Figure 9. Spatial and structural characterization of the largest trade communities. Color indicates the community membership. a) Circular plot for intra- and inter-community movement flows. Each sector of the circle represents a community. The outgoing animal flow starts from the base of each sector. (b) Map of the state of Santa Catarina, Brazil with the geographical locations of the communities by the municipality. NA represents municipalities without reported movements.
Discussion
In this research, we use a two-pronged approach (static and temporal) network analysis aimed at exploring and characterizing pig trade at global and node levels in Santa Catarina, Brazil. We also propose a methodology for ranking high-risk areas for enhancing control and surveillance in communicable diseases considering the dynamics of swine trade. We used a static network analysis approach to describe the general structure of the network (Table 3 and Fig. 2) and temporal analysis to describe the dynamic trends using monthly snapshots (Fig. 4). Since we found a low value of causal fidelity, we used the OCC approach that considers time-respecting paths to analyze the vulnerability of the network to targeted node removal (Fig. 5 and Fig 6.). To understand the spatial distribution of risk, we calculated a risk index to prioritize the control and surveillance actions at the municipality level (Fig. 7 and Fig. 8) and performed a community analysis to describe the flux of movements between municipalities (Fig. 9).
In the static network analysis, the results of our loyalty analysis (nodes and edges) suggest that the commercial relationships from one year to another were not highly conserved despite the fact that a large portion of the nodes were active in both periods of time. There was also a drastic decrease in edge loyalty from 0.59 to 0.19 across the two periods observed. In addition, the proportion of nodes that remained active from year-to-year fell from 0.88 to 0.79. These patterns could exacerbate the potential for the spread of infectious diseases because many connections over time are not predictable.
The observed degree distributions showed scale-free properties, with many premises trading animals with only a few direct partners and a small number of premises trading with many direct partners. Above a value of 30, high out-degree premises were more common than high in-degree premises (Fig. 3). This is mainly given by the degree distribution of Breeding-farms and Nursery-farms (supplementary Fig. 2), reflecting vertical integration of production chains. The pyramidal structure of the production chain also may explain the low sizes of GSCCs, whereas GWCCs showed high levels of connectivity, compromising more than 95% of the network (table 4).
In the analysis of temporal trends, we found a decreasing number of active nodes and edges but an increasing number of swine moving throughout the study (Fig. 4). These findings suggest an increase in the size of premises and number of animals mobilized. Similar trends also were observed in other Brazilian state, and Swedish and Danish pig trade, (NÖREMARK et al., 2011; SCHULZ et al., 2017; STERCHI et al., 2019; MACHADO et al., 2020). Moreover, monthly values for the clustering coefficient and graph density were similar to mid-range values reported in other livestock networks (NÖREMARK et al., 2011; MWEU et al., 2013; VANDERWAAL et al., 2016b; FIELDING et al., 2019). We could not detect clear seasonal activity patterns as observed in others pig trade networks (KONSCHAKE et al., 2013; BÜTTNER; SALAU; KRIETER, 2016).
Given that static networks are more straight-forward to analyze, it is essential to understand the fidelity of the static network in representing a temporally dynamic network. To answer this, we followed the methodology proposed by Lentz et al., and demonstrated a low causal fidelity value. This indicates that the static networks may lead to an over-representation of the true connectivity of the network (LENTZ; SELHORST; SOKOLOV, 2013; LEBL et al., 2016), and thus inappropriate assessments of risk or design of control strategies. If the disease dynamics are slow in relation to the dynamics of the network, the results of the static network analysis may be sufficient to explain and predict a possible disease transmission (HOLME; SARAMÄKI, 2012). However, the use of a static representation for disease models may systematically overestimate the results of outbreak size, particularly for rapidly spreading diseases (LENTZ; SELHORST; SOKOLOV, 2013; KNIFIC et al., 2020).
Therefore, the use of temporal OCC analyses provides a better approach to evaluate the impact of target control because it incorporates the chronological nature of animal movements. The literature on temporal network analysis uses many terms to describe the OCC concept, such as time-directed paths, source counts, accessible worlds, output domains, reachability, unfolding accessibility, and recently spreading cascades (PAYEN; TABOURIER; LATAPY, 2019; KNIFIC et al., 2020). All of these terms describe a temporally sequential network to identify the nodes that are accessible through edges to/from each index node within a selected time period (FIELDING et al., 2019). We selected the term OCC to describe the number of nodes that could be reached from a certain premise, and this process represents a simple Susceptible-Infected (SI) model assuming a 100% infection rate via animal movements using the time-respecting paths. Thus, testing targeted control actions under this scenario provides useful information for field performance (VIDONDO; VOELKL, 2018; PAYEN; TABOURIER; LATAPY, 2019).
The most common strategies to contain an epidemic outbreak include culling, isolation of holdings, increased hygiene measures, and vaccination, among others (MOTTA et al., 2017). Targeting these measures towards premises with high centrality can be an effective strategy for efficient disease control. Analysis of the impact of targeted node removal on network connectivity generally measure the impact of removals on the size of the GWCC and GSCC (BÜTTNER et al., 2013; LENTZ et al., 2016; MARQUETOUX et al., 2016; MOTTA et al., 2017; CHATERS et al., 2019), which does not account for temporal dynamics. For this reason, we used reductions in the mean size of OCC to measure the efficacy of targeted removals, thus accounting for time-respecting paths.
Based on this analysis, we showed that prioritizing the removal of farms based on degree substantially reduced the potential for transmission of an infectious pathogen in the contact network as compared to removing farms at random. Therefore, control actions should be focused on high degree farms, such as Nursery and Breeding-farms (see supplementary Fig 2). In our study, a >90% decrease in the mean OCC mean was achieved by removing just 1000 nodes, which is particularly important in surveillance and control systems with limited resources.
We proposed a network-based index classification to target surveillance actions and assist surveillance authorities to classify areas (municipalities) according to the probability and consequence of certain areas becoming infected via in/out movements. The selection of the metrics to compose the indexes was based on the network metrics that were most effective at reducing the size of the OCC (Degree, Betweenness, Closeness) and the reverse of PageRank). Hence, we identified nodes at the beginning of the contact chain that traded with hubs of the network that, in theory, might be the beginning of the production chain and therefore have an important role in the disease spreading. Based on these, we implemented the Reverse of PageRank as network metric, due these nodes that can induce bigger changes in the mean OCC after node removal.
We also standardized these indexes according to the swine population of each region, thus creating a visualization of the most important regions which could be prioritized for control actions. These geographical areas were highly correlated with farm density (Figs. 1 and 8), which was one of the motivations to carry out the community analysis.
We found 9 large trade communities in SC State. Communities 1, 2 and 4 were geographically connected and registered the 60.8% of animal movements. Inter-community trade flux represented just 23.6% of movements, and most main flows were from community 1 to communities 2 and 4 (11.1%). The main purposes for the latter were slaughter (8.17%), fattening (2.28%) and reproduction (0.64%), thus the southwest region of SC state is the most important for swine trade based on both high internal trade and density of premises (See figure 1 and 9). The use of communities offers the opportunity to control outbreaks through zonation or compartmentalization by sub-dividing the state into sectors in which movements are more frequent within sectors than between sectors (OIE, 2019). Thus, if one sector were to become infected, trade in other sectors could potentially be protected via coordination of inter- and intra-sector disease management strategies (CHRISTLEY et al., 2005; LENTZ et al., 2011; GRISI-FILHO et al., 2013; GORSICH et al., 2016).
Animal movements are just one aspect of the epidemiology of infectious diseases. Despite the importance of movements (O’HARA et al., 2020; VANDERWAAL et al., 2020) network analysis should be undertaken in conjunction with other epidemiological tools. Several limitations of our work include that we were not able to include the effects of illegal movements and their influence on the network. We also could not rule out the possibility that an animal diseases outbreak could affect the dynamics of the network. This study also assumes that transmission of diseases related to the outgoing contact chain spread only via animal movements and that each movement is successful in disease transmission, which likely results in an overestimate of OCC size. Furthermore, we inherently neglected other potential transmission pathways such as movement of other susceptible or non-susceptible animal species, movement of owners, workers or veterinarians, transmission via vehicles, shared equipment or bioaerosols (KNIFIC et al., 2020), etc., which may have resulted in an under-approximation of the worst-case scenario for the introduction and spread of an exotic animal disease.