# Analysis of cattle movement networks in Paraguay: Implications for the spread and control of infectious diseases

Amaias Avalos, Benoit Durand, José Naranjo, Victor Maldonado, Laetitia Canini, Gina Zanella

<figure><img src="image_1.png" /></figure>

## To cite this version:

Amaias Avalos, Benoit Durand, José Naranjo, Victor Maldonado, Laetitia Canini, et al., Analysis of cattle movement networks in Paraguay: Implications for the spread and control of infectious diseases. PLoS ONE, 2022, 17 (12), pp.e0278999. 10.1371/journal.pone.0278999. anses-03926648

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Submitted on 2 Jan 2024

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RESEARCH ARTICLE

# Analysis of cattle movement networks in Paraguay: Implications for the spread and control of infectious diseases

Amaias Avalos<sup>1,2</sup>, Benoit Durand<sup>1</sup>, José Naranjo<sup>3</sup>, Victor Maldonado<sup>4</sup>, Laetitia Canini<sup>1</sup>,
Gina Zanella<sup>1*</sup>

1. ANSES, Laboratory for Animal Health, Epidemiology Unit, Paris-Est University, Maisons-Alfort, France,

2. Faculté de Médecine, Université Paris-Saclay, Le Kremlin-Bicêtre, France, 3. National Animal Health and Quality Service (SENACSA) Consultant—Animal Health Services Foundation (FUNDASSA), Mariano Roque Alonso, Paraguay, 4. National Animal Health and Quality Service (SENACSA), General Directorate of Animal Health, Identity and Traceability, San Lorenzo, Paraguay

* gina.zanella@anses.fr

<figure><img src="image_1.png" /></figure>

## Abstract

Beef exports represent a substantial part of Paraguay's agricultural sector. Cattle movements involve a high risk due to the possible spread of bovine diseases that can have a significant impact on the country's economy. We analyzed cattle movements from 2014 to 2018 using the networks analysis methodology at the holding and district levels at different temporal scales. We built two types of networks to identify network characteristics that may contribute to the spread of two diseases with different epidemiological characteristics: i) a network including all cattle movements to consider the transmission of a disease of rapid spread like foot and mouth disease, and ii) a network including only cow movements to account for bovine brucellosis, a disease of slow spread that occurs mainly in adult females. Network indicators did not vary substantially among the cattle and cow only networks. The holdings/districts included in the largest strongly connected components were distributed throughout the country. Percolation analysis performed at the holding level showed that a large number of holdings should be removed to make the largest strongly connected component disappear. Higher values of the centrality indicators were found for markets than for farms, indicating that they may play an important role in the spread of an infectious disease. At the holding level (but not at the district level), the networks exhibited characteristics of small-world networks. This property may facilitate the spread of foot and mouth disease in case of re-emergence, or of bovine brucellosis in the country through cattle movements. They should be taken into account when implementing surveillance or control measures for these diseases.

## Introduction

Animal trade is an important mode of transmission of infectious diseases [1], such as foot and mouth disease (FMD) and brucellosis, two major diseases of livestock [2–7].

FMD is caused by a virus of the genus *Aphthovirus*, family *Picornaviridae*. There are seven serotypes of FMD virus, namely O, A, C, SAT 1, SAT 2, SAT 3 and Asia 1, which infect cloven-

<figure><img src="image_2.png" /></figure>

OPEN ACCESS

**Citation:** Avalos A, Durand B, Naranjo J, Maldonado V, Canini L, Zanella G (2022) Analysis of cattle movement networks in Paraguay: Implications for the spread and control of infectious diseases. PLoS ONE 17(12): e0278999.
https://doi.org/10.1371/journal.pone.0278999

**Editor:** Fernanda C. Dórea, Swedish National Veterinary Institute, SWEDEN

**Received:** March 7, 2022

**Accepted:** November 29, 2022

**Published:** December 19, 2022

**Copyright:** © 2022 Avalos et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Data Availability Statement:** Data on cattle movements belongs to the Paraguayan Veterinary Services and cannot be publicly shared. For the purpose of this study it was requested from the General Directorate of Technical Services (DIGESETEC).

**Funding:** Amaias Avalos is supported by the Programa Nacional de Becas de Postgrado en el Exterior "Don Carlos Antonio Lopez" - BECAL, approved by Resolution of the Fund for Excellence
<figure><img src="image_3.png" /></figure>

RESEARCH ARTICLE

# Analysis of cattle movement networks in Paraguay: Implications for the spread and control of infectious diseases

Amaias Avalos<sup>1,2</sup>, Benoit Durand<sup>1</sup>, José Naranjo<sup>3</sup>, Victor Maldonado<sup>4</sup>, Laetitia Canini<sup>1</sup>,
Gina Zanella<sup>1*</sup>

1. ANSES, Laboratory for Animal Health, Epidemiology Unit, Paris-Est University, Maisons-Alfort, France,

2. Faculté de Médecine, Université Paris-Saclay, Le Kremlin-Bicêtre, France, 3. National Animal Health and Quality Service (SENACSA) Consultant—Animal Health Services Foundation (FUNDASSA), Mariano Roque Alonso, Paraguay, 4. National Animal Health and Quality Service (SENACSA), General Directorate of Animal Health, Identity and Traceability, San Lorenzo, Paraguay

* gina.zanella@anses.fr

## Abstract

Beef exports represent a substantial part of Paraguay's agricultural sector. Cattle movements involve a high risk due to the possible spread of bovine diseases that can have a significant impact on the country's economy. We analyzed cattle movements from 2014 to 2018 using the networks analysis methodology at the holding and district levels at different temporal scales. We built two types of networks to identify network characteristics that may contribute to the spread of two diseases with different epidemiological characteristics: i) a network including all cattle movements to consider the transmission of a disease of rapid spread like foot and mouth disease, and ii) a network including only cow movements to account for bovine brucellosis, a disease of slow spread that occurs mainly in adult females. Network indicators did not vary substantially among the cattle and cow only networks. The holdings/districts included in the largest strongly connected components were distributed throughout the country. Percolation analysis performed at the holding level showed that a large number of holdings should be removed to make the largest strongly connected component disappear. Higher values of the centrality indicators were found for markets than for farms, indicating that they may play an important role in the spread of an infectious disease. At the holding level (but not at the district level), the networks exhibited characteristics of small-world networks. This property may facilitate the spread of foot and mouth disease in case of re-emergence, or of bovine brucellosis in the country through cattle movements. They should be taken into account when implementing surveillance or control measures for these diseases.

## Introduction

Animal trade is an important mode of transmission of infectious diseases [1], such as foot and mouth disease (FMD) and brucellosis, two major diseases of livestock [2–7].

FMD is caused by a virus of the genus *Aphthovirus*, family *Picornaviridae*. There are seven serotypes of FMD virus, namely O, A, C, SAT 1, SAT 2, SAT 3 and Asia 1, which infect cloven-

<figure><img src="image_4.png" /></figure>

OPEN ACCESS

**Citation:** Avalos A, Durand B, Naranjo J, Maldonado V, Canini L, Zanella G (2022) Analysis of cattle movement networks in Paraguay: Implications for the spread and control of infectious diseases. PLoS ONE 17(12): e0278999.
https://doi.org/10.1371/journal.pone.0278999

**Editor:** Fernanda C. Dórea, Swedish National Veterinary Institute, SWEDEN

**Received:** March 7, 2022

**Accepted:** November 29, 2022

**Published:** December 19, 2022

**Copyright:** © 2022 Avalos et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Data Availability Statement:** Data on cattle movements belongs to the Paraguayan Veterinary Services and cannot be publicly shared. For the purpose of this study it was requested from the General Directorate of Technical Services (DIGESETEC).

**Funding:** Amaias Avalos is supported by the Programa Nacional de Becas de Postgrado en el Exterior "Don Carlos Antonio Lopez" - BECAL, approved by Resolution of the Fund for Excellence
in Education and Research N°19/2015 (NOTE PNB/ GB N°17/18).

**Competing interests:** The authors have declared that no competing interests exist.

hoofed animals. Infection with one serotype does not confer immunity against another [8–10]. Ruminants of both sexes and of all age categories may be infected and their trade may allow transmission of the virus from farm to farm. For this reason, FMD is considered a transboundary animal disease. It is an economically important disease due to direct losses for farmers [11] and trade barriers [12], which justifies the implementation of surveillance and control programs. In South America, the Pan American Foot and Mouth Disease Center (PANAFTOSA), within the Pan American Health Organization (PAHO), has supervised these programs since their creation in 1951, in agreement with the Organization of American States (OAS) and the Government of Brazil, [7, 13, 14]. In 1988, PANAFTOSA proposed a preliminary action plan for the eradication of FMD, the implementation of which allowed most South American countries to obtain and consolidate a status of FMD-free countries where vaccination is not practiced (Chile, Peru) or practiced (Paraguay and Uruguay), or where vaccination is practiced alongside non-vaccination zones (Argentina, Bolivia, Brazil, Colombia and Ecuador) [15]. The 2021–2025 action plan aims to eliminate the use of vaccination in order to achieve the FMD-free status without vaccination, thereby gaining access to a more economically profitable market than with vaccination.

Brucellosis is a zoonotic disease, considered extremely infectious by the OIE, and is transmitted by contact between infected animals, and from infected animals to humans [16]. The disease is caused by several bacteria belonging to the genus *Brucella*, which affects many mammalian species, including cattle, goats, pigs, and sheep [3, 17]. Bovine brucellosis (BB), predominantly caused by *Brucella abortus*, mainly affects pregnant females that abort, and trade of heifers and cows may allow transmission of the bacteria from farm to farm. Human exposure is occupational (i.e., in livestock farmers, veterinarians and slaughterhouse personnel), but is also linked to consumption of infected milk and milk products [18–20]. Control of BB in animal populations is therefore important to improve the productive capacity of the herd and to protect human health from future infections [21]. Brucellosis is present in South America [22, 23] and has been reported in Argentina [24, 25], Brazil [26] and Paraguay [27], among others [28]. Eradication by testing and culling is a costly investment for the producer without government assistance, which is the case in the vast majority of South American countries, where the producer absorbs most of the control measure costs. Vaccination with S19 or RB51 vaccines is an effective method of preventing and controlling infection, but it requires strict control of animal movements and the application of rigorous rules when introducing breeding animals into the herd [24, 26].

Paraguay is a country with a large beef cattle production sector and has great potential to be among the world's largest beef exporters [27]. FMD and BB are the two animal diseases that the Paraguayan health authorities consider priorities for control and eradication. Since its creation in 1967, the National Animal Health and Quality Service (SENACSA) has worked for animal health in Paraguay. At that time, the main objective was to implement an FMD control program, which began in 1968 and was a component of regional level disease control activities. In 1992, an official FMD Eradication Program was initiated with the implementation of vaccination, surveillance, and stamping-out of part of the FMD outbreaks, to eventually allow farmers access to the international commercial market for animals and meat [6, 29]. The last reported outbreak of FMD in Paraguay occurred in 2012 and led to increasingly strict and severe surveillance and control measures until recovery of the “Free of FMD with vaccination” status in 2017 that has been maintained until now [30, 31].

Currently, epidemiological surveillance of BB in Paraguay consists of the collection of information from control activities carried out by official veterinarians, which is processed by local, regional, and central health offices. Official veterinarians perform serological control tests with a testing protocol (Rose Bengal test and fluorescence polarization assay) on females and males
in Education and Research N°19/2015 (NOTE PNB/ GB N°17/18).

**Competing interests:** The authors have declared that no competing interests exist.

hoofed animals. Infection with one serotype does not confer immunity against another [8–10]. Ruminants of both sexes and of all age categories may be infected and their trade may allow transmission of the virus from farm to farm. For this reason, FMD is considered a transboundary animal disease. It is an economically important disease due to direct losses for farmers [11] and trade barriers [12], which justifies the implementation of surveillance and control programs. In South America, the Pan American Foot and Mouth Disease Center (PANAFTOSA), within the Pan American Health Organization (PAHO), has supervised these programs since their creation in 1951, in agreement with the Organization of American States (OAS) and the Government of Brazil, [7, 13, 14]. In 1988, PANAFTOSA proposed a preliminary action plan for the eradication of FMD, the implementation of which allowed most South American countries to obtain and consolidate a status of FMD-free countries where vaccination is not practiced (Chile, Peru) or practiced (Paraguay and Uruguay), or where vaccination is practiced alongside non-vaccination zones (Argentina, Bolivia, Brazil, Colombia and Ecuador) [15]. The 2021–2025 action plan aims to eliminate the use of vaccination in order to achieve the FMD-free status without vaccination, thereby gaining access to a more economically profitable market than with vaccination.

Brucellosis is a zoonotic disease, considered extremely infectious by the OIE, and is transmitted by contact between infected animals, and from infected animals to humans [16]. The disease is caused by several bacteria belonging to the genus *Brucella*, which affects many mammalian species, including cattle, goats, pigs, and sheep [3, 17]. Bovine brucellosis (BB), predominantly caused by *Brucella abortus*, mainly affects pregnant females that abort, and trade of heifers and cows may allow transmission of the bacteria from farm to farm. Human exposure is occupational (i.e., in livestock farmers, veterinarians and slaughterhouse personnel), but is also linked to consumption of infected milk and milk products [18–20]. Control of BB in animal populations is therefore important to improve the productive capacity of the herd and to protect human health from future infections [21]. Brucellosis is present in South America [22, 23] and has been reported in Argentina [24, 25], Brazil [26] and Paraguay [27], among others [28]. Eradication by testing and culling is a costly investment for the producer without government assistance, which is the case in the vast majority of South American countries, where the producer absorbs most of the control measure costs. Vaccination with S19 or RB51 vaccines is an effective method of preventing and controlling infection, but it requires strict control of animal movements and the application of rigorous rules when introducing breeding animals into the herd [24, 26].

Paraguay is a country with a large beef cattle production sector and has great potential to be among the world's largest beef exporters [27]. FMD and BB are the two animal diseases that the Paraguayan health authorities consider priorities for control and eradication. Since its creation in 1967, the National Animal Health and Quality Service (SENACSA) has worked for animal health in Paraguay. At that time, the main objective was to implement an FMD control program, which began in 1968 and was a component of regional level disease control activities. In 1992, an official FMD Eradication Program was initiated with the implementation of vaccination, surveillance, and stamping-out of part of the FMD outbreaks, to eventually allow farmers access to the international commercial market for animals and meat [6, 29]. The last reported outbreak of FMD in Paraguay occurred in 2012 and led to increasingly strict and severe surveillance and control measures until recovery of the “Free of FMD with vaccination” status in 2017 that has been maintained until now [30, 31].

Currently, epidemiological surveillance of BB in Paraguay consists of the collection of information from control activities carried out by official veterinarians, which is processed by local, regional, and central health offices. Official veterinarians perform serological control tests with a testing protocol (Rose Bengal test and fluorescence polarization assay) on females and males
introduced on farms that are willing to obtain an official certificate as free from brucellosis, as well as milk ring-tests on certain dairy farms. The current BB control, prevention, and eradication program driven mainly by SENACSA does not include, in the short term, the elimination of positive animals with compensation to owners, as established by the Law for the Promotion of Dairy Production (Law 5264/2014), mainly due to lack of funds. Two vaccination campaigns should be carried out per year on all farms in young females from 3 to 8 months of age, using the S19 and RB51 strains.

It is well known that animal movements play an important role in disease transmission between farms. Data on the commercial movements of animals can be represented by means of networks [4, 32–34]. The properties of these networks can be studied using network analysis methods [35].

The main route of BB transmission between farms is the trade of infected cows. For FMD, other routes than cattle trade may play a role in the transmission of the disease between farms: local airborne contagion, pig and small ruminant movements or movements of people, vehicles and livestock equipment. Creating national databases is an important requirement for the control of diseases such as FMD [36]. In Paraguay, the main domestic species raised is cattle (96% of the livestock that includes cattle, sheep, goats and pigs [37] and, therefore, cattle trade could be considered as the major risk for FMD propagation. In 2008, the cattle movement information system, called SIGOR, was developed by SENACSA in the frame of the FMD control campaign [29]. Considering that cattle trade is the main source of BB and FMD spread in Paraguay and that network analysis may enable better understanding of the propagation of an exotic disease (such as FMD in Paraguay), in the case of its introduction, or the mechanisms of circulation of enzootic diseases (such as BB in Paraguay) [38–42], the objective of this work was to analyze and compare two cattle trade networks in Paraguay: the general cattle trade network (relevant for FMD), and the cow trade network (relevant for BB). Both networks were studied during the period 2014–2018 and analyzed at holding and district levels, for the entire period or using monthly and annual time steps.

# Materials and methods

## Data

Information on the cattle inventory, list of cattle markets and slaughterhouses, and cattle movements from 2014 to 2018 was obtained from the Paraguayan Veterinary Services (SENACSA).

The database on cattle inventory gathered information on farm location, specifying three administrative units (from the smallest to the largest: district, department and region) and the number of cattle per farm. This information was used to establish two maps of farm and cattle densities per km² using the average of annual numbers of farms and cattle from 2014 to 2018.

Data on cattle movements from January 2014 to December 2018 were extracted from the cattle movement database that was developed in the context of the Paraguayan national control program for FMD. Each movement included the following information: date, holding identification number, type of holding at origin and destination (farm, market, or slaughterhouse), location, and number of animals moved by category (cows, heifers, bullocks, bulls, steers, weaned male/female and calves). Movements concerning import or export were excluded.

## Network construction and analysis

We aggregated the movement data to construct static networks in which the nodes were either holdings (farms or markets, referred to below as “holding level”) or districts (referred to below as “district level”) and cattle movements between nodes were links. The networks were
introduced on farms that are willing to obtain an official certificate as free from brucellosis, as well as milk ring-tests on certain dairy farms. The current BB control, prevention, and eradication program driven mainly by SENACSA does not include, in the short term, the elimination of positive animals with compensation to owners, as established by the Law for the Promotion of Dairy Production (Law 5264/2014), mainly due to lack of funds. Two vaccination campaigns should be carried out per year on all farms in young females from 3 to 8 months of age, using the S19 and RB51 strains.

It is well known that animal movements play an important role in disease transmission between farms. Data on the commercial movements of animals can be represented by means of networks [4, 32–34]. The properties of these networks can be studied using network analysis methods [35].

The main route of BB transmission between farms is the trade of infected cows. For FMD, other routes than cattle trade may play a role in the transmission of the disease between farms: local airborne contagion, pig and small ruminant movements or movements of people, vehicles and livestock equipment. Creating national databases is an important requirement for the control of diseases such as FMD [36]. In Paraguay, the main domestic species raised is cattle (96% of the livestock that includes cattle, sheep, goats and pigs [37] and, therefore, cattle trade could be considered as the major risk for FMD propagation. In 2008, the cattle movement information system, called SIGOR, was developed by SENACSA in the frame of the FMD control campaign [29]. Considering that cattle trade is the main source of BB and FMD spread in Paraguay and that network analysis may enable better understanding of the propagation of an exotic disease (such as FMD in Paraguay), in the case of its introduction, or the mechanisms of circulation of enzootic diseases (such as BB in Paraguay) [38–42], the objective of this work was to analyze and compare two cattle trade networks in Paraguay: the general cattle trade network (relevant for FMD), and the cow trade network (relevant for BB). Both networks were studied during the period 2014–2018 and analyzed at holding and district levels, for the entire period or using monthly and annual time steps.

# Materials and methods

## Data

Information on the cattle inventory, list of cattle markets and slaughterhouses, and cattle movements from 2014 to 2018 was obtained from the Paraguayan Veterinary Services (SENACSA).

The database on cattle inventory gathered information on farm location, specifying three administrative units (from the smallest to the largest: district, department and region) and the number of cattle per farm. This information was used to establish two maps of farm and cattle densities per km² using the average of annual numbers of farms and cattle from 2014 to 2018.

Data on cattle movements from January 2014 to December 2018 were extracted from the cattle movement database that was developed in the context of the Paraguayan national control program for FMD. Each movement included the following information: date, holding identification number, type of holding at origin and destination (farm, market, or slaughterhouse), location, and number of animals moved by category (cows, heifers, bullocks, bulls, steers, weaned male/female and calves). Movements concerning import or export were excluded.

## Network construction and analysis

We aggregated the movement data to construct static networks in which the nodes were either holdings (farms or markets, referred to below as “holding level”) or districts (referred to below as “district level”) and cattle movements between nodes were links. The networks were
directed because the origin and destination of cattle movements were taken into account. Slaughterhouses were not included in the analysis since they do not play a role in the spread of pathogens. Considering that FMD or BB propagation depend on the cattle categories they may affect, we differentiated networks including all cattle movements (referred to below as “all cattle networks”) from networks including only cow movements (referred to below as “cow networks”). Time interval was either the entire period (“global network”), one of the 5 years (“annual network”), or one of the 60 months (“monthly networks”) in our data set. The global or annual scales would be more suitable for diseases of slow spread that are enzootic, such as brucellosis, to identify patterns that could assist in the implementation of control measures. For a disease that spreads faster, such as foot and mouth disease, the monthly networks would be more adapted. A month would be the period of time in which animals in a herd are still infectious and could propagate the infection through movements. Indeed, it has been reported that in a herd of vaccinated cattle, FMD clinical signs may be displayed over a 39-day period [43] and, by modelling, it has been found that transmission within a cattle farm can occur until one month post-infection [44]. All scales were studied for both all cattle and only cow networks to compare them. The different combinations yielded a total of 264 networks. Different indicators were calculated for all networks and are briefly described in Table 1.

We calculated the Jaccard coefficient for the different pairs of networks to compare the nodes and links included in each network, from year to year and from month to month. The Jaccard index measures the degree of similarity between two sets A and B (regardless of the type of elements) with the formula:

$$J(A, B) = |A \cap B| / |A \cup B|$$

It has a value between 0 (no similarity) and 1 (identical sets).

To establish whether the networks had scale-free properties, whose degree distribution follows a power law, we plotted the degrees on a logarithmic scale [52]. When relevant, the exponent of the power law distribution was determined using the method proposed by Clauset *et al*

<table><caption>**Table 1.** Description of general network indicators calculated in this study. *Calculated for the global and annual networks.</caption><thead><tr><td>Network indicator</td><td>Description</td></tr></thead><tbody><tr><td>Size</td><td>Number of nodes [35]</td></tr><tr><td>Density</td><td>Number of existing links divided by the total possible links [35]</td></tr><tr><td>Diameter</td><td>The most extensive shortest path among all the shortest paths in the network [45]</td></tr><tr><td>Average degree</td><td>The degree of a node is the number of links it has with other nodes [35]</td></tr><tr><td>Betweenness</td><td>Frequency with which a node appears on the shortest path between other pairs of nodes [46]</td></tr><tr><td>Average path length</td><td>Average number of links along the shortest paths for all possible pairs of nodes [35]</td></tr><tr><td>Assortativity</td><td>Tendency of nodes to have links with similar nodes in terms of degree [47]</td></tr><tr><td>Clustering coefficient</td><td>Proportion of nearby nodes of a node that are linked to each other [48]</td></tr><tr><td>Reciprocity</td><td>Proportion of nodes in a directed network that are mutually linked [35]</td></tr><tr><td>Connected component*</td><td>Sub-network where all nodes are connected. In a strongly connected component, any node can be accessed by any other node through directed links, while in a weakly connected component, all nodes are linked without taking into account the direction of the links [49, 50]</td></tr><tr><td>Closeness*</td><td>Inverse of the average length of the shortest paths to/from all other nodes in the graph (the largest facilities will have high and fast accessibility to anywhere in the network). It was calculated within the largest strongly connected component [46]</td></tr><tr><td>Community*</td><td>Densely connected subgraphs identified using an algorithm based on random walks, the walktrap algorithm [51]</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t001
directed because the origin and destination of cattle movements were taken into account. Slaughterhouses were not included in the analysis since they do not play a role in the spread of pathogens. Considering that FMD or BB propagation depend on the cattle categories they may affect, we differentiated networks including all cattle movements (referred to below as “all cattle networks”) from networks including only cow movements (referred to below as “cow networks”). Time interval was either the entire period (“global network”), one of the 5 years (“annual network”), or one of the 60 months (“monthly networks”) in our data set. The global or annual scales would be more suitable for diseases of slow spread that are enzootic, such as brucellosis, to identify patterns that could assist in the implementation of control measures. For a disease that spreads faster, such as foot and mouth disease, the monthly networks would be more adapted. A month would be the period of time in which animals in a herd are still infectious and could propagate the infection through movements. Indeed, it has been reported that in a herd of vaccinated cattle, FMD clinical signs may be displayed over a 39-day period [43] and, by modelling, it has been found that transmission within a cattle farm can occur until one month post-infection [44]. All scales were studied for both all cattle and only cow networks to compare them. The different combinations yielded a total of 264 networks. Different indicators were calculated for all networks and are briefly described in Table 1.

We calculated the Jaccard coefficient for the different pairs of networks to compare the nodes and links included in each network, from year to year and from month to month. The Jaccard index measures the degree of similarity between two sets A and B (regardless of the type of elements) with the formula:

$$J(A, B) = |A \cap B| / |A \cup B|$$

It has a value between 0 (no similarity) and 1 (identical sets).

To establish whether the networks had scale-free properties, whose degree distribution follows a power law, we plotted the degrees on a logarithmic scale [52]. When relevant, the exponent of the power law distribution was determined using the method proposed by Clauset *et al*

<table><caption>**Table 1.** Description of general network indicators calculated in this study. *Calculated for the global and annual networks.</caption><thead><tr><td>Network indicator</td><td>Description</td></tr></thead><tbody><tr><td>Size</td><td>Number of nodes [35]</td></tr><tr><td>Density</td><td>Number of existing links divided by the total possible links [35]</td></tr><tr><td>Diameter</td><td>The most extensive shortest path among all the shortest paths in the network [45]</td></tr><tr><td>Average degree</td><td>The degree of a node is the number of links it has with other nodes [35]</td></tr><tr><td>Betweenness</td><td>Frequency with which a node appears on the shortest path between other pairs of nodes [46]</td></tr><tr><td>Average path length</td><td>Average number of links along the shortest paths for all possible pairs of nodes [35]</td></tr><tr><td>Assortativity</td><td>Tendency of nodes to have links with similar nodes in terms of degree [47]</td></tr><tr><td>Clustering coefficient</td><td>Proportion of nearby nodes of a node that are linked to each other [48]</td></tr><tr><td>Reciprocity</td><td>Proportion of nodes in a directed network that are mutually linked [35]</td></tr><tr><td>Connected component*</td><td>Sub-network where all nodes are connected. In a strongly connected component, any node can be accessed by any other node through directed links, while in a weakly connected component, all nodes are linked without taking into account the direction of the links [49, 50]</td></tr><tr><td>Closeness*</td><td>Inverse of the average length of the shortest paths to/from all other nodes in the graph (the largest facilities will have high and fast accessibility to anywhere in the network). It was calculated within the largest strongly connected component [46]</td></tr><tr><td>Community*</td><td>Densely connected subgraphs identified using an algorithm based on random walks, the walktrap algorithm [51]</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t001
<table><caption>Table 2. Number of cattle and cattle farms censused in Paraguay from 2014 to 2018.</caption><thead><tr><th></th><th>2014</th><th>2015</th><th>2016</th><th>2017</th><th>2018</th></tr></thead><tbody><tr><td>Number of cattle farms</td><td>147,320</td><td>151,084</td><td>150,689</td><td>148,536</td><td>145,025</td></tr><tr><td>Number of cattle</td><td>14,465,581</td><td>14,216,256</td><td>13,858,584</td><td>13,821,526</td><td>13,500,965</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t002

[53]. We also generated random networks according to the Erdos-Rényi model [54], with the same number of nodes and links as real networks and compared their average path length and clustering coefficient to those of the real networks to detect scale-free or small world properties [35, 55].

Finally, percolation allowed us to analyze the effect of eliminating nodes on the size of the largest strongly connected component (LSCC), to assess control measures that could be implemented to prevent the spread of bovine infectious diseases. The percolation analysis was performed at the holding level for the global and annual networks for all cattle and cows. Considering the results obtained in other studies [39, 42], nodes with high betweenness were sequentially removed to identify a threshold at which the LSCC would rapidly reduce in size.

Network analyses were performed using the Igraph Network Analysis and Visualization package [56], ggplot packages [57], and RStudio software (v 1.4.1106, 2009–2021) [58].

# Results

## Cattle census description

According to data from the 2014–2018 cattle census, there were an average of ~14 million cattle and ~148,000 holdings in Paraguay during the study period (Table 2).

The average cattle density was high throughout the country. Cattle farms were present all over the Paraguayan territory, with a higher density in the eastern region compared to the western region called El Chaco (Fig 1). A total of 54 markets and 312 cattle slaughterhouses were active during the study period (Fig 1). The highest number of markets was concentrated in the eastern region of Paraguay.

## Cattle movement database description

According to the database, a total number of 73,904 farms were involved in cattle movements during the study period, representing ~50% of the total number of farms present in the cattle census conducted by SENACSA. The Chaco region had 402,289 origin movements and 318,055 destination movements; while the eastern region had a higher number of origin movements (1,000,121) and destination movements (1,084,355).

The highest number of movements between 2014 and 2018 occurred from farm to farm, regardless of the categories of animals moved (685,591 for all cattle and 194,388 for only cows), followed by movements from farms to slaughterhouses (416,738 for all cattle and 178,412 for only cows) (Table 3). The main destination of movements originating at markets were the slaughterhouses. The number of cow movements was 37% of all cattle movements (523,597 of 1,402,410). The number of cows moved from farms to slaughterhouses (3,050,147) exceeded that from farms to farms (2,340,498), while for the non-cows, the animals moved from farms to slaughterhouses (7,352,360) were half of those moved from farms to farms (12,061,614).

Most cattle movements occurred between districts (72%). This percentage dropped to 60% when movements occurred only between farms, and to 50% when only cows were taken into account.
<table><caption>Table 2. Number of cattle and cattle farms censused in Paraguay from 2014 to 2018.</caption><thead><tr><th></th><th>2014</th><th>2015</th><th>2016</th><th>2017</th><th>2018</th></tr></thead><tbody><tr><td>Number of cattle farms</td><td>147,320</td><td>151,084</td><td>150,689</td><td>148,536</td><td>145,025</td></tr><tr><td>Number of cattle</td><td>14,465,581</td><td>14,216,256</td><td>13,858,584</td><td>13,821,526</td><td>13,500,965</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t002

[53]. We also generated random networks according to the Erdos-Rényi model [54], with the same number of nodes and links as real networks and compared their average path length and clustering coefficient to those of the real networks to detect scale-free or small world properties [35, 55].

Finally, percolation allowed us to analyze the effect of eliminating nodes on the size of the largest strongly connected component (LSCC), to assess control measures that could be implemented to prevent the spread of bovine infectious diseases. The percolation analysis was performed at the holding level for the global and annual networks for all cattle and cows. Considering the results obtained in other studies [39, 42], nodes with high betweenness were sequentially removed to identify a threshold at which the LSCC would rapidly reduce in size.

Network analyses were performed using the igraph Network Analysis and Visualization package [56], ggplot packages [57], and RStudio software (v 1.4.1106, 2009–2021) [58].

# Results

## Cattle census description

According to data from the 2014–2018 cattle census, there were an average of ~14 million cattle and ~148,000 holdings in Paraguay during the study period (Table 2).

The average cattle density was high throughout the country. Cattle farms were present all over the Paraguayan territory, with a higher density in the eastern region compared to the western region called El Chaco (Fig 1). A total of 54 markets and 312 cattle slaughterhouses were active during the study period (Fig 1). The highest number of markets was concentrated in the eastern region of Paraguay.

## Cattle movement database description

According to the database, a total number of 73,904 farms were involved in cattle movements during the study period, representing ~50% of the total number of farms present in the cattle census conducted by SENACSA. The Chaco region had 402,289 origin movements and 318,055 destination movements; while the eastern region had a higher number of origin movements (1,000,121) and destination movements (1,084,355).

The highest number of movements between 2014 and 2018 occurred from farm to farm, regardless of the categories of animals moved (685,591 for all cattle and 194,388 for only cows), followed by movements from farms to slaughterhouses (416,738 for all cattle and 178,412 for only cows) (Table 3). The main destination of movements originating at markets were the slaughterhouses. The number of cow movements was 37% of all cattle movements (523,597 of 1,402,410). The number of cows moved from farms to slaughterhouses (3,050,147) exceeded that from farms to farms (2,340,498), while for the non-cows, the animals moved from farms to slaughterhouses (7,352,360) were half of those moved from farms to farms (12,061,614).

Most cattle movements occurred between districts (72%). This percentage dropped to 60% when movements occurred only between farms, and to 50% when only cows were taken into account.
<figure><img src="image_3.png" /><figcaption>**Fig 1.** Density of cattle farms and cattle per km² and market location in Paraguay. Average annual number of farms and cattle from 2014 to 2018 were used.
https://doi.org/10.1371/journal.pone.0278999.g001</figcaption></figure>

## Size and stability of networks

**Holding level.** The global network was composed of 72,096 nodes and 366,626 links for all cattle, and 57,097 nodes and 126,359 links for only cows (Table 4).

<table><caption>**Table 3.** Summary of cattle movements within and between districts in Paraguay from 2014 to 2018. *The percentages represent the proportion of movements that occurred within districts.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Destination</th><th colspan="4">Number of movements * (% within district)</th><th colspan="4">Number of moved cattle * (% within district)</th></tr><tr><th>Origin</th><th>Farm</th><th>Market</th><th>Slaughterhouse</th><th>Total</th><th>Farm</th><th>Market</th><th>Slaughterhouse</th><th>Total</th></tr></thead><tbody><tr><td rowspan="3">All cattle</td><td>Farm</td><td>685,591 (40%)</td><td>68,691 (5%)</td><td>416,738 (16%)</td><td>1,171,020 (30%)</td><td>15,319,772 (29%)</td><td>1,381,055 (6%)</td><td>11,353,034 (6%)</td><td>28,053,861 (18%)</td></tr><tr><td>Market</td><td>68,799 (11%)</td><td>34 (6%)</td><td>162,557 (28%)</td><td>231,390 (23%)</td><td>670,144 (11%)</td><td>265 (2%)</td><td>661,144 (31%)</td><td>1,331,553 (21%)</td></tr><tr><td>Total</td><td>754,390 (38%)</td><td>68,725 (5%)</td><td>579,295 (19%)</td><td>1,402,410 (28%)</td><td>15,989,916 (28%)</td><td>1,381,320 (6%)</td><td>12,014,178 (7%)</td><td>29,385,414 (19%)</td></tr><tr><td rowspan="3">Only cows</td><td>Farm</td><td>194,388 (50%)</td><td>39,706 (3%)</td><td>178,421 (22%)</td><td>412,515 (33%)</td><td>2,340,498 (39%)</td><td>533,432 (2%)</td><td>3,050,147 (9%)</td><td>5,924,077 (20%)</td></tr><tr><td>Market</td><td>21,615 (11%)</td><td>13 (0%)</td><td>89,454 (28%)</td><td>111,082 (25%)</td><td>159,974 (10%)</td><td>43 (0%)</td><td>350,233 (28%)</td><td>510,250 (23%)</td></tr><tr><td>Total</td><td>216,003 (46%)</td><td>39,719 (3%)</td><td>267,875 (24%)</td><td>523,597 (32%)</td><td>2,500,472 (11%)</td><td>533,475 (2%)</td><td>3,400,380 (37%)</td><td>6,434,327 (20%)</td></tr><tr><td rowspan="3">Excluding cows*</td><td>Farm</td><td>491,203 (36%)</td><td>28,985 (8%)</td><td>238,317 (28%)</td><td>758,505 (25%)</td><td>12,061,614 (25%)</td><td>667,583 (10%)</td><td>7,352,360 (5%)</td><td>20,081,557 (17%)</td></tr><tr><td>Market</td><td>47,184 (11%)</td><td>21 (10%)</td><td>73,103 (21%)</td><td>120,308 (32%)</td><td>489,634 (11%)</td><td>185 (2%)</td><td>293,698 (33%)</td><td>783,517 (20%)</td></tr><tr><td>Total</td><td>538,387 (34%)</td><td>29,006 (8%)</td><td>311,420 (27%)</td><td>878,813 (25%)</td><td>12,551,248 (24%)</td><td>667,768 (10%)</td><td>7,646,058 (6%)</td><td>20,865,074 (17%)</td></tr></tbody></table>

<footnote>*Males, calves and heifers</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig 1.** Density of cattle farms and cattle per km² and market location in Paraguay. Average annual number of farms and cattle from 2014 to 2018 were used.
https://doi.org/10.1371/journal.pone.0278999.g001</figcaption></figure>

## Size and stability of networks

**Holding level.** The global network was composed of 72,096 nodes and 366,626 links for all cattle, and 57,097 nodes and 126,359 links for only cows (Table 4).

<table><caption>**Table 3.** Summary of cattle movements within and between districts in Paraguay from 2014 to 2018. *The percentages represent the proportion of movements that occurred within districts.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Destination</th><th colspan="4">Number of movements * (% within district)</th><th colspan="4">Number of moved cattle * (% within district)</th></tr><tr><th>Origin</th><th>Farm</th><th>Market</th><th>Slaughterhouse</th><th>Total</th><th>Farm</th><th>Market</th><th>Slaughterhouse</th><th>Total</th></tr></thead><tbody><tr><td rowspan="3">All cattle</td><td>Farm</td><td>685,591 (40%)</td><td>68,691 (5%)</td><td>416,738 (16%)</td><td>1,171,020 (30%)</td><td>15,319,772 (29%)</td><td>1,381,055 (6%)</td><td>11,353,034 (6%)</td><td>28,053,861 (18%)</td></tr><tr><td>Market</td><td>68,799 (11%)</td><td>34 (6%)</td><td>162,557 (28%)</td><td>231,390 (23%)</td><td>670,144 (11%)</td><td>265 (2%)</td><td>661,144 (31%)</td><td>1,331,553 (21%)</td></tr><tr><td>Total</td><td>754,390 (38%)</td><td>68,725 (5%)</td><td>579,295 (19%)</td><td>1,402,410 (28%)</td><td>15,989,916 (28%)</td><td>1,381,320 (6%)</td><td>12,014,178 (7%)</td><td>29,385,414 (19%)</td></tr><tr><td rowspan="3">Only cows</td><td>Farm</td><td>194,388 (50%)</td><td>39,706 (3%)</td><td>178,421 (22%)</td><td>412,515 (33%)</td><td>2,340,498 (39%)</td><td>533,432 (2%)</td><td>3,050,147 (9%)</td><td>5,924,077 (20%)</td></tr><tr><td>Market</td><td>21,615 (11%)</td><td>13 (0%)</td><td>89,454 (28%)</td><td>111,082 (25%)</td><td>159,974 (10%)</td><td>43 (0%)</td><td>350,233 (28%)</td><td>510,250 (23%)</td></tr><tr><td>Total</td><td>216,003 (46%)</td><td>39,719 (3%)</td><td>267,875 (24%)</td><td>523,597 (32%)</td><td>2,500,472 (11%)</td><td>533,475 (2%)</td><td>3,400,380 (37%)</td><td>6,434,327 (20%)</td></tr><tr><td rowspan="3">Excluding cows*</td><td>Farm</td><td>491,203 (36%)</td><td>28,985 (8%)</td><td>238,317 (28%)</td><td>758,505 (25%)</td><td>12,061,614 (25%)</td><td>667,583 (10%)</td><td>7,352,360 (5%)</td><td>20,081,557 (17%)</td></tr><tr><td>Market</td><td>47,184 (11%)</td><td>21 (10%)</td><td>73,103 (21%)</td><td>120,308 (32%)</td><td>489,634 (11%)</td><td>185 (2%)</td><td>293,698 (33%)</td><td>783,517 (20%)</td></tr><tr><td>Total</td><td>538,387 (34%)</td><td>29,006 (8%)</td><td>311,420 (27%)</td><td>878,813 (25%)</td><td>12,551,248 (24%)</td><td>667,768 (10%)</td><td>7,646,058 (6%)</td><td>20,865,074 (17%)</td></tr></tbody></table>

<footnote>*Males, calves and heifers</footnote>
<table><caption>Table 4. Indicators for the global networks for all cattle and cows in Paraguay. Nodes and links were aggregated from 2014 to 2018.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Holding level</th><th colspan="2">District level</th></tr><tr><th>All cattle (range)</th><th>Cows (range)</th><th>All cattle (range)</th><th>Cows (range)</th></tr></thead><tbody><tr><td>Number of nodes</td><td>72,096</td><td>57,097</td><td>299</td><td>299</td></tr><tr><td>Number of links</td><td>366,626</td><td>126,359</td><td>22,077</td><td>11,306</td></tr><tr><td>Diameter</td><td>20</td><td>26</td><td>4</td><td>4</td></tr><tr><td>Density</td><td>7.05.10<sup>-05</sup></td><td>3.87.10<sup>-05</sup></td><td>0.25</td><td>0.12</td></tr><tr><td>Average degree</td><td>10.17 (1-4,669)</td><td>4.42 (1-3,261)</td><td>147.67 (2-466)</td><td>75.62 (2-411)</td></tr><tr><td>Average in-degree</td><td>5.08 (0-3,948)</td><td>2.21 (0-2,878)</td><td>73.83 (1-235)</td><td>37.81 (1-228)</td></tr><tr><td>Average out-degree</td><td>5.08 (0-1,215)</td><td>2.21 (0-392)</td><td>73.83 (1-231)</td><td>37.81 (1-183)</td></tr><tr><td>Average betweenness</td><td>7.89.10<sup>-10</sup> (0-2.72.10<sup>-06</sup>)</td><td>7.74<sup>-10</sup> (0-2.82.10<sup>-06</sup>)</td><td>1.78.10<sup>-05</sup> (0-0.0003)</td><td>2.32.10<sup>-05</sup> (0-0.0007)</td></tr><tr><td>Average path length</td><td>5.53</td><td>7.18</td><td>1.79</td><td>2.03</td></tr><tr><td>Assortativity</td><td>-0.04</td><td>-0.03</td><td>-0.06</td><td>-0.06</td></tr><tr><td>Clustering coefficient</td><td>0.02</td><td>0.01</td><td>0.57</td><td>0.39</td></tr><tr><td>Reciprocity</td><td>0.05</td><td>0.04</td><td>0.38</td><td>0.34</td></tr><tr><td colspan="5"><strong>Strong components</strong></td></tr><tr><td>Number</td><td>39,639</td><td>43,727</td><td>1</td><td>1</td></tr><tr><td>Largest component size (% total nodes)</td><td>32,149 (44%)</td><td>12,390 (21%)</td><td>299 (100%)</td><td>299 (100%)</td></tr><tr><td colspan="5"><strong>Weak components</strong></td></tr><tr><td>Number</td><td>913</td><td>2,777</td><td>1</td><td>1</td></tr><tr><td>Largest component size (total nodes)</td><td>70,070 (97%)</td><td>50,593 (88%)</td><td>299 (100%)</td><td>299 (100%)</td></tr><tr><td>Average closeness</td><td>0.19 (0.09-0.30)</td><td>0.15 (0.07-0.21)</td><td>0.56 (0.38-0.81)</td><td>0.49 (0.32-0.72)</td></tr><tr><td colspan="5"><strong>Communities</strong></td></tr><tr><td>Number</td><td>3,589</td><td>6,264</td><td>5</td><td>8</td></tr><tr><td>Size of the first three largest communities (% total nodes)</td><td>16,288 (40%) - 7,076-5,311</td><td>11,630 (38%) - 5,992-4,139</td><td>120 (92%) - 100-56</td><td>77 (63%) - 61-53</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t004

In the annual networks, the average numbers of nodes and links for all cattle were 41,251 (range: 39,589-43,496) and 90,556 (range: 88,101-94,295), respectively, of which 61.3% of nodes and 33.9% of links corresponded to only cows (Fig 2). The Jaccard index (JI) values for the nodes of the two types of annual networks (all cattle and cows) were around 0.5, indicating that almost 50% of the same holdings were involved in cattle trade from one year to the next (Fig 2). Forty-eight percent of the nodes of the all cattle global network were present in one or two years and 25% in all the five years. The JI values for the links ranged from 0.1 for all cattle to values <0.1 for only cows, which means that a small part of the exchanges were made between the same farms from one year to the next. Sixty percent of the nodes of the cow global network were present in one or two years and 10% in all the five years.

For the monthly networks, there was an average of 9,436 nodes, (range: 2,035-15,499) and an average of 9,283 links (range: 1,919-16,240) for all cattle (S1 Fig). Very close figures were obtained for the only cow monthly networks. The monthly values of the JI (S2 Fig) at the holdings level for all cattle and only cows only ranged from 0.6 to 1 for nodes and from 0.15 to 0.35 for links. Fifty-three percent of the nodes were present in 4 or less months for all cattle and only cow networks.

**District level.** The global network included 299 nodes for both all cattle and cow networks. This means that all Paraguayan districts presented in this study were involved in cattle trade. The number of links of the global cow network represented 50% of the number of links of the global network for all cattle (Table 4).

The number of nodes in the annual networks was high and close to the number of nodes in the global network. The number of links in the cow networks was half that in the all cattle
<table><caption>Table 4. Indicators for the global networks for all cattle and cows in Paraguay. Nodes and links were aggregated from 2014 to 2018.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Holding level</th><th colspan="2">District level</th></tr><tr><th>All cattle (range)</th><th>Cows (range)</th><th>All cattle (range)</th><th>Cows (range)</th></tr></thead><tbody><tr><td>Number of nodes</td><td>72,096</td><td>57,097</td><td>299</td><td>299</td></tr><tr><td>Number of links</td><td>366,626</td><td>126,359</td><td>22,077</td><td>11,306</td></tr><tr><td>Diameter</td><td>20</td><td>26</td><td>4</td><td>4</td></tr><tr><td>Density</td><td>7.05.10<sup>-05</sup></td><td>3.87.10<sup>-05</sup></td><td>0.25</td><td>0.12</td></tr><tr><td>Average degree</td><td>10.17 (1-4,669)</td><td>4.42 (1-3,261)</td><td>147.67 (2-466)</td><td>75.62 (2-411)</td></tr><tr><td>Average in-degree</td><td>5.08 (0-3,948)</td><td>2.21 (0-2,878)</td><td>73.83 (1-235)</td><td>37.81 (1-228)</td></tr><tr><td>Average out-degree</td><td>5.08 (0-1,215)</td><td>2.21 (0-392)</td><td>73.83 (1-231)</td><td>37.81 (1-183)</td></tr><tr><td>Average betweenness</td><td>7.89.10<sup>-10</sup> (0-2.72.10<sup>-06</sup>)</td><td>7.74<sup>-10</sup> (0-2.82.10<sup>-06</sup>)</td><td>1.78.10<sup>-05</sup> (0-0.0003)</td><td>2.32.10<sup>-05</sup> (0-0.0007)</td></tr><tr><td>Average path length</td><td>5.53</td><td>7.18</td><td>1.79</td><td>2.03</td></tr><tr><td>Assortativity</td><td>-0.04</td><td>-0.03</td><td>-0.06</td><td>-0.06</td></tr><tr><td>Clustering coefficient</td><td>0.02</td><td>0.01</td><td>0.57</td><td>0.39</td></tr><tr><td>Reciprocity</td><td>0.05</td><td>0.04</td><td>0.38</td><td>0.34</td></tr><tr><td colspan="5"><strong>Strong components</strong></td></tr><tr><td>Number</td><td>39,639</td><td>43,727</td><td>1</td><td>1</td></tr><tr><td>Largest component size (% total nodes)</td><td>32,149 (44%)</td><td>12,390 (21%)</td><td>299 (100%)</td><td>299 (100%)</td></tr><tr><td colspan="5"><strong>Weak components</strong></td></tr><tr><td>Number</td><td>913</td><td>2,777</td><td>1</td><td>1</td></tr><tr><td>Largest component size (total nodes)</td><td>70,070 (97%)</td><td>50,593 (88%)</td><td>299 (100%)</td><td>299 (100%)</td></tr><tr><td>Average closeness</td><td>0.19 (0.09-0.30)</td><td>0.15 (0.07-0.21)</td><td>0.56 (0.38-0.81)</td><td>0.49 (0.32-0.72)</td></tr><tr><td colspan="5"><strong>Communities</strong></td></tr><tr><td>Number</td><td>3,589</td><td>6,264</td><td>5</td><td>8</td></tr><tr><td>Size of the first three largest communities (% total nodes)</td><td>16,288 (40%) - 7,076-5,311</td><td>11,630 (38%) - 5,992-4,139</td><td>120 (92%) - 100-56</td><td>77 (63%) - 61-53</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t004

In the annual networks, the average numbers of nodes and links for all cattle were 41,251 (range: 39,589-43,496) and 90,556 (range: 88,101-94,295), respectively, of which 61.3% of nodes and 33.9% of links corresponded to only cows (Fig 2). The Jaccard index (JI) values for the nodes of the two types of annual networks (all cattle and cows) were around 0.5, indicating that almost 50% of the same holdings were involved in cattle trade from one year to the next (Fig 2). Forty-eight percent of the nodes of the all cattle global network were present in one or two years and 25% in all the five years. The JI values for the links ranged from 0.1 for all cattle to values <0.1 for only cows, which means that a small part of the exchanges were made between the same farms from one year to the next. Sixty percent of the nodes of the cow global network were present in one or two years and 10% in all the five years.

For the monthly networks, there was an average of 9,436 nodes, (range: 2,035-15,499) and an average of 9,283 links (range: 1,919-16,240) for all cattle (S1 Fig). Very close figures were obtained for the only cow monthly networks. The monthly values of the JI (S2 Fig) at the holdings level for all cattle and only cows only ranged from 0.6 to 1 for nodes and from 0.15 to 0.35 for links. Fifty-three percent of the nodes were present in 4 or less months for all cattle and only cow networks.

**District level.** The global network included 299 nodes for both all cattle and cow networks. This means that all Paraguayan districts presented in this study were involved in cattle trade. The number of links of the global cow network represented 50% of the number of links of the global network for all cattle (Table 4).

The number of nodes in the annual networks was high and close to the number of nodes in the global network. The number of links in the cow networks was half that in the all cattle
<figure><img src="image_4.png" /><figcaption>**Fig 2.** Nodes, links, largest connected components sizes and Jaccard index for the annual networks. (A) Number of nodes, (B) Number of links, (C) Largest strongly connected component (LSCC) size, (D) Largest weakly connected component (LWCC) size, (E) Jaccard index for nodes, and (F) Jaccard index for links at the holding (main graphs) and district levels (insets) for all cattle (plain lines) and for only cows (dashed lines).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g002
<figure><img src="image_6.png" /><figcaption>**Fig 2.** Nodes, links, largest connected components sizes and Jaccard index for the annual networks. (A) Number of nodes, (B) Number of links, (C) Largest strongly connected component (LSCC) size, (D) Largest weakly connected component (LWCC) size, (E) Jaccard index for nodes, and (F) Jaccard index for links at the holding (main graphs) and district levels (insets) for all cattle (plain lines) and for only cows (dashed lines).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g002
networks (Fig 2). At the district level, the JI values of nodes were close to 1 for the all cattle and cow networks; these values were higher compared to those for holdings (Fig 2). The JI values for the links ranged between 0.1 and 0.4 for all cattle; 0.36 and 0.37 for only cows.

In the monthly networks, there was an average of 282 nodes (range: 240–291) and an average of 2,443 links (range: 936–3,500) for all cattle (S1 Fig). For only cows, the means of nodes and links represented 92% and 43%, respectively, of the mean total number of nodes and links. For the holding level, the mean JI for nodes was 0.18 (range: 0.08–0.27) for all cattle, and 0.11 (range: 0.05–0.15) for only cows (S2 Fig). Mean JI values for links were 0.03 (range: 0.01–0.04) for all cattle, and 0.03 (range: 0.01–0.05) for only cows.

## Connected components analysis

**Holding level.** The number of nodes included in the largest strongly connected component (LSCC) represented 44% of the nodes of the global network for all cattle and 21% for cows (Table 4). Holdings included in both LSCCs were distributed all over the country (Fig 3).

In the case of annual networks, the average size of the LSCCs in holdings was 8,635 for all cattle (range: 8,073–9,282) and 1,097 for cows (range: 980–1,319), which represents approximately 21% and 4.3% of the total number of nodes for all cattle and cows (Fig 2). For the monthly networks, the average size of the LSCCs was 139 for all cattle (range: 18–326) and 30 for cows (range: 5–77); this average represented 1.5% of the average total number of nodes for all cattle and 0.8% of the average total number of nodes for cows. The LSCCs size showed a seasonality mainly for the all cattle networks: it was higher from July to October (S3 Fig).

<figure><img src="image_5.png" /><figcaption>**Fig 3.** Spatial distribution of the holdings in the largest strongly and weakly connected components. Largest strongly connected component (LSCC) (A): all cattle, (B): cows and largest weakly connected component (LWCC) (C): all cattle, (D): cows for the global network (aggregated nodes and links from 2014 to 2018). Percentage of holdings in each district corresponds to the number of holdings belonging to the largest component over the size of that largest component.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g003
networks (Fig 2). At the district level, the JI values of nodes were close to 1 for the all cattle and cow networks; these values were higher compared to those for holdings (Fig 2). The JI values for the links ranged between 0.1 and 0.4 for all cattle; 0.36 and 0.37 for only cows.

In the monthly networks, there was an average of 282 nodes (range: 240–291) and an average of 2,443 links (range: 936–3,500) for all cattle (S1 Fig). For only cows, the means of nodes and links represented 92% and 43%, respectively, of the mean total number of nodes and links. For the holding level, the mean JI for nodes was 0.18 (range: 0.08–0.27) for all cattle, and 0.11 (range: 0.05–0.15) for only cows (S2 Fig). Mean JI values for links were 0.03 (range: 0.01–0.04) for all cattle, and 0.03 (range: 0.01–0.05) for only cows.

## Connected components analysis

**Holding level.** The number of nodes included in the largest strongly connected component (LSCC) represented 44% of the nodes of the global network for all cattle and 21% for cows (Table 4). Holdings included in both LSCCs were distributed all over the country (Fig 3).

In the case of annual networks, the average size of the LSCCs in holdings was 8,635 for all cattle (range: 8,073–9,282) and 1,097 for cows (range: 980–1,319), which represents approximately 21% and 4.3% of the total number of nodes for all cattle and cows (Fig 2). For the monthly networks, the average size of the LSCCs was 139 for all cattle (range: 18–326) and 30 for cows (range: 5–77); this average represented 1.5% of the average total number of nodes for all cattle and 0.8% of the average total number of nodes for cows. The LSCCs size showed a seasonality mainly for the all cattle networks: it was higher from July to October (S3 Fig).

A

<figure><img src="image_7.png" /></figure>

B

<figure><img src="image_8.png" /></figure>

C

<figure><img src="image_9.png" /></figure>

D

<figure><img src="image_10.png" /></figure>

**Fig 3.** Spatial distribution of the holdings in the largest strongly and weakly connected components. Largest strongly connected component (LSCC) (A): all cattle, (B): cows and largest weakly connected component (LWCC) (C): all cattle, (D): cows for the global network (aggregated nodes and links from 2014 to 2018). Percentage of holdings in each district corresponds to the number of holdings belonging to the largest component over the size of that largest component.

https://doi.org/10.1371/journal.pone.0278999.g003
The largest weakly connected component (LWCC) included almost all nodes in the global network for all cattle (97%) and (88%) for cows (Table 4, Fig 3). For the annual networks, the LWCC average size was 38,632 nodes for all cattle (range: 37,496–40,561) and 18,054 nodes for cows (range: 17,413–18,893), representing 93% and 71% of the average total number of nodes for all cattle and cows, respectively. For the monthly networks, the LWCC had a mean of 5,688 nodes for all cattle (range: 906–10,810) and 1,084 nodes for cows (range: 354–2,239), representing 58% and 27% of the average total number of nodes for all cattle and cows.

**District level.** All districts were included in the global LSCC and LWCC for all cattle and cow networks (Table 4). In the annual networks, around 97% of all districts were included in the LSCC for all cattle and only cow networks. For the monthly LSCC network, an average of 87% of the total number of nodes was observed for all cattle networks, and 65% for only cow networks. Almost all districts were included in the LWCC of all the annual and monthly networks.

Communities (global networks)

At the holding level, the first three communities represented 40% of the total number of nodes for the all cattle global network and 38% for the cow global network (Table 4, Fig 4). The spatial distribution of the holdings included in the first community for both global networks covered most of the country.

At the district level, there were fewer communities (Table 4) and the districts belonging to the first three communities were more geographically clustered (Fig 5), representing 92% of

<figure><img src="image_6.png" /><figcaption>**Fig 4.** Spatial distribution of the first three communities of the global networks at the holding level. Communities (A-B-C): all cattle and (D-E-F): only cows in Paraguay (aggregated nodes and links from 2014 to 2018). Percentage of holdings in each district corresponds to the number of holdings belonging to the community over the size of that community.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g004
The largest weakly connected component (LWCC) included almost all nodes in the global network for all cattle (97%) and (88%) for cows (Table 4, Fig 3). For the annual networks, the LWCC average size was 38,632 nodes for all cattle (range: 37,496–40,561) and 18,054 nodes for cows (range: 17,413–18,893), representing 93% and 71% of the average total number of nodes for all cattle and cows, respectively. For the monthly networks, the LWCC had a mean of 5,688 nodes for all cattle (range: 906–10,810) and 1,084 nodes for cows (range: 354–2,239), representing 58% and 27% of the average total number of nodes for all cattle and cows.

**District level.** All districts were included in the global LSCC and LWCC for all cattle and cow networks (Table 4). In the annual networks, around 97% of all districts were included in the LSCC for all cattle and only cow networks. For the monthly LSCC network, an average of 87% of the total number of nodes was observed for all cattle networks, and 65% for only cow networks. Almost all districts were included in the LWCC of all the annual and monthly networks.

Communities (global networks)

At the holding level, the first three communities represented 40% of the total number of nodes for the all cattle global network and 38% for the cow global network (Table 4, Fig 4). The spatial distribution of the holdings included in the first community for both global networks covered most of the country.

At the district level, there were fewer communities (Table 4) and the districts belonging to the first three communities were more geographically clustered (Fig 5), representing 92% of

<figure><img src="image_11.png" /><figcaption>**Fig 4.** Spatial distribution of the first three communities of the global networks at the holding level. Communities (A-B-C): all cattle and (D-E-F): only cows in Paraguay (aggregated nodes and links from 2014 to 2018). Percentage of holdings in each district corresponds to the number of holdings belonging to the community over the size of that community.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g004
A

B

<figure><img src="image_7.png" /><figcaption>Fig 5. Spatial distribution of the first three communities of the global networks at the district level. (A) All cattle and (B) only cows. Nodes and links were aggregated from 2014 to 2018.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g005

the total number of nodes for the all cattle global network and 63% for the only cow global network.

## Network indicators

**Centrality indicators.** At the holding level, the node degrees in the global network for all cattle ranged from 1 to 4,669, with an average value of 10.17 (Table 4). This average value was lower for the global cow network (4.42), with degrees ranging from 1 to 3,260. Average in-degree and out-degree values had the same values for the global networks, however, the maximum value was higher for the in-degree. Average betweenness and closeness were low and similar for both networks. However, when distinguishing the nodes by type of holding (farms vs markets), significantly higher values of the three centrality indicators were found for markets for all cattle (Wilcoxon's tests, *p*<0.0001) (Fig 6). Centrality indicators for the annual networks were similar to those for the global networks (Fig 7). The average of the node degrees for the five years ranged from 4.23 to 4.56 for all cattle, and from 2.36 to 2.50 for only cows; the average in-degree was of 2.12 for all cattle and 1.18 for only cows for each year; the out-degree value was the same for each year (2.284 for all cattle and 1.25 for only cows); the average betweenness 1.32·10⁻⁹ and 1.78·10⁻⁹ for all cattle, and 5·10⁻¹⁰ and 8.29·10⁻¹⁰ for only cows; and the average closeness 0.15 and 0.16 for all cattle, and 0.15 and 0.16 for only cows. For the monthly networks, the average degree varied between 1.70 and 2.10 for all cattle; in cow networks the values were lower. Concerning betweenness, the values ranged from 3.61·10⁻⁷ to 2.48·10⁻⁵ for all cattle, and from 3.92·10⁻⁷ to 4.88·10⁻⁵ for only cows (S1 Fig).

At the district level, the node degrees in the global network for all cattle presented values between 2 and 466, with a mean value of 147 (Table 4); the values for only cow networks were
A

B

<figure><img src="image_12.png" /><figcaption>Fig 5. Spatial distribution of the first three communities of the global networks at the district level. (A) All cattle and (B) only cows. Nodes and links were aggregated from 2014 to 2018.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g005

the total number of nodes for the all cattle global network and 63% for the only cow global network.

## Network indicators

**Centrality indicators.** At the holding level, the node degrees in the global network for all cattle ranged from 1 to 4,669, with an average value of 10.17 (Table 4). This average value was lower for the global cow network (4.42), with degrees ranging from 1 to 3,260. Average in-degree and out-degree values had the same values for the global networks, however, the maximum value was higher for the in-degree. Average betweenness and closeness were low and similar for both networks. However, when distinguishing the nodes by type of holding (farms vs markets), significantly higher values of the three centrality indicators were found for markets for all cattle (Wilcoxon's tests, *p*<0.0001) (Fig 6). Centrality indicators for the annual networks were similar to those for the global networks (Fig 7). The average of the node degrees for the five years ranged from 4.23 to 4.56 for all cattle, and from 2.36 to 2.50 for only cows; the average in-degree was of 2.12 for all cattle and 1.18 for only cows for each year; the out-degree value was the same for each year (2.284 for all cattle and 1.25 for only cows); the average betweenness 1.32·10⁻⁹ and 1.78·10⁻⁹ for all cattle, and 5·10⁻¹⁰ and 8.29·10⁻¹⁰ for only cows; and the average closeness 0.15 and 0.16 for all cattle, and 0.15 and 0.16 for only cows. For the monthly networks, the average degree varied between 1.70 and 2.10 for all cattle; in cow networks the values were lower. Concerning betweenness, the values ranged from 3.61·10⁻⁷ to 2.48·10⁻⁵ for all cattle, and from 3.92·10⁻⁷ to 4.88·10⁻⁵ for only cows (S1 Fig).

At the district level, the node degrees in the global network for all cattle presented values between 2 and 466, with a mean value of 147 (Table 4); the values for only cow networks were
<figure><img src="image_8.png" /><figcaption>**Fig 6.** Distribution of centrality indicators for all cattle and cows in global networks differentiating farms and markets. (A) Degrees, (B) betweenness, and (C) closeness calculated in the largest strongly component (nodes and links aggregated from 2014 to 2018).</figcaption></figure>

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lower. Average values for betweenness for all cattle were 1.78·10⁻⁵ (0–3.10⁻⁴) and were higher for the only cow networks. Closeness ranged from 0.38 to 0.81 for all cattle, and from 0.32 to 0.72 for the only cow networks. For the annual networks, the average degree ranged from 63.83 to 77.26 for all cattle, and from 30.48 to 34.20 for only cow; the betweenness 2.34·10⁻⁵ to 2.52·10⁻⁵ for all cattle, and 3.25·10⁻⁵ to 3.47·10⁻⁵ for only cows; and the closeness around 0.47 to 0.49 for all cattle and 0.40 to 0.41 for only cows. For monthly networks, the average degree presented values between 7.7 and 24, with lower values in cows (4.5–10.7), for betweenness values ranged from 0.005 to 0.008 for all cattle, and 0.003 to 0.009 for only cows.

**Other indicators.** Density values were slightly higher for the all cattle global networks compared to those for the only cow networks at the holding level (Table 4). The holdings in global networks were linked on average by fewer edges in the all cattle global network (average
<figure><img src="image_13.png" /><figcaption>**Fig 6.** Distribution of centrality indicators for all cattle and cows in global networks differentiating farms and markets. (A) Degrees, (B) betweenness, and (C) closeness calculated in the largest strongly component (nodes and links aggregated from 2014 to 2018).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g006

lower. Average values for betweenness for all cattle were 1.78·10⁻⁵ (0–3.10⁻⁴) and were higher for the only cow networks. Closeness ranged from 0.38 to 0.81 for all cattle, and from 0.32 to 0.72 for the only cow networks. For the annual networks, the average degree ranged from 63.83 to 77.26 for all cattle, and from 30.48 to 34.20 for only cow; the betweenness 2.34·10⁻⁵ to 2.52·10⁻⁵ for all cattle, and 3.25·10⁻⁵ to 3.47·10⁻⁵ for only cows; and the closeness around 0.47 to 0.49 for all cattle and 0.40 to 0.41 for only cows. For monthly networks, the average degree presented values between 7.7 and 24, with lower values in cows (4.5–10.7), for betweenness values ranged from 0.005 to 0.008 for all cattle, and 0.003 to 0.009 for only cows.

**Other indicators.** Density values were slightly higher for the all cattle global networks compared to those for the only cow networks at the holding level (Table 4). The holdings in global networks were linked on average by fewer edges in the all cattle global network (average
<figure><img src="image_9.png" /><figcaption>**Fig 7.** Network indicators for the annual networks for all cattle and only cows in Paraguay. Holding level (main graphs), district level (insets), all cattle (plain line) and only cows (dashed line).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g007

path length: 5.53) than in the only cow global network (average path length: 7.18) (Table 4). The diameter at the holding level was 20 for all cattle and 26 for only cows (Table 4). Assortativity was negative for all the networks at the holding level, indicating that nodes were more frequently linked to nodes with a different degree. Clustering coefficient values were lower for the networks at the holding level. The low reciprocity values obtained for all networks, mainly at the holding level, indicated that very few holdings received cattle from holdings to which they sent animals. (Fig 7). For the annual networks, densities ranged from 4.86·10⁻⁵⁵ to
<figure><img src="image_14.png" /><figcaption>**Fig 7.** Network indicators for the annual networks for all cattle and only cows in Paraguay. Holding level (main graphs), district level (insets), all cattle (plain line) and only cows (dashed line).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g007

path length: 5.53) than in the only cow global network (average path length: 7.18) (Table 4). The diameter at the holding level was 20 for all cattle and 26 for only cows (Table 4). Assortativity was negative for all the networks at the holding level, indicating that nodes were more frequently linked to nodes with a different degree. Clustering coefficient values were lower for the networks at the holding level. The low reciprocity values obtained for all networks, mainly at the holding level, indicated that very few holdings received cattle from holdings to which they sent animals. (Fig 7). For the annual networks, densities ranged from 4.86·10⁻⁵⁵ to
<figure><img src="image_10.png" /><figcaption>**Fig 8.** Degree distribution in a logarithmic scale for all cattle and cows in the global networks. (A) Holding level, (B) district level, all cattle (main graph) and cows (inset) (nodes and links were aggregated from 2014 to 2018).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g008

$5.73 \cdot 10^{-05}$ for all cattle and $4.47 \cdot 10^{-05}$ to $5.29 \cdot 10^{-05}$ for only cows. There were also on average the same number of steps as in the global networks for all cattle (average path length: 6.7–7.1) and only cows between 7.3 and 7.6. The diameter ranged from 24 to 29 for all cattle, and from 24 to 31 for only cows. The monthly networks had densities between $6.76 \cdot 10^{-5}$ and $4.63 \cdot 10^{-4}$ for all cattle and for only cows, the average path length at the holding level ranged from 2.5 to 8.2 for all cattle, and 2 to 6 for only cows, the diameter ranged from 7 to 25 for all cattle and for only cows (S1 Fig).

As for the district level, the density value was higher for the all cattle global network (Table 4). Average path length values followed the same trend, as well as the average path length values at the holding level (Table 4). The diameter was 4 for both all cattle and only cow networks (Table 4). For the annual networks, densities ranged from 0.107 to 0.130 for all cattle, and from 0.051 to 0.057 for only cows, and the diameter from 4 to 5 for all cattle, and 4 to 6 for only cows. For both the all cattle and only cows networks, the monthly network densities ranged from 0.01 to 0.04, and the diameters from 6 to 14.

**Global network topology**

**Holding level.** The degree distribution in a log-log scale for both the all cattle and only cow global networks showed a linear shape (Fig 8) and appeared heavy tailed, suggesting a scale-free structure for both types of network. However, there were only two orders of magnitude between the minimum degree and maximum degree, which do not allow to conclude about a scale-free property of the networks. Nevertheless, we calculated the variance to mean degree ratio, which is linked to the basic reproductive rate $R_0$ for an infection transmitted across a network [59]. The ratio was 127 for the all cattle network and 106 for the only cow network, indicating a strong heterogeneity between nodes. The clustering coefficient values of the real networks were much higher than those of the random networks (Table 5), while the values of the average path length were close, indicating that they exhibited small-world properties.

The power law exponent $\alpha$ value oscillated around 2.5 for degree values >21 for the all cattle global network, and degree values >13 for the only cow global network. Practically, for each annual network, the $\alpha$ value was around 2.5, for all cattle (2014: 2.5; 2015: 2.4; 2016: 2.5;
<figure><img src="image_15.png" /><figcaption>**Fig 8.** Degree distribution in a logarithmic scale for all cattle and cows in the global networks. (A) Holding level, (B) district level, all cattle (main graph) and cows (inset) (nodes and links were aggregated from 2014 to 2018).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g008

$5.73 \cdot 10^{-05}$ for all cattle and $4.47 \cdot 10^{-05}$ to $5.29 \cdot 10^{-05}$ for only cows. There were also on average the same number of steps as in the global networks for all cattle (average path length: 6.7-7.1) and only cows between 7.3 and 7.6. The diameter ranged from 24 to 29 for all cattle, and from 24 to 31 for only cows. The monthly networks had densities between $6.76 \cdot 10^{-5}$ and $4.63 \cdot 10^{-4}$ for all cattle and for only cows, the average path length at the holding level ranged from 2.5 to 8.2 for all cattle, and 2 to 6 for only cows, the diameter ranged from 7 to 25 for all cattle and for only cows (S1 Fig).

As for the district level, the density value was higher for the all cattle global network (Table 4). Average path length values followed the same trend, as well as the average path length values at the holding level (Table 4). The diameter was 4 for both all cattle and only cow networks (Table 4). For the annual networks, densities ranged from 0.107 to 0.130 for all cattle, and from 0.051 to 0.057 for only cows, and the diameter from 4 to 5 for all cattle, and 4 to 6 for only cows. For both the all cattle and only cows networks, the monthly network densities ranged from 0.01 to 0.04, and the diameters from 6 to 14.

**Global network topology**

**Holding level.** The degree distribution in a log-log scale for both the all cattle and only cow global networks showed a linear shape (Fig 8) and appeared heavy tailed, suggesting a scale-free structure for both types of network. However, there were only two orders of magnitude between the minimum degree and maximum degree, which do not allow to conclude about a scale-free property of the networks. Nevertheless, we calculated the variance to mean degree ratio, which is linked to the basic reproductive rate $R_0$ for an infection transmitted across a network [59]. The ratio was 127 for the all cattle network and 106 for the only cow network, indicating a strong heterogeneity between nodes. The clustering coefficient values of the real networks were much higher than those of the random networks (Table 5), while the values of the average path length were close, indicating that they exhibited small-world properties.

The power law exponent $\alpha$ value oscillated around 2.5 for degree values >21 for the all cattle global network, and degree values >13 for the only cow global network. Practically, for each annual network, the $\alpha$ value was around 2.5, for all cattle (2014: 2.5; 2015: 2.4; 2016: 2.5;
<table><caption>**Table 5. Clustering coefficient and average path length for the global real and random networks in Paraguay.** The nodes and links were aggregated from 2014 to 2018.</caption><thead><tr><th></th><th></th><th>Indicators</th><th>Real</th><th>Random</th></tr></thead><tbody><tr><td rowspan="4">Holding level</td><td rowspan="2">All Cattle</td><td>Clustering coefficient</td><td>0.023</td><td>0.00015</td></tr><tr><td>Average path length</td><td>5.531</td><td>5.076</td></tr><tr><td rowspan="2">Cows</td><td>Clustering coefficient</td><td>0.011</td><td>5.9.10<sup>-05</sup></td></tr><tr><td>Average path length</td><td>7.184</td><td>7.516</td></tr><tr><td rowspan="4">District level</td><td rowspan="2">All Cattle</td><td>Clustering coefficient</td><td>0.57</td><td>0.50</td></tr><tr><td>Average path length</td><td>1.79</td><td>1.49</td></tr><tr><td rowspan="2">Cows</td><td>Clustering coefficient</td><td>0.39</td><td>0.25</td></tr><tr><td>Average path length</td><td>2.03</td><td>1.74</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t005

2017: 2.4; 2018: 3.9) and the α value ranged from 2.5 to 2.6 for the only cow annual network. At the monthly level, the power law exponent α ranged from 2.5 to 3.0 for the degree values >21 (S4 Fig).

**District level.** The distribution of node degrees in global networks showed a unimodal distribution (Fig 8). The clustering coefficient and average path length of the real networks were similar to those of the random networks (Table 5), indicating that the global networks did not exhibit small-world properties.

## Percolation analysis

No thresholds at which the LSCC would rapidly disappear were identified at the global level for either all the cattle network or the only cow networks (Fig 9). At the annual level, from 4% to 6% of the nodes with higher betweenness should be removed to notice a fragmentation of the LSCC for the all cattle networks. For only cow networks, that threshold was around 3%.

<figure><img src="image_11.png" /><figcaption>**Fig 9. Percolation results for the global (inset) and annual networks (main graphs).** (A): all cattle, (B): only cows in Paraguay.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g009
<table><caption>**Table 5. Clustering coefficient and average path length for the global real and random networks in Paraguay.** The nodes and links were aggregated from 2014 to 2018.</caption><thead><tr><th></th><th></th><th>Indicators</th><th>Real</th><th>Random</th></tr></thead><tbody><tr><td rowspan="4">Holding level</td><td rowspan="2">All Cattle</td><td>Clustering coefficient</td><td>0.023</td><td>0.00015</td></tr><tr><td>Average path length</td><td>5.531</td><td>5.076</td></tr><tr><td rowspan="2">Cows</td><td>Clustering coefficient</td><td>0.011</td><td>5.9.10<sup>-05</sup></td></tr><tr><td>Average path length</td><td>7.184</td><td>7.516</td></tr><tr><td rowspan="4">District level</td><td rowspan="2">All Cattle</td><td>Clustering coefficient</td><td>0.57</td><td>0.50</td></tr><tr><td>Average path length</td><td>1.79</td><td>1.49</td></tr><tr><td rowspan="2">Cows</td><td>Clustering coefficient</td><td>0.39</td><td>0.25</td></tr><tr><td>Average path length</td><td>2.03</td><td>1.74</td></tr></tbody></table>

https://doi.org/10.1371/journal.pone.0278999.t005

2017: 2.4; 2018: 3.9) and the α value ranged from 2.5 to 2.6 for the only cow annual network. At the monthly level, the power law exponent α ranged from 2.5 to 3.0 for the degree values >21 (S4 Fig).

**District level.** The distribution of node degrees in global networks showed a unimodal distribution (Fig 8). The clustering coefficient and average path length of the real networks were similar to those of the random networks (Table 5), indicating that the global networks did not exhibit small-world properties.

## Percolation analysis

No thresholds at which the LSCC would rapidly disappear were identified at the global level for either all the cattle network or the only cow networks (Fig 9). At the annual level, from 4% to 6% of the nodes with higher betweenness should be removed to notice a fragmentation of the LSCC for the all cattle networks. For only cow networks, that threshold was around 3%.

<figure><img src="image_16.png" /><figcaption>**Fig 9. Percolation results for the global (inset) and annual networks (main graphs).** (A): all cattle, (B): only cows in Paraguay.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0278999.g009
However, it should be taken into account that the size of the initial annual LSCCs represented only 20% of all nodes for all cattle networks and 4% for only cow networks.

Discussion

Cattle movements in Paraguay between 2014 and 2018 were analyzed at two levels (holding and district) and at different temporal scales (monthly, annually, and globally), using the networks analysis methodology and network indicators. We also considered the implications for control and surveillance of two important diseases affecting cattle production through the use of: (i) all cattle data, as an approach to spread and control analysis in case of FMD re-introduction, and (ii) only cow data to describe relevant characteristics of the generated networks for surveillance and control of BB, an endemic disease, which mainly affects cows.

The fundamental characteristic of Paraguayan cattle raising is that it is extensive. Many cattle are raised in extensive farming systems in the western region (Chaco), which represents more than 60% of the country's area. The Chaco region has a semi-arid climate, with pastures of high productivity, compared to the east which is a low fertile area with constant rains. The eastern regions have tropical and subtropical forests with a pleasant climate. These regions concentrate most of the human population as well as semi-intensive dairy farms. This regional contrast is reflected in the spatial density of farms found in this study, with a higher farm density in the east of the country.

The cattle trade data analyzed showed that a larger number of cattle movements occurred in the eastern region (2 to 3 times), which may be linked to its higher farm density compared to Chaco. Most movements of cows and cattle excluding cows occurred between farms, but more cows were moved to slaughterhouses than cattle excluding cows. This could be explained by the fact that young cattle included in the cattle excluding cow category are often moved to other farms for breeding or fattening.

The analyzed cattle movements included only 50% of the recorded cattle farms of the country. It is very likely that farms that did not record any movement are small properties that trade cattle with other small farms in their vicinity or do not exchange cattle at all. This phenomenon has been studied in other South American countries by estimating the number of unrecorded movements, such as reciprocal practices between neighbors or illegal movements [60, 61]. Surveys could be implemented on small cattle farms to determine their trade practices. Based on JI node values, which were not very high, holdings involved in all cattle/only cow movements were stable from one year or month to another. Between 50% and 60% of the global nodes were present in less than two years or in 4 or less months. It is very likely that those nodes correspond to small family farms that do not exchange cattle very often and that nodes that appear every year or more often at the monthly level are commercial farms or markets that commercialize cattle throughout the year. Similarly, JI link values were low, indicating that cattle trade did not occur systematically between the same holdings.

Holding networks in Paraguay had a stable heavy-tailed degree distribution over time, low average path lengths and an important variance-to-mean ratio of degrees. These characteristics would allow for a rapid and persistent spread in the case of a possible introduction of a disease like FMD or considering an endemic disease such as brucellosis, which could potentially affect most nodes if appropriate control measures are not taken [38, 62]. This is because many low degree nodes are connected to high degree nodes known as “hubs” that act as centers increasing the existing connections within the network. Disassortativity of the networks confirmed the presence of hubs. For animal movements, the main hubs are markets, like we found in our study, and they are considered holdings involved in super-spreading events. Because of their central position in the network, hubs are highly susceptible to infection and they play a pivotal
However, it should be taken into account that the size of the initial annual LSCCs represented only 20% of all nodes for all cattle networks and 4% for only cow networks.

Discussion

Cattle movements in Paraguay between 2014 and 2018 were analyzed at two levels (holding and district) and at different temporal scales (monthly, annually, and globally), using the networks analysis methodology and network indicators. We also considered the implications for control and surveillance of two important diseases affecting cattle production through the use of: (i) all cattle data, as an approach to spread and control analysis in case of FMD re-introduction, and (ii) only cow data to describe relevant characteristics of the generated networks for surveillance and control of BB, an endemic disease, which mainly affects cows.

The fundamental characteristic of Paraguayan cattle raising is that it is extensive. Many cattle are raised in extensive farming systems in the western region (Chaco), which represents more than 60% of the country's area. The Chaco region has a semi-arid climate, with pastures of high productivity, compared to the east which is a low fertile area with constant rains. The eastern regions have tropical and subtropical forests with a pleasant climate. These regions concentrate most of the human population as well as semi-intensive dairy farms. This regional contrast is reflected in the spatial density of farms found in this study, with a higher farm density in the east of the country.

The cattle trade data analyzed showed that a larger number of cattle movements occurred in the eastern region (2 to 3 times), which may be linked to its higher farm density compared to Chaco. Most movements of cows and cattle excluding cows occurred between farms, but more cows were moved to slaughterhouses than cattle excluding cows. This could be explained by the fact that young cattle included in the cattle excluding cow category are often moved to other farms for breeding or fattening.

The analyzed cattle movements included only 50% of the recorded cattle farms of the country. It is very likely that farms that did not record any movement are small properties that trade cattle with other small farms in their vicinity or do not exchange cattle at all. This phenomenon has been studied in other South American countries by estimating the number of unrecorded movements, such as reciprocal practices between neighbors or illegal movements [60, 61]. Surveys could be implemented on small cattle farms to determine their trade practices. Based on JI node values, which were not very high, holdings involved in all cattle/only cow movements were stable from one year or month to another. Between 50% and 60% of the global nodes were present in less than two years or in 4 or less months. It is very likely that those nodes correspond to small family farms that do not exchange cattle very often and that nodes that appear every year or more often at the monthly level are commercial farms or markets that commercialize cattle throughout the year. Similarly, JI link values were low, indicating that cattle trade did not occur systematically between the same holdings.

Holding networks in Paraguay had a stable heavy-tailed degree distribution over time, low average path lengths and an important variance-to-mean ratio of degrees. These characteristics would allow for a rapid and persistent spread in the case of a possible introduction of a disease like FMD or considering an endemic disease such as brucellosis, which could potentially affect most nodes if appropriate control measures are not taken [38, 62]. This is because many low degree nodes are connected to high degree nodes known as “hubs” that act as centers increasing the existing connections within the network. Disassortativity of the networks confirmed the presence of hubs. For animal movements, the main hubs are markets, like we found in our study, and they are considered holdings involved in super-spreading events. Because of their central position in the network, hubs are highly susceptible to infection and they play a pivotal
role in the spread and maintenance of infection [63], so targeted surveillance and control methods applied in these holdings could provide effective benefits for disease control.

Many countries in South America have used network analysis as a veterinary epidemiological tool. For example, the analysis of static annual cattle networks in Uruguay made it possible to identify potential surveillance and control measures based on the heterogeneity of movement patterns and the identification of farms that could be involved in possible super-spread-ing events through indicators of centrality [64]. Likewise, in the case of cattle in Argentina, movements with high risk were identified for the months of April and June due to animal management characteristics. Districts with high degrees of connection were identified to plan possible future control measures [65]. In Brazil, suspension of vaccination against FMD was proposed in 2017 and therefore, several investigations were conducted, including a study on cattle movements. The results showed that connectivity and thus FMD transmission could be reduced with the elimination of nodes with high intermediation [60, 66].

The size of the LSCC has been considered an estimate of the lower bound of the maximum epidemic size in case of introduction of an exotic disease [50, 55]. The LSCC covered 44% of the holdings for the all cattle network at the global level, and had a wide geographic distribution across the country. This value is not far from that found for the holding network in Uruguay (51%) [64]. In contrast, at the district level, the LSCC for all cattle included all the districts in Paraguay, while in Argentina it included between 64% and 70% according to the season in the studied year [65]. At the monthly level, larger sizes of the LSCC of the all cattle networks were found between July and October, the period when young cattle are moved to fattening holdings. This could be a high risk period for FMD propagation.

Several studies have shown that performing node removal in a network with scale-free properties reduces the vulnerability of the network and limits the scope of a potential epidemic, as these networks tend to become unstructured upon node removal [39, 42]. We found that at the global level the LSCC would not be easily fragmented by removing the nodes with higher betweenness of the global networks at the holding level, which means that controlling the long-distance (i.e. trade-mediated) spread of FMD would imply the total stoppage of commercial cattle activities. This can be attributed to the small-world properties that the global networks exhibited at the holding level: even after the hubs were removed, the high clustering coefficient allowed the LSCC size to remain high. The studies conducted in other countries in South America have shown that cattle trade networks displayed scale-free properties for the whole country (Uruguay, Argentina) [65], or at a regional level (Mato Grosso do Sul in Brazil) [60]. An outbreak of an FMD serotype not covered by the vaccine currently implemented in Paraguay would imply large economic losses for the livestock sector. This concern is shared by neighboring countries that have also conducted network analyses of cattle movements. A shared characteristic of all these countries is that cattle raising is one of the main production sectors and that the risk of transborder spread of a highly transmissible disease, such as FMD, is not negligible, as has been shown in studies aimed at establishing FMD risk areas [66, 67].

The presence of properties similar to small-world networks and an important variance-to-mean ratio of degrees, at the holding level, for the global only cow network in Paraguay, suggests that trade could allow BB, like FMD, to spread far from an outbreak through markets, but also locally. In terms of control of BB and in a context of limited resources, community identification could allow the authorities to first target control measures in the less affected communities, in order to gradually constitute brucellosis-free subpopulations, which could later provide healthy animals to other communities. Communities at the district level could also facilitate the enforcement of control measures by zones in the country. Control measures could include a vaccination program and the requirement for BB vaccination certificates when trading cattle.
role in the spread and maintenance of infection [63], so targeted surveillance and control methods applied in these holdings could provide effective benefits for disease control.

Many countries in South America have used network analysis as a veterinary epidemiological tool. For example, the analysis of static annual cattle networks in Uruguay made it possible to identify potential surveillance and control measures based on the heterogeneity of movement patterns and the identification of farms that could be involved in possible super-spread-ing events through indicators of centrality [64]. Likewise, in the case of cattle in Argentina, movements with high risk were identified for the months of April and June due to animal management characteristics. Districts with high degrees of connection were identified to plan possible future control measures [65]. In Brazil, suspension of vaccination against FMD was proposed in 2017 and therefore, several investigations were conducted, including a study on cattle movements. The results showed that connectivity and thus FMD transmission could be reduced with the elimination of nodes with high intermediation [60, 66].

The size of the LSCC has been considered an estimate of the lower bound of the maximum epidemic size in case of introduction of an exotic disease [50, 55]. The LSCC covered 44% of the holdings for the all cattle network at the global level, and had a wide geographic distribution across the country. This value is not far from that found for the holding network in Uruguay (51%) [64]. In contrast, at the district level, the LSCC for all cattle included all the districts in Paraguay, while in Argentina it included between 64% and 70% according to the season in the studied year [65]. At the monthly level, larger sizes of the LSCC of the all cattle networks were found between July and October, the period when young cattle are moved to fattening holdings. This could be a high risk period for FMD propagation.

Several studies have shown that performing node removal in a network with scale-free properties reduces the vulnerability of the network and limits the scope of a potential epidemic, as these networks tend to become unstructured upon node removal [39, 42]. We found that at the global level the LSCC would not be easily fragmented by removing the nodes with higher betweenness of the global networks at the holding level, which means that controlling the long-distance (i.e. trade-mediated) spread of FMD would imply the total stoppage of commercial cattle activities. This can be attributed to the small-world properties that the global networks exhibited at the holding level: even after the hubs were removed, the high clustering coefficient allowed the LSCC size to remain high. The studies conducted in other countries in South America have shown that cattle trade networks displayed scale-free properties for the whole country (Uruguay, Argentina) [65], or at a regional level (Mato Grosso do Sul in Brazil) [60]. An outbreak of an FMD serotype not covered by the vaccine currently implemented in Paraguay would imply large economic losses for the livestock sector. This concern is shared by neighboring countries that have also conducted network analyses of cattle movements. A shared characteristic of all these countries is that cattle raising is one of the main production sectors and that the risk of transborder spread of a highly transmissible disease, such as FMD, is not negligible, as has been shown in studies aimed at establishing FMD risk areas [66, 67].

The presence of properties similar to small-world networks and an important variance-to-mean ratio of degrees, at the holding level, for the global only cow network in Paraguay, suggests that trade could allow BB, like FMD, to spread far from an outbreak through markets, but also locally. In terms of control of BB and in a context of limited resources, community identification could allow the authorities to first target control measures in the less affected communities, in order to gradually constitute brucellosis-free subpopulations, which could later provide healthy animals to other communities. Communities at the district level could also facilitate the enforcement of control measures by zones in the country. Control measures could include a vaccination program and the requirement for BB vaccination certificates when trading cattle.
We used static networks that do not take into account the temporality of movements that could be fundamental to understanding disease dynamics. However, static networks are appropriate and widely used in veterinary epidemiology to understand network topology [68, 69], which was also the case in our study. Nevertheless, future studies on cattle movement data in Paraguay should integrate temporal network methods. For simplicity reasons we only considered non-weighted networks in the present study. Using the number of traded animals as link weights may change the results obtained as has been reported by some authors [70]. Concerning FMD, we have only considered cattle, but this disease also affects pigs and small ruminants. In addition, there are other transmission routes, more local than trade, between farms that raise susceptible species (airborne contagion, movement of people, vehicles and livestock equipment). These elements should be taken into account to understand the risk of FMD diffusion in Paraguay. However, as cattle is the main species raised in Paraguay, our study allowed us to analyze the main risk of FMD virus dissemination over long distances, induced by cattle trade.

In conclusion, the networks of cattle movements in Paraguay have properties similar to and small-world networks and an important variance-to-mean ratio of degrees that would favor the spread of animal infectious diseases in the country. The spread of an exotic FMD serotype would be difficult to control, and therefore effective surveillance measures should be implemented. Control of animal movements at the borders should be among the measures to enforce as part of a transborder FMD surveillance program with Brazil and Argentina, as has been suggested previously [66, 67]. Regarding BB control, scale-free and small-world properties should also be taken into account when designing control protocols.

**Supporting information**

**S1 Fig. Monthly network indicators from 2014 to 2018 in Paraguay.** Holding level (main graphs), district levels (insets), all cattle (plain lines) and only cows (dashed lines).
(TIFF)

**S2 Fig. Monthly Jaccard index values for nodes and links from 2014 to 2018 in Paraguay.**
Holding level (main graphs), district levels (insets), all cattle (plain lines) and only cows
(dashed lines).
(TIFF)

**S3 Fig. Monthly largest strongly connected component size at the holding level from 2014 to 2018 in Paraguay.** (A): All cattle, (B): Only cows, annual networks.
(TIFF)

**S4 Fig. Monthly power law exponent values at the holding level from 2014 to 2018 in Paraguay.** All cattle (plain lines) and only cows (dashed lines).
(TIFF)

**Acknowledgments**

We thank the Official Veterinary Service (SENACSA), especially the General Directorate of Animal Health, Identity and Traceability (DIGESIT), the General Directorate of Technical Services (DIGESETEC), and the General Directorate of Quality and Safety of Animal Products (DIGECIPOA), for providing the data used in this work.

**Author Contributions**

**Conceptualization:** Amaias Avalos, Benoit Durand, Gina Zanella.
We used static networks that do not take into account the temporality of movements that could be fundamental to understanding disease dynamics. However, static networks are appropriate and widely used in veterinary epidemiology to understand network topology [68, 69], which was also the case in our study. Nevertheless, future studies on cattle movement data in Paraguay should integrate temporal network methods. For simplicity reasons we only considered non-weighted networks in the present study. Using the number of traded animals as link weights may change the results obtained as has been reported by some authors [70]. Concerning FMD, we have only considered cattle, but this disease also affects pigs and small ruminants. In addition, there are other transmission routes, more local than trade, between farms that raise susceptible species (airborne contagion, movement of people, vehicles and livestock equipment). These elements should be taken into account to understand the risk of FMD diffusion in Paraguay. However, as cattle is the main species raised in Paraguay, our study allowed us to analyze the main risk of FMD virus dissemination over long distances, induced by cattle trade.

In conclusion, the networks of cattle movements in Paraguay have properties similar to and small-world networks and an important variance-to-mean ratio of degrees that would favor the spread of animal infectious diseases in the country. The spread of an exotic FMD serotype would be difficult to control, and therefore effective surveillance measures should be implemented. Control of animal movements at the borders should be among the measures to enforce as part of a transborder FMD surveillance program with Brazil and Argentina, as has been suggested previously [66, 67]. Regarding BB control, scale-free and small-world properties should also be taken into account when designing control protocols.

**Supporting information**

**S1 Fig. Monthly network indicators from 2014 to 2018 in Paraguay.** Holding level (main graphs), district levels (insets), all cattle (plain lines) and only cows (dashed lines).
(TIFF)

**S2 Fig. Monthly Jaccard index values for nodes and links from 2014 to 2018 in Paraguay.**
Holding level (main graphs), district levels (insets), all cattle (plain lines) and only cows
(dashed lines).
(TIFF)

**S3 Fig. Monthly largest strongly connected component size at the holding level from 2014 to 2018 in Paraguay.** (A): All cattle, (B): Only cows, annual networks.
(TIFF)

**S4 Fig. Monthly power law exponent values at the holding level from 2014 to 2018 in Paraguay.** All cattle (plain lines) and only cows (dashed lines).
(TIFF)

**Acknowledgments**

We thank the Official Veterinary Service (SENACSA), especially the General Directorate of Animal Health, Identity and Traceability (DIGESIT), the General Directorate of Technical Services (DIGESETEC), and the General Directorate of Quality and Safety of Animal Products (DIGECIPOA), for providing the data used in this work.

**Author Contributions**

**Conceptualization:** Amaias Avalos, Benoit Durand, Gina Zanella.
**Data curation:** Amaias Avalos, José Naranjo, Victor Maldonado, Gina Zanella.

**Formal analysis:** Amaias Avalos, Benoit Durand, Gina Zanella.

**Investigation:** Amaias Avalos.

**Methodology:** Amaias Avalos, Benoit Durand, Gina Zanella.

**Writing – review & editing:** Amaias Avalos, Benoit Durand, Laetitia Canini, Gina Zanella.

## References

1. Fèvre EM, Bronsvoort BMDC, Hamilton KA, Cleaveland S. Animal movements and the spread of infectious diseases. *Trends Microbiol. 2006 Mar 1; 14(3):125–31.* https://doi.org/10.1016/j.tim.2006.01.004 PMID: 16460942

2. Thanidtha Te-chaniyom S.N., Watthanakul M, Choomkasean P, Chuxnum T, Smithsuwan P, Pimprapai W HS. An Investigation of Human Brucellosis and Goat Farm Network Analysis in Ratchaburi Province, 2013. Outbreak Surveillance Investig Rep [Internet]. 2015 Jun [cited 2021 Sep 22]; 8(2):7–12. Available from: https://www.researchgate.net/publication/341553259_An_Investigation_of_Human_Brucellosis_and_Goat_Farm_Network_Analysis_in_Ratchaburi_Province_2013

3. Kumar Khurana S, Sehrawat A, Tiwari R, Prasad M, Gulati B, Zubair Shabbir M, et al. Bovine brucellosis-a comprehensive review. *Vet Q [Internet]. 2021; 41(1):61–88. Available from: https://doi.org/10.1080/01652176.2020.1868616 PMID: 33353489

4. Cipullo RI, Grisi-Filho JHH, Dias RA, Ferreira F, Neto JSF, Gonçalves VSP, et al. Cattle movement network, herd size, and bovine brucellosis in the State of Mato Grosso, Brazil. *Semin Ciências Agrárias [Internet]. 2016 Nov 9 [cited 2021 Sep 21];37(5Supl2):3777–92. Available from: https://www.uel.br/revistas/uel/index.php/semagrarias/article/view/27206

5. Sherman D. The spread of pathogens through trade in small ruminants and their products. *Rev Sci Tech [Internet]. 2011 [cited 2021 Sep 21]; 30(1):207–17. Available from: https://pubmed.ncbi.nlm.nih.gov/21809765/ https://doi.org/10.20506/rst.30.1.2036 PMID: 21809765

6. Correa Melo E, Saraiva V, Astudillo V. Review of the status of foot and mouth disease in countries of South America and approaches to control and eradication. *OIE Rev Sci Tech. 2002; 21(3):429–36.* https://doi.org/10.20506/rst.21.3.1350 PMID: 12523684

7. Saraiva V. Foot-and-Mouth Disease in the Americas: Epidemiology and Ecologic Changes Affecting Distribution. *Ann N Y Acad Sci [Internet]. 2004 Oct 1 [cited 2021 Sep 21]; 1026(1):73–8. Available from: https://onlinelibrary.wiley.com/doi/full/10.1196/annals.1307.009 PMID: 15604472

8. Maradei E, Malirat V, Beascoechea C, Benitez E, Pedemonte A, Seki C, et al. Characterization of a type O foot-and-mouth disease virus re-emerging in the year 2011 in free areas of the Southern Cone of South America and cross-protection studies with the vaccine strain in use in the region. *Vet Microbiol [Internet]. 2013 Mar 23 [cited 2021 Sep 23]; 162(2–4):479–90. Available from: https://pubmed.ncbi.nlm.nih.gov/23182909/ https://doi.org/10.1016/j.vetmic.2012.10.035 PMID: 23182909

9. Brito BP, Rodriguez LL, Hammond JM, Pinto J, Perez AM. Review of the Global Distribution of Foot-and-Mouth Disease Virus from 2007 to 2014. *Transbound Emerg Dis [Internet]. 2017; 64(2):316–32. Available from: https://pubmed.ncbi.nlm.nih.gov/25996568/ https://doi.org/10.1111/tbed.12373 PMID: 25996568

10. Paton DJ, Nardo A Di, Knowles NJ, Wadsworth J, Pituco EM, Cosivi O, et al. The history of foot-and-mouth disease virus serotype C: the first known extinct serotype? *Virus Evol [Internet]. 2021; 7(1):9. Available from: http://orcid.org/0000-0002-9097-2262‡ https://doi.org/10.1093/ve/veab009 PMID: 35186323

11. Knight-Jones TJ D., McLaws M, Rushton J, D Knight-Jones International TJ. Foot-and-Mouth Disease Impact on Smallholders - What Do We Know, What Don't We Know and How Can We Find Out More? 2016; Available from: https://www.woah.org/en/what-we-do/animal-health-and-welfare/official-disease-status/ https://doi.org/10.1111/tbed.12507 PMID: 27167976

12. Knight-Jones TJD, Rushton J. The economic impacts of foot and mouth disease—What are they, how big are they and where do they occur? *Prev Vet Med. 2013 Nov 1; 112(3–4):161–73.* https://doi.org/10.1016/j.prevetmed.2013.07.013 PMID: 23958457

13. Clavijo A, Sanchez-Vazquez MJ, Buzanovsky LP, Martini M, Pompei JC, Cosivi O. Current Status and Future Prospects to Achieve Foot-and-Mouth Disease Eradication in South America. 2015.
**Data curation:** Amaias Avalos, José Naranjo, Victor Maldonado, Gina Zanella.

**Formal analysis:** Amaias Avalos, Benoit Durand, Gina Zanella.

**Investigation:** Amaias Avalos.

**Methodology:** Amaias Avalos, Benoit Durand, Gina Zanella.

**Writing – review & editing:** Amaias Avalos, Benoit Durand, Laetitia Canini, Gina Zanella.

## References

1. Fèvre EM, Bronsvoort BMDC, Hamilton KA, Cleaveland S. Animal movements and the spread of infectious diseases. *Trends Microbiol. 2006 Mar 1; 14(3):125–31.* https://doi.org/10.1016/j.tim.2006.01.004 PMID: 16460942

2. Thanidtha Te-chaniyom S.N., Watthanakul M, Choomkasean P, Chuxnum T, Smithsuwan P, Pimprapai W HS. An Investigation of Human Brucellosis and Goat Farm Network Analysis in Ratchaburi Province, 2013. Outbreak Surveillance Investig Rep [Internet]. 2015 Jun [cited 2021 Sep 22]; 8(2):7–12. Available from: https://www.researchgate.net/publication/341553259_An_Investigation_of_Human_Brucellosis_and_Goat_Farm_Network_Analysis_in_Ratchaburi_Province_2013

3. Kumar Khurana S, Sehrawat A, Tiwari R, Prasad M, Gulati B, Zubair Shabbir M, et al. Bovine brucellosis-a comprehensive review. *Vet Q [Internet]. 2021; 41(1):61–88. Available from: https://doi.org/10.1080/01652176.2020.1868616 PMID: 33353489

4. Cipullo RI, Grisi-Filho JHH, Dias RA, Ferreira F, Neto JSF, Gonçalves VSP, et al. Cattle movement network, herd size, and bovine brucellosis in the State of Mato Grosso, Brazil. *Semin Ciências Agrárias [Internet]. 2016 Nov 9 [cited 2021 Sep 21];37(5Supl2):3777–92. Available from: https://www.uel.br/revistas/uel/index.php/semagrarias/article/view/27206

5. Sherman D. The spread of pathogens through trade in small ruminants and their products. *Rev Sci Tech [Internet]. 2011 [cited 2021 Sep 21]; 30(1):207–17. Available from: https://pubmed.ncbi.nlm.nih.gov/21809765/ https://doi.org/10.20506/rst.30.1.2036 PMID: 21809765

6. Correa Melo E, Saraiva V, Astudillo V. Review of the status of foot and mouth disease in countries of South America and approaches to control and eradication. *OIE Rev Sci Tech. 2002; 21(3):429–36.* https://doi.org/10.20506/rst.21.3.1350 PMID: 12523684

7. Saraiva V. Foot-and-Mouth Disease in the Americas: Epidemiology and Ecologic Changes Affecting Distribution. *Ann N Y Acad Sci [Internet]. 2004 Oct 1 [cited 2021 Sep 21]; 1026(1):73–8. Available from: https://onlinelibrary.wiley.com/doi/full/10.1196/annals.1307.009 PMID: 15604472

8. Maradei E, Malirat V, Beascoechea C, Benitez E, Pedemonte A, Seki C, et al. Characterization of a type O foot-and-mouth disease virus re-emerging in the year 2011 in free areas of the Southern Cone of South America and cross-protection studies with the vaccine strain in use in the region. *Vet Microbiol [Internet]. 2013 Mar 23 [cited 2021 Sep 23]; 162(2–4):479–90. Available from: https://pubmed.ncbi.nlm.nih.gov/23182909/ https://doi.org/10.1016/j.vetmic.2012.10.035 PMID: 23182909

9. Brito BP, Rodriguez LL, Hammond JM, Pinto J, Perez AM. Review of the Global Distribution of Foot-and-Mouth Disease Virus from 2007 to 2014. *Transbound Emerg Dis [Internet]. 2017; 64(2):316–32. Available from: https://pubmed.ncbi.nlm.nih.gov/25996568/ https://doi.org/10.1111/tbed.12373 PMID: 25996568

10. Paton DJ, Nardo A Di, Knowles NJ, Wadsworth J, Pituco EM, Cosivi O, et al. The history of foot-and-mouth disease virus serotype C: the first known extinct serotype? *Virus Evol [Internet]. 2021; 7(1):9. Available from: http://orcid.org/0000-0002-9097-2262‡ https://doi.org/10.1093/ve/veab009 PMID: 35186323

11. Knight-Jones TJ D., McLaws M, Rushton J, D Knight-Jones International TJ. Foot-and-Mouth Disease Impact on Smallholders - What Do We Know, What Don't We Know and How Can We Find Out More? 2016; Available from: https://www.woah.org/en/what-we-do/animal-health-and-welfare/official-disease-status/ https://doi.org/10.1111/tbed.12507 PMID: 27167976

12. Knight-Jones TJD, Rushton J. The economic impacts of foot and mouth disease—What are they, how big are they and where do they occur? *Prev Vet Med. 2013 Nov 1; 112(3–4):161–73.* https://doi.org/10.1016/j.prevetmed.2013.07.013 PMID: 23958457

13. Clavijo A, Sanchez-Vazquez MJ, Buzanovsky LP, Martini M, Pompei JC, Cosivi O. Current Status and Future Prospects to Achieve Foot-and-Mouth Disease Eradication in South America. 2015.
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20. Peck ME, Chanachai K, Jenpanich C, Amonsin A, Alexander BH, Bender JB, et al. Seroprevalence of brucellosis in goats and sheep in Thailand: Results from the Thai National Brucellosis Surveillance System from 2013 to 2015 Ministry of Agriculture. 2018.

21. Dadar M, Tiwari R, Sharun K, Dhama K. Importance of brucellosis control programs of livestock on the improvement of one health. Vet Q. 2021; 41(1):137-51. https://doi.org/10.1080/01652176.2021.1894501 PMID: 33618618

22. Cárdenas L, Awada L, Tizzani P, Cáceres P, Casal J. Characterization and evolution of countries affected by bovine brucellosis (1996-2014). Transbound Emerg Dis [Internet]. 2019 May 1 [cited 2021 Aug 16]; 66(3):1280-90. Available from: https://pubmed.ncbi.nlm.nih.gov/30739391/ https://doi.org/10.1111/tbed.13144 PMID: 30739391

23. Lucero NE, Ayala SM, Escobar GJ, Jacob NR. Brucella isolated in humans and animals in Latin America from 1968 to 2006. Epidemiol Infect. 2008 Apr; 136(4):496-503. https://doi.org/10.1017/S0950268807008795 PMID: 17559694

24. Samartino L. Brucellosis in Argentina. Vet Microbiol [Internet]. 2002 Dec 20 [cited 2021 Aug 16]; 90(1-4):71-80. Available from: https://pubmed.ncbi.nlm.nih.gov/12414136/ https://doi.org/10.1016/s0378-1135(02)00247-x PMID: 12414136

25. Aznar MN, Samartino LE, Humblet MF, Saegerman C. Bovine Brucellosis in Argentina and Bordering Countries: Update. Transbound Emerg Dis. 2014 Apr; 61(2):121-33. https://doi.org/10.1111/tbed.12018 PMID: 23046031

26. Poester FP, Gonçalves VSP, Lage AP. Brucellosis in Brazil. Vet Microbiol. 2002 Dec 20; 90(1-4):55-62. https://doi.org/10.1016/s0378-1135(02)00245-6 PMID: 12414134

27. Baumgarten D. Brucellosis: a short review of the disease situation in Paraguay. Vet Microbiol. 2002 Dec 20; 90(1-4):63-9. https://doi.org/10.1016/s0378-1135(02)00246-8 PMID: 12414135

28. Bastos A, Dev Thakur S, Sarwan Kumar Himachal Pradesh Krishi Vishvavidyalaya C, Alejandro Ramirez I, Arenas-Gamboa AM, Avila-Granados LM, et al. Brucellosis in Colombia: Current Status and Challenges in the Control of an Endemic Disease. Front Vet Sci | www.frontiersin.org [Internet]. 2019; 6:321. Available from: www.frontiersin.org

29. Jori F. Sustained training mission. Food and mouth disease control Paraguay. Monday 19 July—friday 23 november 2012 [Internet]. Bruxelles, Belgique: European Commission; 2012 [cited 2021 Sep 12]. Available from: http://agritrop.cirad.fr/566661/1/document_566661.pdf

30. Geale DW, Barnett P V, Clarke GW, Davis J, Kasari TR, Geale Canadian DW. A Review of OIE Country Status Recovery UsingVaccinate-to-Live Versus Vaccinate-to-Die Foot-and-MouthDisease Response Policies II: Waiting Periods AfterEmergency Vaccination in FMD Free Countries. Transbound Emerg Dis. 2013; 62:388-406.

31. Naranjo J, Cosivi O. Elimination of foot-and-mouth disease in South America: lessons and challenges. R Soc [Internet]. 2013;12. Available from: http://dx.doi.org/10.1098/rstb.2012.0381

32. Savini L, Candeloro L, Conte A, De Massis F, Giovannini A. Development of a forecasting model for brucellosis spreading in the Italian cattle trade network aimed to prioritise the field interventions. 2017; Available from: https://doi.org/10.1371/journal.pone.0177313 PMID: 28654703
14. Rodriguez-Torres JG. International approach to eradication and surveillance for foot-and-mouth disease in the Americas. Ann N Y Acad Sci. 2000; 916:194-8. https://doi.org/10.1111/j.1749-6632.2000.tb05290.x PMID: 11193621

15. PAHO. Hemispheric Program for the Eradication of Foot-and-Mouth Disease PHEFA [Internet]. 2011 [cited 2021 Oct 19]. 51 p. Available from: https://iris.paho.org/handle/10665.2/49641

16. Animale OOM de la S. Terrestrial Code Online Access—OIE—World Organisation for Animal Health [Internet]. 2021 [cited 2021 Aug 16]. Available from: https://www.oie.int/en/what-we-do/standards/codes-and-manuals/terrestrial-code-online-access/

17. Godfroid J, Cloeckaert A, Liautard JP, Kohler S, Fretin D, Walravens K, et al. From the discovery of the Malta fever's agent to the discovery of a marine mammal reservoir, brucellosis has continuously been a re-emerging zoonosis. Vet Res [Internet]. 2005; 36:313-26. Available from: http://www.oie.int https://doi.org/10.1051/vetres:2005003 PMID: 15845228

18. Mamani M, Majzoobi MM, Keramat F, Varmaghani N, Moghimbeigi A. Seroprevalence of Brucellosis in Butchers, Veterinarians and Slaughterhouse Workers in Hamadan, Western Iran. J Res Health Sci [Internet]. 2018 Dec 1 [cited 2021 Sep 21];18(1). Available from: http://jrhs.umsha.ac.ir/index.php/JRHS/article/view/3738 PMID: 29777092

19. Pereira CR, de Oliveira IRC, de Oliveira LF, de Oliveira CSF, Lage AP, Dorneles EMS. Accidental exposure to Brucella abortus vaccines and occupational brucellosis among veterinarians in Minas Gerais state, Brazil. Transbound Emerg Dis. 2021 May 1; 68(3):1363-76. https://doi.org/10.1111/tbed.13797 PMID: 32810924

20. Peck ME, Chanachai K, Jenpanich C, Amonsin A, Alexander BH, Bender JB, et al. Seroprevalence of brucellosis in goats and sheep in Thailand: Results from the Thai National Brucellosis Surveillance System from 2013 to 2015 Ministry of Agriculture. 2018.

21. Dadar M, Tiwari R, Sharun K, Dhama K. Importance of brucellosis control programs of livestock on the improvement of one health. Vet Q. 2021; 41(1):137-51. https://doi.org/10.1080/01652176.2021.1894501 PMID: 33618618

22. Cárdenas L, Awada L, Tizzani P, Cáceres P, Casal J. Characterization and evolution of countries affected by bovine brucellosis (1996-2014). Transbound Emerg Dis [Internet]. 2019 May 1 [cited 2021 Aug 16]; 66(3):1280-90. Available from: https://pubmed.ncbi.nlm.nih.gov/30739391/ https://doi.org/10.1111/tbed.13144 PMID: 30739391

23. Lucero NE, Ayala SM, Escobar GJ, Jacob NR. Brucella isolated in humans and animals in Latin America from 1968 to 2006. Epidemiol Infect. 2008 Apr; 136(4):496-503. https://doi.org/10.1017/S0950268807008795 PMID: 17559694

24. Samartino L. Brucellosis in Argentina. Vet Microbiol [Internet]. 2002 Dec 20 [cited 2021 Aug 16]; 90(1-4):71-80. Available from: https://pubmed.ncbi.nlm.nih.gov/12414136/ https://doi.org/10.1016/s0378-1135(02)00247-x PMID: 12414136

25. Aznar MN, Samartino LE, Humblet MF, Saegerman C. Bovine Brucellosis in Argentina and Bordering Countries: Update. Transbound Emerg Dis. 2014 Apr; 61(2):121-33. https://doi.org/10.1111/tbed.12018 PMID: 23046031

26. Poester FP, Gonçalves VSP, Lage AP. Brucellosis in Brazil. Vet Microbiol. 2002 Dec 20; 90(1-4):55-62. https://doi.org/10.1016/s0378-1135(02)00245-6 PMID: 12414134

27. Baumgarten D. Brucellosis: a short review of the disease situation in Paraguay. Vet Microbiol. 2002 Dec 20; 90(1-4):63-9. https://doi.org/10.1016/s0378-1135(02)00246-8 PMID: 12414135

28. Bastos A, Dev Thakur S, Sarwan Kumar Himachal Pradesh Krishi Vishvavidyalaya C, Alejandro Ramirez I, Arenas-Gamboa AM, Avila-Granados LM, et al. Brucellosis in Colombia: Current Status and Challenges in the Control of an Endemic Disease. Front Vet Sci | www.frontiersin.org [Internet]. 2019; 6:321. Available from: www.frontiersin.org

29. Jori F. Sustained training mission. Food and mouth disease control Paraguay. Monday 19 July—friday 23 november 2012 [Internet]. Bruxelles, Belgique: European Commission; 2012 [cited 2021 Sep 12]. Available from: http://agritrop.cirad.fr/566661/1/document_566661.pdf

30. Geale DW, Barnett P V, Clarke GW, Davis J, Kasari TR, Geale Canadian DW. A Review of OIE Country Status Recovery UsingVaccinate-to-Live Versus Vaccinate-to-Die Foot-and-MouthDisease Response Policies II: Waiting Periods AfterEmergency Vaccination in FMD Free Countries. Transbound Emerg Dis. 2013; 62:388-406.

31. Naranjo J, Cosivi O. Elimination of foot-and-mouth disease in South America: lessons and challenges. R Soc [Internet]. 2013;12. Available from: http://dx.doi.org/10.1098/rstb.2012.0381

32. Savini L, Candeloro L, Conte A, De Massis F, Giovannini A. Development of a forecasting model for brucellosis spreading in the Italian cattle trade network aimed to prioritise the field interventions. 2017; Available from: https://doi.org/10.1371/journal.pone.0177313 PMID: 28654703
33. Martínez-López B, Perez AM, Sánchez-Vizcaíno JM. Social Network Analysis. Review of General Concepts and Use in Preventive Veterinary Medicine. Transbound Emerg Dis. 2008; 56:120.

34. Natale F, Giovannini A, Savini L, Palma D, Possenti L, Fiore G, et al. Network analysis of Italian cattle trade patterns and evaluation of risks for potential disease spread. Prev Vet Med. 2009 Dec 1; 92 (4):341-50. https://doi.org/10.1016/j.prevetmed.2009.08.026 PMID: 19775765

35. Wasserman S., Faust K. Social Network Analysis Methods and Applications. Cambridg. New York, NY; 1994.

36. van Andel M, Tildesley MJ, Gates MC. Challenges and opportunities for using national animal datasets to support foot-and-mouth disease control. Transbound Emerg Dis. 2021 Jul 1; 68(4):1800-13. https://doi.org/10.1111/tbed.13858 PMID: 32986919

37. FAO. Food and Agriculture Organization of the United Nations—FAOSTAT statistical database [Internet]. 1997 [cited 2022 Jul 16]. Available from: https://search.library.wisc.edu/catalog/999890171702121/cite

38. Mweu MM, Fournié G, Halasa T, Toft N, Nielsen SS. Temporal characterisation of the network of Danish cattle movements and its implication for disease control: 2000–2009. Prev Vet Med. 2013 Jul 1; 110 (3-4):379–87. https://doi.org/10.1016/j.prevetmed.2013.02.015 PMID: 23473852

39. Dutta Ezanno, Vergu. Characteristics of the spatio-temporal network of cattle movements in France over a 5-year period. Prev Vet Med [Internet]. 2014 Nov 1 [cited 2021 Aug 16]; 117(1):79-94. Available from: https://pubmed.ncbi.nlm.nih.gov/25287322/

40. Knific T, Ocepek M, Kirbiš A, Lentz HHK. Implications of Cattle Trade for the Spread and Control of Infectious Diseases in Slovenia. Front Vet Sci. 2020 Jan 14;6. https://doi.org/10.3389/fvets.2019.00454 PMID: 31993442

41. Dubé C, Ribble C, Kelton D, Mcnab B. A Review of Network Analysis Terminology and its Application to Foot-and-Mouth Disease Modelling and Policy Development. Transbound Emerg Dis. 2008; 56(73-85).

42. Rautureau S, Dufour B, Durand B. Vulnerability of Animal Trade Networks to The Spread of Infectious Diseases: A Methodological Approach Applied to Evaluation and Emergency Control Strategies in Cattle, France, 2005. Transbound Emerg Dis [Internet]. 2005;120. Available from: http://igraph.

43. Hayer SS, VanderWaal K, Ranjan R, Biswal JK, Subramaniam S, Mohapatra JK, et al. Foot-and-mouth disease virus transmission dynamics and persistence in a herd of vaccinated dairy cattle in India. Trans-bound Emerg Dis [Internet]. 2018 Apr 1 [cited 2022 Nov 17]; 65(2):e404-15. Available from: https://onlinelibrary.wiley.com/doi/full/10.1111/tbed.12774 PMID: 29205858

44. Chis Ster I, Dodd PJ, Ferguson NM. Within-farm transmission dynamics of foot and mouth disease as revealed by the 2001 epidemic in Great Britain. Epidemics. 2012 Aug 1; 4(3):158-69. https://doi.org/10.1016/j.epidem.2012.07.002 PMID: 22939313

45. Newman M. Networks: An introduction. Oxford Uni. New York, USA; 2010. 1-784 p.

46. Freeman LC. Centrality in social networks conceptual clarification. Soc Networks. 1979 Jan 1; 1 (3):215-39.

47. Newman M. Mixing patterns in networks. Phys Rev E [Internet]. 2003 Feb 27 [cited 2021 Aug 17]; 67 (2):026126. Available from: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.67.026126 PMID: 12636767

48. Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nat 1998 3936684 [Internet]. 1998 Jun 4 [cited 2021 Nov 2]; 393(6684):440-2. Available from: https://www.nature.com/articles/30918 https://doi.org/10.1038/30918 PMID: 9623998

49. Kiss IZ, Green DM, Kao RR. The network of sheep movements within Great Britain: network properties and their implications for infectious disease spread. J R Soc Interface. 2006.

50. Kao RR, Danon L, Green DM, Kiss IZ. Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain. Proc R Soc B [Internet]. 2006; Available from: http://dx.doi/10.1098/rspb.2006.3505.

51. Pons P, Latapy M. Computing communities in large networks using random walks (long version). Comput Inf Sci—Isc 2005 [Internet]. 2005 Dec 12 [cited 2021 Oct 9];3733(2):20. Available from: https://arxiv.org/abs/physics/0512106v1

52. Barabási A.L. Linked. Penguin Bo. London, England; 2003.

53. Clauset A, Rohilla Shalizi C, J Newman ME. Power-Law Distributions in Empirical Data *. Soc Ind Appl Math [Internet]. 2009 [cited 2021 Aug 17]; Available from: http://www.siam.org/journals/sirev/51-4/71011.html

54. Erdős P, Rényi A. On the evolution of random graphs. Publ Math Inst Hungar Acad Sci. 1960; 5(17):61.

55. Dubé C, Ribble C, Kelton D, McNab B. Estimating potential epidemic size following introduction of a long-incubation disease in scale-free connected networks of milking-cow movements in Ontario,
33. Martínez-López B, Perez AM, Sánchez-Vizcaíno JM. Social Network Analysis. Review of General Concepts and Use in Preventive Veterinary Medicine. Transbound Emerg Dis. 2008; 56:120.

34. Natale F, Giovannini A, Savini L, Palma D, Possenti L, Fiore G, et al. Network analysis of Italian cattle trade patterns and evaluation of risks for potential disease spread. Prev Vet Med. 2009 Dec 1; 92 (4):341-50. https://doi.org/10.1016/j.prevetmed.2009.08.026 PMID: 19775765

35. Wasserman S., Faust K. Social Network Analysis Methods and Applications. Cambridg. New York, NY; 1994.

36. van Andel M, Tildesley MJ, Gates MC. Challenges and opportunities for using national animal datasets to support foot-and-mouth disease control. Transbound Emerg Dis. 2021 Jul 1; 68(4):1800-13. https://doi.org/10.1111/tbed.13858 PMID: 32986919

37. FAO. Food and Agriculture Organization of the United Nations—FAOSTAT statistical database [Internet]. 1997 [cited 2022 Jul 16]. Available from: https://search.library.wisc.edu/catalog/999890171702121/cite

38. Mweu MM, Fournié G, Halasa T, Toft N, Nielsen SS. Temporal characterisation of the network of Danish cattle movements and its implication for disease control: 2000–2009. Prev Vet Med. 2013 Jul 1; 110 (3-4):379–87. https://doi.org/10.1016/j.prevetmed.2013.02.015 PMID: 23473852

39. Dutta Ezanno, Vergu. Characteristics of the spatio-temporal network of cattle movements in France over a 5-year period. Prev Vet Med [Internet]. 2014 Nov 1 [cited 2021 Aug 16]; 117(1):79-94. Available from: https://pubmed.ncbi.nlm.nih.gov/25287322/

40. Knific T, Ocepek M, Kirbiš A, Lentz HHK. Implications of Cattle Trade for the Spread and Control of Infectious Diseases in Slovenia. Front Vet Sci. 2020 Jan 14;6. https://doi.org/10.3389/fvets.2019.00454 PMID: 31993442

41. Dubé C, Ribble C, Kelton D, Mcnab B. A Review of Network Analysis Terminology and its Application to Foot-and-Mouth Disease Modelling and Policy Development. Transbound Emerg Dis. 2008; 56(73-85).

42. Rautureau S, Dufour B, Durand B. Vulnerability of Animal Trade Networks to The Spread of Infectious Diseases: A Methodological Approach Applied to Evaluation and Emergency Control Strategies in Cattle, France, 2005. Transbound Emerg Dis [Internet]. 2005;120. Available from: http://igraph.

43. Hayer SS, VanderWaal K, Ranjan R, Biswal JK, Subramaniam S, Mohapatra JK, et al. Foot-and-mouth disease virus transmission dynamics and persistence in a herd of vaccinated dairy cattle in India. Trans-bound Emerg Dis [Internet]. 2018 Apr 1 [cited 2022 Nov 17]; 65(2):e404-15. Available from: https://onlinelibrary.wiley.com/doi/full/10.1111/tbed.12774 PMID: 29205858

44. Chis Ster I, Dodd PJ, Ferguson NM. Within-farm transmission dynamics of foot and mouth disease as revealed by the 2001 epidemic in Great Britain. Epidemics. 2012 Aug 1; 4(3):158-69. https://doi.org/10.1016/j.epidem.2012.07.002 PMID: 22939313

45. Newman M. Networks: An introduction. Oxford Uni. New York, USA; 2010. 1-784 p.

46. Freeman LC. Centrality in social networks conceptual clarification. Soc Networks. 1979 Jan 1; 1 (3):215-39.

47. Newman M. Mixing patterns in networks. Phys Rev E [Internet]. 2003 Feb 27 [cited 2021 Aug 17]; 67 (2):026126. Available from: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.67.026126 PMID: 12636767

48. Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nat 1998 3936684 [Internet]. 1998 Jun 4 [cited 2021 Nov 2]; 393(6684):440-2. Available from: https://www.nature.com/articles/30918 https://doi.org/10.1038/30918 PMID: 9623998

49. Kiss IZ, Green DM, Kao RR. The network of sheep movements within Great Britain: network properties and their implications for infectious disease spread. J R Soc Interface. 2006.

50. Kao RR, Danon L, Green DM, Kiss IZ. Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain. Proc R Soc B [Internet]. 2006; Available from: http://dx.doi/10.1098/rspb.2006.3505.

51. Pons P, Latapy M. Computing communities in large networks using random walks (long version). Comput Inf Sci—Isc 2005 [Internet]. 2005 Dec 12 [cited 2021 Oct 9];3733(2):20. Available from: https://arxiv.org/abs/physics/0512106v1

52. Barabási A.L. Linked. Penguin Bo. London, England; 2003.

53. Clauset A, Rohilla Shalizi C, J Newman ME. Power-Law Distributions in Empirical Data *. Soc Ind Appl Math [Internet]. 2009 [cited 2021 Aug 17]; Available from: http://www.siam.org/journals/sirev/51-4/71011.html

54. Erdős P, Rényi A. On the evolution of random graphs. Publ Math Inst Hungar Acad Sci. 1960; 5(17):61.

55. Dubé C, Ribble C, Kelton D, McNab B. Estimating potential epidemic size following introduction of a long-incubation disease in scale-free connected networks of milking-cow movements in Ontario,
Canada. Prev Vet Med [Internet]. 2011 May 1 [cited 2021 Aug 17]; 99(2-4):102-11. Available from: https://pubmed.ncbi.nlm.nih.gov/21388696/ https://doi.org/10.1016/j.prevetmed.2011.01.013 PMID: 21388696

56. Gábor Csárdi T N. The igraph software package for complex network research. Com-plex Syst [Internet]. 2006 [cited 2021 Aug 17];23. Available from: https://igraph.org

57. Wickham H. ggplot2. ggplot2. Springer New York; 2009.

58. R Core Team. R: A language and environment for statistical computing [Internet]. Vienna, Austria: R foundation for Statistical Computing; 2021. Available from: http://www.r-project.org

59. May RM, Anderson RM. Transmission dynamics of HIV infection. Nat 1987 3266109 [Internet]. 1987 Mar 1 [cited 2022 Nov 17]; 326(6109):137-42. Available from: https://www.nature.com/articles/326137a0

60. Menezes TC d., Luna I, Miranda SHG d. Network Analysis of Cattle Movement in Mato Grosso Do Sul (Brazil) and Implications for Foot-and-Mouth Disease. Front Vet Sci. 2020 Apr 29; 7. https://doi.org/10.3389/fvets.2020.00219 PMID: 32411738

61. Luís Giehl A, Mondardo M. Dinâmica e características da produção de bovinos para autoconsumo em santa catarina. Rev Grifos [Internet]. 2021 Mar 31 [cited 2021 Nov 24]; 30(54):292-314. Available from: http://bell.unochapeco.edu.br/revistas/index.php/grifos/article/view/5936

62. Marquetoux N, Stevenson MA, Wilson P, Ridler A, Heuer C. Using social network analysis to inform disease control interventions. Prev Vet Med [Internet]. 2016 Apr 1 [cited 2021 Aug 16]; 126:94-104. Available from: https://pubmed.ncbi.nlm.nih.gov/26883965/ https://doi.org/10.1016/j.prevetmed.2016.01.022 PMID: 26883965

63. Keeling MJ, Eames KTD. Networks and epidemic models [Internet]. Vol. 2, Journal of the Royal Society Interface. J R Soc Interface; 2005 [cited 2021 Aug 16]. p. 295-307. Available from: https://pubmed.ncbi.nlm.nih.gov/16849187/ https://doi.org/10.1098/rsif.2005.0051 PMID: 16849187

64. VanderWaal KL, Picasso C, Enns EA, Craft ME, Alvarez J, Fernandez F, et al. Network analysis of cattle movements in Uruguay: Quantifying heterogeneity for risk-based disease surveillance and control. Prev Vet Med. 2016 Jan 1; 123:12-22. https://doi.org/10.1016/j.prevetmed.2015.12.003 PMID: 26708252

65. Aznar MN, Stevenson MA, Zarich L, León EA. Analysis of cattle movements in Argentina, 2005. Prev Vet Med [Internet]. 2011 Feb [cited 2021 Aug 16];98(2-3):119-27. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0167587710003272

66. Amaral TB, Gond V, Tran A. Mapping the likelihood of foot-and-mouth disease introduction along the border between Brazil and Paraguay. Pesq agropec bras. 2016;(5):661-70.

67. Viali dos Santos D, Sousa Silva G, José Weber E, Hasenack H, Henrique Sautter Groff F, Todeschini B, et al. Identification of foot and mouth disease risk areas using a multi-criteria analysis approach. 2017; Available from: https://doi.org/10.1371/journal.pone.0178464

68. Tajbakhsh S, Coon J, Simmons D. Accessibility and delay in random temporal networks. Phys Rev E [Internet]. 2017 Sep 12 [cited 2021 Sep 20];96(3-1). Available from: https://pubmed.ncbi.nlm.nih.gov/29346936/ https://doi.org/10.1103/PhysRevE.96.032309 PMID: 29346936

69. Li A, Cornelius SP, Liu YY, Wang L, Barabási AL. The fundamental advantages of temporal networks. Science (80-). 2017 Nov 24; 358(6366):1042-6. https://doi.org/10.1126/science.aai7488 PMID: 29170233

70. Büttner K, Krieter J. Comparison of weighted and unweighted network analysis in the case of a pig trade network in Northern Germany. Prev Vet Med [Internet]. 2018 [cited 2022 Jul 16]; 156:49-57. Available from: https://doi.org/10.1016/j.prevetmed.2018.05.008 PMID: 29891145
Canada. Prev Vet Med [Internet]. 2011 May 1 [cited 2021 Aug 17]; 99(2-4):102-11. Available from: https://pubmed.ncbi.nlm.nih.gov/21388696/ https://doi.org/10.1016/j.prevetmed.2011.01.013 PMID: 21388696

56. Gábor Csárdi T N. The igraph software package for complex network research. Com-plex Syst [Internet]. 2006 [cited 2021 Aug 17];23. Available from: https://igraph.org

57. Wickham H. ggplot2. ggplot2. Springer New York; 2009.

58. R Core Team. R: A language and environment for statistical computing [Internet]. Vienna, Austria: R foundation for Statistical Computing; 2021. Available from: http://www.r-project.org

59. May RM, Anderson RM. Transmission dynamics of HIV infection. Nat 1987 3266109 [Internet]. 1987 Mar 1 [cited 2022 Nov 17]; 326(6109):137-42. Available from: https://www.nature.com/articles/326137a0

60. Menezes TC d., Luna I, Miranda SHG d. Network Analysis of Cattle Movement in Mato Grosso Do Sul (Brazil) and Implications for Foot-and-Mouth Disease. Front Vet Sci. 2020 Apr 29; 7. https://doi.org/10.3389/fvets.2020.00219 PMID: 32411738

61. Luís Giehl A, Mondardo M. Dinâmica e características da produção de bovinos para autoconsumo em santa catarina. Rev Grifos [Internet]. 2021 Mar 31 [cited 2021 Nov 24]; 30(54):292-314. Available from: http://bell.unochapeco.edu.br/revistas/index.php/grifos/article/view/5936

62. Marquetoux N, Stevenson MA, Wilson P, Ridler A, Heuer C. Using social network analysis to inform disease control interventions. Prev Vet Med [Internet]. 2016 Apr 1 [cited 2021 Aug 16]; 126:94-104. Available from: https://pubmed.ncbi.nlm.nih.gov/26883965/ https://doi.org/10.1016/j.prevetmed.2016.01.022 PMID: 26883965

63. Keeling MJ, Eames KTD. Networks and epidemic models [Internet]. Vol. 2, Journal of the Royal Society Interface. J R Soc Interface; 2005 [cited 2021 Aug 16]. p. 295-307. Available from: https://pubmed.ncbi.nlm.nih.gov/16849187/ https://doi.org/10.1098/rsif.2005.0051 PMID: 16849187

64. VanderWaal KL, Picasso C, Enns EA, Craft ME, Alvarez J, Fernandez F, et al. Network analysis of cattle movements in Uruguay: Quantifying heterogeneity for risk-based disease surveillance and control. Prev Vet Med. 2016 Jan 1; 123:12-22. https://doi.org/10.1016/j.prevetmed.2015.12.003 PMID: 26708252

65. Aznar MN, Stevenson MA, Zarich L, León EA. Analysis of cattle movements in Argentina, 2005. Prev Vet Med [Internet]. 2011 Feb [cited 2021 Aug 16];98(2-3):119-27. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0167587710003272

66. Amaral TB, Gond V, Tran A. Mapping the likelihood of foot-and-mouth disease introduction along the border between Brazil and Paraguay. Pesq agropec bras. 2016;(5):661-70.

67. Viali dos Santos D, Sousa Silva G, José Weber E, Hasenack H, Henrique Sautter Groff F, Todeschini B, et al. Identification of foot and mouth disease risk areas using a multi-criteria analysis approach. 2017; Available from: https://doi.org/10.1371/journal.pone.0178464

68. Tajbakhsh S, Coon J, Simmons D. Accessibility and delay in random temporal networks. Phys Rev E [Internet]. 2017 Sep 12 [cited 2021 Sep 20];96(3-1). Available from: https://pubmed.ncbi.nlm.nih.gov/29346936/ https://doi.org/10.1103/PhysRevE.96.032309 PMID: 29346936

69. Li A, Cornelius SP, Liu YY, Wang L, Barabási AL. The fundamental advantages of temporal networks. Science (80-). 2017 Nov 24; 358(6366):1042-6. https://doi.org/10.1126/science.aai7488 PMID: 29170233

70. Büttner K, Krieter J. Comparison of weighted and unweighted network analysis in the case of a pig trade network in Northern Germany. Prev Vet Med [Internet]. 2018 [cited 2022 Jul 16]; 156:49-57. Available from: https://doi.org/10.1016/j.prevetmed.2018.05.008 PMID: 29891145