system of a large pig producer company in the United States. Results reveal that pig movement networks follow a hierarchical structure and some of the production sites have a more central role in the networks, displaying heterogeneities in the contact levels between farms. Moreover, percolation analysis combined with heavy-tailed degree distributions and degree disassortative indicated that each movement network is highly responsive to target interventions (i.e. vaccination, increase quarantine, and improve hygiene protocols). This information is critical for decision-making in the case of an epidemic, as well as to design costeffective approaches to monitor, control, prevent, and eradicate infectious diseases. Understanding swine movement within the multi-site system can potentially reduce economic losses caused by an epidemic, and can also improve animal welfare by keeping pigs free of diseases. In addition, our study shows that the transmission dynamics of different 9

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