Social network analysis reveals the failure of between-farm movement restrictions to reduce Salmonella transmission

An increasing number of countries are investigating options to stop the spread of the emerging zoonotic infection Salmonella Dublin ( S. Dublin), which mainly spreads among bovines and with cattle manure. Detailed surveillance and cattle movement data from an 11-yr period in Denmark provided an opportunity to gain new knowledge for mitigation options through a combined social network and simulation modeling approach. The analysis revealed similar network trends for noninfected and infected cattle farms despite stringent cattle movement restrictions imposed on infected farms in the national control program. The strongest predictive factor for farms becoming infected was their cattle movement activities in the previous month, with twice the effect of local transmission. The simulation model indicated an endemic S . Dublin occurrence, with peaks in outbreak probabilities and sizes around observed cattle movement activities. Therefore, pre-and postmovement measures within a 1-mo time window may help reduce S. Dublin spread.


INTRODUCTION
Salmonella enterica subspecies enterica serovar Dublin (S.Dublin) differs from other Salmonella serovars by being host-adapted to cattle.Zoonotic infections may be acquired by any of the following means: direct contact with cattle, direct contact with fecal matter, ingestion of unpasteurized milk products, and consumption of contaminated beef products (Henderson and Mason, 2017).
The infection is a serious emerging zoonosis that has been reported to be spreading into new geographical areas in North America, with reports of multidrug resistant strains emerging in the same regions (McDonough et al., 1999;Srednik et al., 2021;Perry et al., 2023).This may lead to an increase in human health consequences, such as untreatable, severe, and invasive infections with a high case-fatality risk (Helms et al., 2003), in addition to animal welfare concerns and economic losses due to decreased cattle productivity (Nielsen et al., 2013).
More than 10,000 human Salmonella cases occurred in Denmark from 2013 to 2023, and 2.3% of these were S. Dublin infections mainly attributed to cattle and beef produced in Denmark, excluding travel-related cases (Kudirkiene et al., 2020;SSI, 2023).To safeguard animal and public health, voluntary surveillance efforts in the cattle sector (i.e., projects and communication campaigns) were implemented in 2000, with a national eradication program established in 2008 with the aim of eradicating S. Dublin from the Danish cattle population by the end of 2014.In this context, new legislation was implemented in 2010 with consequences for cattle properties that tested positive for S. Dublin (BEK no. 1723(BEK no. 22/12/2010;;BEK, 2010).After the implementation, the legislation was changed and tightened several times.Despite all mitigation efforts such as cattle movement restrictions between S. Dublin test-positive and test-negative cattle farms since 2010, an increase in the apparent prevalence has been observed since 2015.For instance, the apparent prevalence of S. Dublin test-positive farms in the dairy sector has almost doubled from 6.2% to 11.5% between 2015 and 2023 (Leekitcharoenphon et al., 2023;SEGES communication, 2023).
The surveillance and eradication program initially grouped cattle properties into 1 of 3 levels: level 1 (L1: most likely not infected with S. Dublin), level 2 (L2: likely infected with S. Dublin), and level 3 (L3: S. Dublin infection detected), based on serological testing Social network analysis reveals the failure of between-farm movement restrictions to reduce Salmonella transmission of bulk-tank milk or blood samples, or both; bacteriological cultures may also be used alone or in addition to serological testing.The bacteriological testing was done based on legislative order or clinical suspicion, or both.Movement of cattle within a test-positive (i.e., L2 and L3) multisite business (i.e., movements between ownfarm properties) was allowed, but not to other farms, whereas test-negative farms (i.e., L1) could freely move cattle (Nielsen et al., 2021).One major control measure that was attempted for a limited period (July 2013-November/December 2017) was "regionalization," in which 2 administrative geographical regions were defined as high and low prevalence, respectively (Supplemental Figure S1, see Notes).Strict cattle movement restrictions were implemented that prevented cattle from being moved to the high-prevalence region for live use to the low-prevalence region, except for calves from L1-farms that were being moved for fattening to a closed-farm and were going straight to slaughter.Supplemental Table S1 (see Notes) provides a detailed description of the surveillance and control program with an overview of legislative changes over time, with cattle movement restrictions and test requirements between 2010 and 2020 in Denmark.
With increasing incidence of S. Dublin infections in the Danish cattle population, despite cattle movement restrictions out of test-positive cattle businesses, there was a need to better understand the roles of movementrelated spread between cattle farms and local spread.The most common route of S. Dublin infection is fecal-oral transmission (Nielsen, 2013a).Salmonella Dublin bacteria can survive outside of the host for a long period and can spread through both direct contacts (e.g., cattle movements) and indirect contacts mainly via manure on, for example, contaminated vehicles (Wray et al., 1991;Ågren et al., 2016).Study of the networks of cattle movements provides a means for understanding the dynamics of diseases through the networks and defining effective mitigation measures (Dubé, et al., 2009;Pinior et al., 2012a,b;Pinior et al., 2015;Lebl et al., 2016;Lentz et al., 2016;Knific et al., 2020).Thus, the objectives of this study were (1) to gain insight into the structure of the animal movement network between S. Dublin test-positive (referred to as infected) and test-negative (referred to as noninfected) cattle farms in Denmark by performing a network analysis on data from 2010 to 2020, during which movement restrictions were implemented between infected and noninfected farms; (2) to quantify the effect of direct contact through cattle movements versus local transmissions on the spread of S. Dublin; (3) to simulate the spread of S. Dublin through cattle movement networks using a stochastic epidemiological compartmental model.This last objective aimed to determine the S. Dublin outbreak probability, size, and duration based on observed cattle movement network activities and a range of hypothetical movement activities between Danish cattle farms.This article illustrates how surveillance and movement data combined with an advanced data science approach can provide meaningful results for decisionmakers in the planning of target surveillance activities and guide potential adaptations of mitigation measures related to animal movements to reduce the prevalence of infection in animal populations.

Data
Data used in this study covered the period from January 1, 2010, to December 31, 2020, and consisted of 4 main datasets: (1) individual cattle movements between premises; (2) geocoordinates and opening and closing dates of premises and herds on the premises; (3) composition of animals per premise; (4) national S. Dublin surveillance test results including classification of all cattle premises into 1 of 3 levels: L1 (most likely not infected with S. Dublin), L2 (likely infected with S. Dublin), and L3 (S.Dublin infection detected).The different datasets were combined based on the individual premises and herd identification numbers.All daily records of cattle movements within Denmark included the unique identifier of the individual cattle involved, date of the event, type of movement, premises, and herd identity of its source and destination.The cattle movements are registered in the Central Herd Register, which is hosted by the Danish Veterinary and Food Administration.In total, 8 production categories were defined and assigned to each premises based on the composition and number of cattle per premises at the monthly level (Table 1).In this context, recorded production classifications of farms from the official database were not used, because these classifications may not be sufficiently updated by the animal owner, and our own analysis suggested implausible changes in the production category of farms within a year (Supplemental Figure S2, see Notes).Further, only cattle movements from cattle farms to other cattle farms were considered, with movements between premises that were not cattle farms excluded (e.g., abattoirs).
In addition to the 3 official S. Dublin infection levels (L1, L2, and L3; Supplemental Table S1), other S. Dublin levels were introduced and removed over the years for control program purposes (e.g., L1a, L1b, and L2R, Supplemental Table S1).Instead of using the official surveillance classifications, which were temporally inconsistent, the following 4 new infection categories were created based on test results (or lack thereof) in the national surveillance database for each farm over the study period: It should be noted that the sensitivity of the S. Dublin bulk-tank milk-testing strategy used in the program was ~95% to 96% (Warnick et al., 2006;Nielsen, 2013b).Unknown status usually occurred when farms were starting up or re-started status allocation in the surveillance program due to a change of owner or due to a lack of samples.For nondairy cattle herds, the sensitivity of herd-testing procedures based on multiple blood samples ranges between ~50% and 95%, depending on the withinherd prevalence.

Network Analysis and Association of S. Dublin Infections with Cattle Movements and Local Transmissions
Static, directed, and weighted trading networks were constructed based on individual cattle movements between source and destination cattle farms in each month from January 2010 to December 2020, resulting in a total of 132 monthly movement networks.Nodes in the movement network represent cattle farms that are trading cattle, and links between the nodes represent live cattle movements.The weight of links between, for example, node A and B, is the number of moved cattle between both nodes divided by total number of moved cattle from farm A. For each of the 132 movement networks, different network properties were calculated (Table 2) separately for infected and noninfected cattle farms and for both infection categories together (Supplemental Table S3, see Notes).Kolmogorov-Smirnov (KS) statistics were calculated to investigate the degree that Danish cattle movement networks are scale-free, because networks that follow a power law distribution are vulnerable to disruption when high-degree nodes are removed.The power law distributions were compared with log-normal distributions, seen as the main alternative to power laws, by overlaying these distributions on the original data and using a likelihood ratio test.For the KS test, the null hypothesis was that the distribution followed a power law, with higher P-values indicating a better fit (Tratalos et al., 2020).
In total, 24 different multiple logistic regression models were run predicting S. Dublin infection via cattle movements between farms and local transmissions (i.e., newly infected farms in a radius of 5 km around the infected farm) in the consecutive 1 to 6 mo based on data from the previous 1, 2, 3, and 4 mo, while controlling for the independent variables (i.e., farm size, the month of cattle movement, and total neighborhood size [number of farms in the radius of 5 km around each farm] and production categories).The 1-to 6-mo period was chosen based on the infection dissemination and antibody-lag periods described by Jordan et al. (2008).The infection category was defined as a binary variable, where it was equal to one if farms were "infected," and it was equal to zero if farms were "noninfected."In detail, the predictor for cattle movement transmission was extracted from the movement networks and was binary, where the exposure to transmission of infection via cattle movement was equal to one if a farm received at least one animal from an infected farm that was identified as infected after the movement in the time window 1 to 4 mo.Only cattle farms with data available for more than 1 yr were Between 10 and 50 animal-years: ≥20% cows; beef or crossbreeds constitute ≤80% of all animals per year Large beef cattle farms >50 animal-years: ≥20% cows and beef or crossbreeds constitute ≤80% of all animals per year Other small farms <10 animals/yr Farms that do not fit into above categories and have <10 animals averaged over the year Other large farms ≥10 animals/yr Farms that do not fit the above categories and have ≥10 animals averaged over the year included in the statistical analysis.Because movement data were grouped on a monthly level, it was possible that an uninfected farm received cattle from an infected farm at the beginning of the month, but later in the same month, the source farm changed its status to infected.In this case, the target farm was marked as trading with an infected farm in the monthly movement networks.Local transmission of infection was used as a predictor and was also binary, where it was equal to one if a farm has had an infected farm in the neighborhood (radius 5 km) in the previous 1 to 4 mo.

Modeling of S. Dublin Spread on Cattle Movement Networks
A stochastic susceptible (S i ), infectious (I i ), and recovered (R i ) compartmental model was used to simulate the spread of S. Dublin infections on monthly timescale networks over two 3-yr periods (i.e., during the regionalization [January 2015-December 2017] and after the regionalization [January 2018-December 2020]).The spread of S. Dublin was simulated based on observed movement activities and a range of hypothetically set movement network activities (α) between cattle farms to investigate the effect of potential changes in the degree of movement activities on the spread of S. Dublin at the monthly level.The same approach for modeling increased and decreased network activities of α at the monthly level was applied, as described by Lebl et al. (2016).In brief, the movement network activity α, where α lies between 0 < α < 1, is defined as the mean link frequency of a network (i.e., how often a certain link between a node pair was active divided by the length of the 3-yr period).Subsequently, for each α (i.e., across degrees of cattle movement), outbreak probability was calculated based on the proportion of the simulation runs (n = 1,000) that resulted in an S. Dublin spread beyond the starting node.The relative outbreak size was calculated as the proportion of infected farms relative to the total number of potentially infectable nodes in the movement network (i.e., on average 1,200 nodes/mo), and outbreak duration was simply the number of months

Average degree
The degree measures the average number of farm links in the monthly network.It is a helpful parameter for characterizing the overall density of a network.For directed networks, the in-degree is the number of incoming links, whereas the out-degree is the number of outgoing links.Cattle farms with higher than an average degree (in and out) are at higher risk of infection via cattle movement or have a higher probability to infect a larger number of other cattle farms, or both (Wasserman and Faust, 1994).

Average path length
The average number of shortest steps to move from one cattle farm in the network to another.It indicates how "quickly" infection can spread from one farm to another (Watts and Strogatz, 1998).

Betweenness
How often a farm appears on the shortest path between pairs of other farms in the network.It measures how important farms are to maintaining connectivity in the network.The average betweenness of a network provides insights into the proportion of nodes that act as intermediaries in the network (i.e., as a "bridge" between 2 subnetworks).Identifying hubs in the cattle movement network may be crucial for control programs aimed at reducing the risk of disease spread (Freeman, 1978).

Density
The ratio between the potential available number of links between nodes in the network and the number of existing links in the network.Higher-density movement networks are associated with higher movement activities between farms (Wasserman and Faust, 1994).

Modularity or clustering coefficient
Modularity: The degree to which a network can be divided into clusters or communities.Networks with high modularity tend to have groups of farms that are more interconnected via movements relative to the rest of the network (i.e., farms outside of their group; Watts and Strogatz, 1998).
Clustering coefficient: Is a measure of the degree to which farms in a network tend to cluster together (i.e., proportion of a farm's neighbors who are also neighbors of one another; Mweu et al., 2013).In summary, while modularity is a broader measure of clusters across the entire network, the clustering coefficient computes the tendency of farms to create groups at a more local level.

Component Weakly or strongly connected component
A group of nodes connected to each other by one or more paths; a component can be weak or strong.
Weakly: A weakly connected component is a group of nodes that are all reachable from each other but may not be firmly connected, whereas a strongly connected component is a group of nodes where every node is reachable from every other node through a directed path.A fully connected network has only one component, whereas a more fragmented network has more components (Robinson et al., 2007).

Closeness
The average closeness of a network measures how quickly nodes can access all other nodes in the network.Networks with high closeness are highly connected, and infections can flow through the network efficiently.In a directed network, out-closeness are the outbound/outgoing links, and in-closeness are the inbound/incoming links (Wasserman and Faust, 1994).Scale-free A network is defined as scale-free if its degree distribution fits a power law distribution.A scale-free network is robust in its resilience to random failures (Mweu et al., 2013;Broido and Clauset, 2019).
the outbreak persisted.Following an animal movement, the receiving node will become infected according to the transmission probability function for each movement link (p e ): p e = P(X >0) ~B(w, p) = 1 − (1 − p) w , where P(X >0) is the probability (P) that a random variable (X) is greater than 0, B(w, p) is a binomial function depending on the transmission probability p = {0.25,0.50, 0.75} and the link weight w (i.e., the number of cattle moved; Lebl et al., 2016).
Because interventions against S. Dublin were carried out at the farms, farms were treated as epidemiological units in the spread model, being assigned to epidemiological states (i.e., compartments) S i , I i , and R i .The simulation model incorporated farms that were part of the largest strongly connected component from the network analysis.Initially, all noninfected farms in the dataset were assigned to S i and, at the randomly chosen time, one randomly selected index farm was set to I i , such that all starting times and farms had the same selection probability (Lebl et al., 2016).The S i farms could only become infected if cattle were moved from I i to S i during the time where I i was infectious.A constant infectious period of 3 wk per cattle farm was assumed (Nielsen et al., 2007) to spread S. Dublin via the randomly chosen time point on the aggregated cattle movement activities at a monthly level to other farms.A natural immunity of 4 wk was presumed, and farms remained in the compartment R i for this period.The compartmental model used to simulate the spread of S. Dublin among cattle farms did not consider the births and deaths of cattle.However, as the cattle movement data (i.e., included both the nonmoves of dead animals and the moves of new births to other farms) was used for the simulation of the spread of S. Dublin, births and deaths of cattle were considered indirectly.
Furthermore, we introduced targeted and randomized intervention measures by removing nodes from the cattle movement networks to analyze the associated impact on the spread of S. Dublin.Targeted removal of nodes was performed based on the highest betweenness of the farms (betweenness ≥100,000).In practice, the removal of farms could be considered as isolation, culling, vaccination, or increased biosecurity measures (Knific et al., 2020).

Movements, Infections, and Production Categories of Danish Cattle Farms
The cattle movement dataset consists of 28,170 nodes (premises), with 9,184,540 individual cattle and 31,464,836 records of movements (links), among a total of 30,439 cattle farms existing between January 2010 and December 2020, with 7.4% (n = 2,269) of farms recording no between-farm movement activities.Only 1.8% of the cattle movement relationships between cattle farms persisted throughout the study period (referred to as inloyalty), and the top 20% (n = 5,521) of the farms accounted for 93.2% of all cattle movements in Denmark.The probability of engaging in a cattle movement event was dependent on the production type of a farm.Most cattle movements, among known production categories, occurred between dairy and heifer-raising facilities (22.8%) and between dairy farms (16.8%) over the 11-yr period.On average, we observed little difference across production types in terms of distance traveled by cattle between farms, with median values of 16.9 km (mean 38.8 km with a range 0-451.0km).Each year, on average, individual animals were moved 2.8 times within Denmark, with moved animals remaining at a farm for an average of 253 d before moving again.Two Danish regions, Southern Denmark and Central Jutland, accounted for 78% of all cattle movement connections in Denmark.For more than half of the movements (56.7% on average), the origin and destination were located within the same region (Supplemental Figure S3, see Notes).The maps of all existing cattle farms in Denmark and the farms that moved cattle are shown in Supplemental Figure S4 (see Notes).
Figure 1a shows how many months farms stayed in 1 of 4 infection categories (i.e., negative, positive, unknown, and likely negative) and how many farms were in each infection category during the study period.It should be noted that a farm could change both its infection category and production category several times over the study period.In total, 88.8% of all farms kept the same infection category for the whole period (2010-2020), 8.8% had 2 different infection categories, and only 2.3% and 0.01% of farms had 3 and 4 infection categories, respectively.In total, 59.7% of farms did not change their production category, whereas 23.5%, 11.6%, and 4.0% of farms had 2, 3, and 4 different production categories over the study period, respectively.Figure 1b shows how many months farms stayed in one production category and how many farms were in each production category during the study period.Most cattle farms were classified as "other small herds <10 animals" (47.4%) and "beef small" (16.7%), and most of the test-positive farms were "dairy" farms (48.0%; Figure 1c).The S. Dublin prevalence of dairy farms over the period stratified by regions is shown in Supplemental Figure S5 (see Notes).

Network Analysis
The network properties of the cattle movement networks were investigated at the monthly level, separately for S. Dublin infected (i.e., infection category positive and unknown) and noninfected (i.e., infection category negative and likely negative) cattle farms in Denmark (Figure 2; Supplemental Table S3), and for both infected and noninfected cattle farms (Supplemental Figure S6 and Supplemental Table S3, see Notes).The proportion of infected farms engaged in cattle movements was relatively small, with an average of 215 (minimum = 61; maximum = 388) of S. Dublin infected farms participating in cattle movement networks (Figure 2).The network analysis indicated similar trends in all parameters for both noninfected and infected farms.However, in 2020, highly heterogeneous patterns were found across infected and noninfected farms in terms of the modularity, degrees, betweenness, density and closeness (Figure 2; Supplemental Table S3).The density and clustering coefficients were ~39 times and 2 times higher for infected farms compared with noninfected farms, respectively.In other words, infected farms had a higher level of cattle movement activities, and they moved cattle more within their own clusters than with the rest of the network over the study period.Nonetheless, the network analysis indicated that control measures regarding movement restriction, such as between region movement restrictions (i.e., prohibiting transportation of animals from Jutland, referred to as regionalization; Figure 2) during the period 2013-2017 had no marked effect on the analyzed network properties for S. Dublin infected farms.Although the inand out-degrees (see Table 2) were similar between both infection categories, infected farms were less prone to bridging different clusters of the cattle movement network.This is shown by the lower median betweenness values of infected farms (minimum = 7.7; maximum = 100.1)compared with noninfected farms (minimum = 2,191.0;maximum = 2,873.0)(Supplemental Table S3).However, at the node level, the betweenness was highly skewed with an average of 17.4% of the farms showing betweenness scores ≥10,000, reflecting a greater capacity of these farms to act as a bridge and spread S. Dublin to other network clusters.
The yearly average shortest path lengths for infected farms ranged 2.3 to 3.9, meaning that a pair of infected cattle farms was separated by ~2 to 4 movements every year on average, whereas for noninfected farms, the average yearly shortest path lengths were up to 3 times higher.The monthly average network diameters (i.e., the longest stratified by the production categories across "negative," "positive," "unknown" and "likely negative" infection categories, with farms in "positive" and "unknown" categories considered as infected farms and farms in "negative" and "likely negative" considered as noninfected farms.S1), with the following implementations reflected: (1) July 15, 2013, when regionalization was implemented, prohibiting the transportation of animals from Jutland to the Islands; (2) October 20, 2015, when regionalization criteria were revised, expanding the low-prevalence area to include certain parts of Jutland; (3) November 29, 2017, when regionalization was discontinued and movement restrictions were extended to all test-positive farms (Supplemental Table S1).Supplemental Figure S6 shows the network properties for both infected and noninfected farms together.
average shortest path lengths) were 5 and 10 for the considered networks of infected and noninfected farms, respectively.For each year, the proportion of nodes in the strong and weak components was quite similar for both infected and noninfected farms (Supplemental Table S3).The network topology indicated a scale-free overall network, as suggested by the high P-value of the KS test (Tratalos et al., 2020).Thus, the null hypothesis that the network observed a power law could be confirmed (Supplemental Figure S7, see Notes).This was also supported by the monthly cattle movement network properties, with mean values generally being greater than the median values.

Association of S. Dublin Infections with Cattle Movements and Local Transmissions
The multiple logistic regression models predicted S. Dublin infections in the first, second, third, fourth, fifth, and sixth consecutive months via cattle movements or local transmissions.The highest predicted odds ratio (OR) for new S. Dublin herd infections was calculated through cattle movement within the first month, while the OR for S. Dublin infections due to local transmissions were relatively constant over the prediction months.The probability to become S. Dublin infected via cattle movements decreased if the prediction time window was extended (Figure 3; Supplemental Figure S8; Supplemental Tables S4-S7; see Notes).
The observed cattle movement activity was α = 0.092 during the regionalization and α = 0.090 after the regionalization.The simulation model outcomes indicated that the outbreak probability (i.e., the probability that S. Dublin will spread beyond the starting node) was between 5 and 13%.The relative outbreak size (i.e., infected farms as a percentage of potentially infected farms) was on average 3% (n = 38 infected farms per simulation iteration).On average, 5 farms were infected per simulation iteration, if p = 0.25; 18 infected farms, if p = 0.50 and 85 infected farms, if p = 0.75, and the average outbreak duration was 5.1 mo.Many fluctuations in the model outcomes (outbreak size and duration) were observed until the cattle movement activity reached α = 0.2, suggesting that the spread of S. Dublin via movements of cattle would reach a limit (Figure 4).A modeling outcome where all nodes in the network became infected was never found, not even for very high network activities (i.e., α > 0.2) and transmission probabilities.A comparison of both simulation periods (during and after regionalization) indicated slightly higher model outcomes, in terms of outbreak sizes and durations, after the regionalization compared with period during the regionalization (Figure 4).Because the outbreak size never reached the value 0, the model suggested an endemic state of S. Dublin in the Danish cattle population.The simulation model showed that targeted removal of the cattle farms with the 1% highest betweenness (i.e., ≥ 100,000) from the movement network would achieve an 88.7% reduction in the spread compared with the removal of random cattle farms.

DISCUSSION
Similar trends in the network properties were observed for both S. Dublin infected and noninfected cattle farms.This suggests that the implemented movement restrictions (e.g., regionalization) in the Danish control program unexpectedly had no significant effect on trading patterns during that period, as the clustering coefficient and average path length did not change for infected farms relative to the other years.This is likely because membership to a region is a large-scale classification for each node, with 56.7% of all cattle movement connections occurring between matching origin and destination regions, suggesting that cattle farmers have a preference to move cattle within the same region (Supplemental Figure S3).The rare long-range animal movements identified in the movement network (only 0.9% of the cattle movement connections covered a long-distance >200 km) favored the resilience against spreading S. Dublin to other regions, which may explain the high S. Dublin prevalence observed within the higher prevalence geographical areas of North, West and South Jutland (Supplemental Figure S1).Thus, the network analysis indicated that control measures regarding movement restriction, such as between region movement restrictions (Figure 2) during the period 2013-2017 have had no marked effect on the analyzed network properties for S. Dublin infected farms.
An observed effect of the implementation of regionalization was an increase in the average path length for noninfected farms (Figure 2).Longer paths in the movement network could span larger geographic distances that may spread infections across geographical borders with just few between-farm events (VanderWaal et al., 2016).This is important because it is likely that endemic or new S. Dublin infections in some farms (including cattle farms with an unknown status of S. Dublin) and periods were undetected (Veling, 2004;Warnick et al., 2006).The latter might explain the spread of S. Dublin via cattle movements.Therefore, regionalization as a control strategy may not be adequate to capture all at-risk cattle farms.This is supported by the simulation model, as only slightly lower model outcomes (outbreak sizes and durations) were observed during the regionalization compared with the period after it was discontinued.
Scale-free networks such as the Danish cattle movement network, where a small number of highly active nodes are responsible for a high proportion of connections, are vulnerable to disruption when those high-degree nodes are removed.In contrast, such networks are relatively immune to disruption if nodes are removed randomly (Büttner et al., 2013), as the probability of choosing weakly connected nodes is relatively high and their deletion would have a nonsignificant influence on the stability of the network structure (Albert, et al., 2000).The latter is reflected in the simulation model, as mitigation measures (i.e., removing or isolating farms) targeting the top 1% of farms, in terms of betweenness, would reduce the spread by 88.7% when compared with the removal or isolation of random farms.This suggests that more effort should be made to understand where these highly central farms are located and how best to control their animal movements in a targeted manner (Tratalos et al., 2020).
Further analysis of how such farms operate, in terms of biosecurity standards or how long the animals remain on these farms (Tratalos et al., 2020), would likely increase the understanding of their epidemiological role in the spread S. Dublin.For example, the transmission probability might be lower for farms with high biosecurity or farms that only keep animals for a short time (Lentz et al., 2016;Knific et al., 2020).Therefore, it is recommended that control strategies based on farm level characteristics, or a more granular geographical level within subregions, are developed, because the influence of nodes is subject to temporal variations (Stärk et al., 2006;Mweu et al., 2013) that may affect the impact of individual farms on the spread of S. Dublin.A first step toward more effective and efficient control could be the ranking of nodes or links using appropriate network centrality measures (e.g., betweenness) by veterinary authorities combined with additional farm meta-data (e.g., biosecurity level) to inform targeted surveillance and control measures (Stärk et al., 2006;Natale et al., 2009;Mweu et al., 2013;Lentz et al., 2016).Nonetheless, the success of an S. Dublin surveillance program critically depends on the ability to rapidly detect infections and their corresponding pathogenic sources, as this allows the implementation of targeted mitigation measures to contain the propagation (Bajardi et al., 2012).Longer delays between the introduction of an infection to a farm and its detection result in increased difficulty identifying the starting point of the spread, and, therefore, increased difficulty preventing further spread.However, even though the identification of clusters can be used to enhance surveillance, the in-loyalty of the cattle movement connections between Danish farmers revealed by this analysis over the study period makes the identification of possible sources of infections and detection of secondary infections using the same cluster particularly difficult for veterinary authorities (Bajardi et al., 2012).
Although the network's properties generally indicated a similar trend over the observation period, in 2020, highly heterogeneous network properties were observed between both infection categories (infected and noninfected) in terms of modularity, degrees, betweenness, density and closeness (Figure 2; Supplemental Table S3).
Infected farms moved cattle more within their clusters in 2020 than with the rest of the network, compared with other years.Supplemental Table S1 shows that the implemented S. Dublin legislation in Denmark in 2020 placed all S. Dublin-tested positive farms under Official Veterinary Supervision with requirements to make an action plan, assisted by the herd health consulting veterinarian, within 3 weeks.This supervisory period would have meant a greater potential for authorities to closely monitor farms, which may have increased farmer awareness of the movement restrictions and could explain the higher clustering of movement activities between infected farms in this year.Furthermore, it was the first COVID year with numerous restrictions aimed at reducing the spread of SARS-CoV-2 worldwide (Haug et al., 2020), which may also have had an impact on farmer behavior, including cattle movements.Despite variations in network characteristics across legislative environments (Supplemental Table S1), this study suggests that Danish cattle farmers were more active, and relevant network properties were higher, compared with other European cattle movement networks (Christley et al., 2005;Nöremark et al., 2011;Rautureau et al., 2011;Dutta et al., 2014;Vidondo and Voelkl, 2018;Knific et al., 2020).For instance, the Danish monthly cattle network showed 19 times more movements, a 178 times greater cluster coefficient, 10 times greater average degree and 662 times greater density compared with the Slovenian cattle network (Knific et al., 2020), whereas the calculated network properties in the present study concur with previous study results from Denmark (Bigras-Poulin et al., 2007 [e.g., pigs]); Mweu et al., 2013 [e.g., cattle]).Similarly, the Danish networks exhibited moderate scale-free topology (the power law distributions in the presented study ranged between 2 and 3 and were in line with both former studies from Denmark; Bigras-Poulin et al., 2007;Mweu et al., 2013), suggesting moderate outbreak sizes in case of infections.In general, strongly scale-free network structures are rare, as log-normal distributions fit the data as well or even better than power law distributions (Broido and Clauset, 2019).
A series of static networks were used to represent a dynamic system, with all movements within a monthly period binned, leading to the loss of daily temporal order (VanderWaal et al., 2016).However, such timeaggregated networks are regularly used in veterinary epidemiology to investigate between-farm transmissions in simulation models, and they provide a good metric of epidemic size (VanderWaal et al., 2016), though they may overrepresent the connectivity of farms in a network (Vernon and Keeling, 2009;VanderWaal et al., 2016).In the present study, a monthly timescale was selected for 2 reasons: (1) there is a need to strike a balance between having sufficient number of nodes and links in any given period and the number of networks to be analyzed (Mweu et al., 2013); (2) the monthly scale was considered a reasonable duration, during which S. Dublin could spread, as aggregated time scales are more important for endemic diseases such as S. Dublin compared with acute rapidly spreading diseases such as foot-and-mouth disease (FMD).When modeling the latter, daily timeframes may be more appropriate for capturing the shortterm variation of highly contagious diseases (Mweu et al., 2013;VanderWaal et al., 2016).Consequently, for some monthly trade periods, stochastically, zero infectious cattle movements might occur (Mweu et al., 2013), indicated in the simulation model via an outbreak probability of S. Dublin between 5% and 13%.As modeled, the potential to spread S. Dublin via cattle movement was limited compared with more infectious diseases, such as FMD (Conrady et al., 2023).This is supported by the epidemiological simulation model, which suggested that a hypothetical increase of cattle movement connections over α = 0.2 would increase neither outbreak probability nor outbreak size.Therefore, it can be concluded that the spread of S. Dublin via cattle movements is asymptotic (i.e., it would approach some limit even if high transmission probabilities are considered).However, because the data reflects some movement restrictions, it is plausible that the model's outcomes (outbreak size and duration) could be greater if the proportion of networks without movement restriction in the dataset were higher.
The overrepresentation of connectivity due to the monthly aggregation of movements might cause an overestimation of not only network properties, but also transmission effects (local and movement-based) and the size, probability, and duration of outbreaks based on observed movement activities and hypothetical movement activities.In addition, the assignment of the official diagnostic test results to newly created infection categories (see Materials and Methods and Supplemental Table S2) may have biased the network analysis and simulation model outcomes.
One important feature of the Danish cattle population structure is the concept of "business" versus "property."A cattle business could consist of one or more farm properties with cattle.For example, a business could consist of 3 properties: a dairy farm where the dairy cows are milked, a heifer-raising facility, and a dry-cow farm, and businesses could have different types of herds on their properties.If one of these farm properties within a business becomes test-positive, the rest of the properties will also become test-positive due to the dependence on cattle movements between properties within the business as part of the production cycles.The movement restrictions for test-positive businesses typically mean that cattle cannot be moved out of the business, but they can still be moved between properties within the same business.Furthermore, some businesses record all movements of cattle within the business, and some record few or none of their movements (only allowed for farms located less than 4 km apart).In this study, properties with cattle were defined as cattle farms and the analyses were performed at this level because detailed information about established businesses and cooperations over time were unavailable.However, the growth of larger and multisite business farms in Denmark's dairy cattle industry is a likely contributor to the lack of success in implementing stringent cattle movement restrictions on infected farms to control the spread of S. Dublin.This is supported by network analysis, which reveals that both infected and noninfected cattle farms exhibit similar network trends.
Further, it should also be noted that the surveillance program of the Danish cattle farms does not allocate S. Dublin infected farms to the "likely infected" status and S. Dublin noninfected farms to the "likely not infected" status with perfect sensitivity and specificity.This is both due to nonperfect diagnostic test procedures and due to the fact that farms according to the current legislation are allocated to the "likely infected" surveillance status, if they receive animals from a farm in the "likely infected" status, even if no transmission of bacteria actually occurred through the animal contact.In the used data, this is mainly relevant for farms in multisite business structures allowing for movement between farms owned by the same farmer, despite one or more farms within the business structure being test-positive.This may also lead to a risk of overestimation of the effect of cattle movement in the previous month on spread of infection, as some of the status-changes may have been purely administrative.It is also possible that the lack of consideration of multifarm cooperation might cause an underestimation of these same aspects.
Additionally, the network analysis did not consider truck movements, because these data were not available in the Danish livestock movement database.Incorporation of such data would likely have increased farm connectivity and might have influenced the interpretation of the spread of S. Dublin via livestock movements and local transmissions.As S. Dublin can survive outside the host for a long period (Nielsen et al., 2021) and truck-sharing is common among Danish cattle farmers, information about truck movements would improve our understanding of the risk of S. Dublin's spread.Further, other pathways are present that may create opportunities to transmit pathogens between farm (Ortiz-Pelaez et al., 2006;Green et al., 2008;VanderWaal et al., 2016;Conrady et al., 2023).For example, the presence of other livestock, personnel or visitor movements and behavior, and the frequency and location of equipment cleaning and sharing between farms can all play roles in the transmission of S. Dublin, and higher temperatures can increase the pathogen's ability to survive in the environment (Dietz et al., 2006;Glawischnig et al., 2017).
Grazing systems are common in Denmark and might be another potential source of S. Dublin infection because animals stay at the designated grazing location for a period and can mix with other animals at that location (Knific et al., 2020).However, temporary movements to and from grazing sites were not fully available in the study because it is not mandatory to records such movements.This could explain why no seasonal peaks in the frequency of cattle movements were identified while seasonality was observed in network analyses of other countries with abundant grazing (Natale et al., 2009;Nöremark et al., 2011;Vidondo and Voelkl, 2018).
Approximately 11% of the Danish farms have more than one livestock species, and movements between these multispecies farms are rare compared with other countries (Conrady et al., 2023).Thus, it was assumed that the network topology would not change significantly by including them in the analysis.However, although the inclusion of multispecies farms may have affected the calculated effect of local transmissions, as S. Dublin has been detected in other species, such as mink (Dietz et al., 2006;Glawischnig et al., 2017), information about the specific characteristics of multispecies farms in Denmark was not available for this study.
Other factors, such as farmer compliance with the legislations and within-herd spread dynamics, including associated compartmental model parameterization such as latent period of S. Dublin, age classes of animals, and farm type-specific transmission parameters, could add important information regarding the risk of S. Dublin introduction and spread to the simulation model.These factors were not considered, as it was assumed that all moved animals were associated with an equal probability of spreading S. Dublin.Analyzing and integrating such data could improve the model predictions, aid in the identification of high-risk cattle farms, and therefore, facilitate the development of targeted surveillance and control strategies for S. Dublin at the farm level, which also require data collection through field and experimental studies.
Despite these omissions, this study's findings are important to share with the international scientific and policymaking communities to assist in the design of future S. Dublin control programs.Moreover, the methodological approaches described herein are relevant to other diseases with high levels of environmental and animal movement spread mechanisms.This study dem- onstrates how an interdisciplinary One Health approach bridging natural and social sciences can be used to refine and formulate policies aimed at reducing the spread of a disease that threatens human and animal health.This work illustrates how useful insight into the contact patterns of cattle populations can be obtained by combining cattle movement and pathogen surveillance data while considering movement-based and local transmission pathways.The results suggest that, in addition to ranking farms in terms of network centrality to inform targeted surveillance and control measures, S. Dublin control programs should focus on pre-and postmovement measures within a 1-mo window.Thus, we suggest that current surveillance and control measures could be adapted to focus on reducing the risk of moving infected cattle between farms by implementing more focused within-herd control measures to reduce the prevalence of infected farms, and either more restrictive movement restrictions (currently mainly relevant for multisite business structures and therefore difficult to implement), pre-movement mitigation measures such as animal or animal group testing or quarantine of moved animals within a 1-mo window to help reduce the movement-related spread of S. Dublin between farms.These adaptations to current programs would likely help to reduce the movement-related transmission of S. Dublin between farms.

CONCLUSIONS
The strongest predictive factor for farms becoming infected was their cattle movement activities in the previous month, with twice the effect of local transmission.The simulation model indicated an endemic S. Dublin occurrence, with peaks in outbreak probabilities and sizes around observed cattle movement activities.Therefore, we suggest that current surveillance and control measures could be adapted to focus on reducing the risk of moving infected cattle between farms by implementing more focused within-herd control measures to reduce the prevalence of infected farms, and either more restrictive movement restrictions (currently mainly relevant for multisite business structures and therefore difficult to implement), pre-movement mitigation measures such as animal or animal group testing or quarantine of moved animals within a 1-mo window to help reduce the movement-related spread of S. Dublin between farms.

NOTES
This work was supported by the Dansk Veterinaer Konsortium (DK-VET), cooperation between the University of Copenhagen (UCPH, Copenhagen, Denmark), Statens Serum Institut (SSI, Copenhagen, Denmark), and the Danish Veterinary and Food Administration (FVST, Glostrup, Denmark) for the performance of the veterinary public service agreement under the Danish Ministry of Environment and Food (Copenhagen, Denmark).We thank the Danish Veterinary and Food Administration (FVST) for the good collaboration and SEGES Innovation P/S for providing the data for the present study.Supplemental material for this article is available at https: / / sid .erda .
Figure 1.(A) Box plots showing the length (months) farms remained in Salmonella Dublin infection categories (left) and the number of farms per infection category over the 11-yr period (right).Note that a farm could change its infection category and production category during the study period, and as a result, a farm could have several infection categories and production categories over the 11-yr period.(B) Box plot showing the length (months) farms remained in production categories (left) and the number of farms per production category over the 11-yr period (right).The figure includes all cattle farms, including those farms without cattle movement connections to other farms.(C) Infection categories of cattle farmsstratified by the production categories across "negative," "positive," "unknown" and "likely negative" infection categories, with farms in "positive" and "unknown" categories considered as infected farms and farms in "negative" and "likely negative" considered as noninfected farms.

Figure 2 .
Figure 2. Network properties of noninfected farms (left side) and Salmonella Dublin infected farms (right side) calculated on monthly networks over the 11-yr period: (A) the total number of farms that moved cattle, (B) average degree, (C) average path length, (D) betweenness, (E) density, (F) modularity, (G) component, and (H) closeness.Light pink lines in each of the plots are dates of main implementations of disease control measures related to movement restrictions between different regions in addition to movement restriction between infected and noninfected farms since 2010 (Supplemental TableS1), with the following implementations reflected: (1) July 15, 2013, when regionalization was implemented, prohibiting

Figure 3 .
Figure3.The odds ratio of Salmonella Dublin infection due to local (radius of 5 km) and cattle movement transmissions, across prediction mo 1 to 6 based on previous 1 mo data (see Materials and Methods).Adjusted for farm size, cattle movement month, production category of farms, and total neighborhood (total number of farms in a radius of 5 km around the infected farm).Note that local transmissions included all premises (i.e., including farms without cattle movements to other premises).

Figure 4 .
Figure 4. Simulation of the spread of Salmonella Dublin in Danish cattle movement networks from 2015 to 2017 during the regionalization (top) and from 2018 to 2020 after regionalization (bottom).Depending on the network movement activity level α and the disease transmission probability p, the spread of S. Dublin was simulated on observed movement network activities (vertical orange lines) and hypothetically increased and decreased movement activities among cattle farmers.(A) Median relative outbreak size (measured as the proportion of infected nodes among all nodes in the movement network) ± quartiles (Q1 and Q3).(B) Median outbreak probability (± 95% CI).(C) Median outbreak duration in months ± quartiles (Q1 and Q3).
dk/ share _redirect/ CbHUHYqXdb.Author contributions are as follows: Led the study: B.C.; conceived and designed the study: B.C., E.D; figure preparation: B.C., E.D; wrote the first draft of the paper: B.C.; computational network analysis: B.C., E.D.; coding of the model: B.C.; review and editing of the paper: B.C., E.D., P.K., L.P., P.R., M.R., O.A., L.R.All authors have read and agreed to the published version of the manuscript.No human or animal subjects were used, so this analysis did not require approval by an Institutional Animal Care and Use Committee or Institutional Review Board.The authors have not stated any conflicts of interest.Nonstandard abbreviations used: FMD = foot-andmouth disease; KS = Kolmogorov-Smirnov; L1 = level 1 (most likely not infected with S. Dublin); L2 = level 2 (likely infected with S. Dublin); L3 = level 3 (S.Dublin infection detected); OR = odds ratio; Q1 = 25% quartile; Q3 = 75% quartile.

Table 1 .
Conrady et al.: SOCIAL NETWORK ANALYSIS TO REDUCE SALMONELLA Definition of the 8 cattle farm production categories used in the present study

Table 2 .
Conrady et al.: SOCIAL NETWORK ANALYSIS TO REDUCE SALMONELLA A description of network properties calculated in the present study Conrady et al.: SOCIAL NETWORK ANALYSIS TO REDUCE SALMONELLA