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.