From network analysis to risk analysis—An approach to risk-based surveillance for bovine tuberculosis in Minnesota, US

Accepted Manuscript Title: From network analysis to risk analysis - An approach to risk-based surveillance for bovine tuberculosis in Minnesota, US Author: J. Ribeiro-Lima E.A. Enns B. Thompson M.E. Craft S.J. Wells PII: DOI: Reference:

S0167-5877(14)00418-8 http://dx.doi.org/doi:10.1016/j.prevetmed.2014.12.007 PREVET 3705

To appear in:

PREVET

Received date: Revised date: Accepted date:

11-2-2014 14-11-2014 4-12-2014

Please cite this article as: Ribeiro-Lima, J., Enns, E.A., Thompson, B., Craft, M.E., Wells, S.J.,From network analysis to risk analysis - An approach to risk-based surveillance for bovine tuberculosis in Minnesota, US, Preventive Veterinary Medicine (2014), http://dx.doi.org/10.1016/j.prevetmed.2014.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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From network analysis to risk analysis - An approach to risk-based surveillance for bovine

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tuberculosis in Minnesota, US.

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Department of Veterinary Population Medicine, University of Minnesota College of Veterinary

Medicine, St Paul MN, United States; 2

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Division of Health Policy and Management, University of Minnesota School of Public Health,

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J. Ribeiro-Lima1, E.A. Enns2, B. Thompson3, M.E. Craft1, S.J. Wells1

Minneapolis MN, United States; 3

Minnesota Board of Animal Health, St. Paul MN, United States

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Corresponding author: Telephone: +351 919207502; email: [email protected] (J. Ribeiro-Lima)

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Current address: Faculdade de Medicina Veterinária, Universidade Lusófona de Humanidades e

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Tecnologias, Av. do Campo Grande, 376, 1749-024 Lisboa – Portugal.

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Abstract

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Bovine tuberculosis (bTB) was first detected in 2005 in cattle in northwestern Minnesota (MN)

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through slaughter surveillance. By the end of 2008, 12 cattle herds were infected with bTB, and

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the main cause for infection was determined to be the movement of infected animals between

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herds. Bovine tuberculosis was contained in a smaller area in northwestern Minnesota classified

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as modified accredited (MA), corresponding to a prevalence inferior to 0.1% in cattle. From

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January 2008 to 2011, all cattle movements within the bTB MA were recorded electronically.

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The primary objectives of this study was to characterize cattle movements within this region and

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identify cattle herds with higher risk of bTB introduction based on network parameters and

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known risk factors from the published literature. During the period that data was collected,

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57,460 cattle were moved in 3,762 movements corresponding to permits issued to 682 premises,

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mostly representing private farms, sale yards, slaughter facilities and county or state fairs.

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Although sale yards represented less than 2% of the premises (nodes), 60% of the movements

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were to or from a sale yard. The network showed an overall density of 0.4%, a clustering

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coefficient of 14.6% and a betweenness centralization index of 12.7%, reflecting the low

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connectivity of this cattle network. The degree distribution showed that 20% of nodes performed

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90% of the movements. Farms were ranked based on the total risk score and divided into high,

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medium, and low risk groups based on the score and its variability. The higher risk group

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included 14% (n=50) of the farms, corresponding to 80% of the cumulative risk for the farms in

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the bTB area. This analysis provides a baseline description about the contact structure of cattle

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movements in an area previously infected with bTB and develops a framework for a targeted

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surveillance approach for bTB to support future surveillance decisions.

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Keywords: Network analysis, cattle movements, bovine tuberculosis, target surveillance

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1. Introduction

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The State-Federal program for eradication of Bovine tuberculosis (bTB) in cattle

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populations in the US was initially developed in 1917 and has been efficient in reducing disease

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prevalence, nearly to the point of eradication (National Research Council, 1994). The backbone

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of the surveillance system for detecting infected animals is slaughter surveillance, which has an

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estimated median time-to-detection at the herd level of 5.75 years, after bTB is introduced into a

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herd (Fischer et al., 2005), and an estimated very low herd-level sensitivity (USDA-APHIS-VS,

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2009a). Individual animal ante-mortem tests for bTB are available; however, testing is not

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routinely performed. Currently, individual ante-mortem animal testing is only performed prior to 2      Page 2 of 41

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cattle movements from states or zones that are not bTB free or during disease eradication efforts

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in infected areas. The main problems with the current surveillance system include: (i) the long time-to-

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detection (often identifying disease years after its introduction into an initially disease-free

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population); and (ii) the unequal probability of inspection of cattle farms of different types and

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sizes, with large dairy herds being tested more frequently than small beef herds (for example,

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due to the former sending more cattle to slaughter) (USDA-APHIS-VS, 2009b). The delay in

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detection allows bTB to spread to other animals and other herds. Once detected, this results in

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high eradication costs due to the widespread herd tracing and animal depopulation that is

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required. In order to detect bTB cases earlier in disease free areas, and as a consequence

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minimize the spread of disease, factors associated with a greater risk of disease introduction or

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transmission should be incorporated into the surveillance system. In the field of animal health,

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risk is defined in the Animal Health Code (OIE) as “the likelihood of the occurrence and the

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likely magnitude of the biological and economic consequences of an adverse event or effect to

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animal or human health” (OIE, 2012). This is the concept behind risk-based surveillance

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programs, which seek to focus funding and resources toward subsets of the population with a

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higher risk of the health event of interest, improving surveillance system sensitivity and cost-

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effectiveness (Stärk et al., 2006).

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A recent assessment conducted by the United States Department of Agriculture (USDA)

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– Animal and Plant Health Inspection Service (APHIS) identified a variety of risk factors

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associated with bTB infection in US areas without a wildlife reservoir, including the importation

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and comingling of Mexican-origin steers, the management and biosecurity practices used by calf

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raisers for dairy replacement heifers, and the influx of purchased cattle (USDA-APHIS-VS, 3      Page 3 of 41

2009b). The role of cattle movement has also been identified to be of primary importance,

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particularly in low prevalence or disease-free areas, where disease can be introduced through the

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importation of cattle from infected areas (Bessell et al., 2012; Gilbert et al., 2005; Gopal et al.,

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2006). Because cattle movements are directed, since cattle moves from one farm to another and

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not in both directions, these risks (risk of becoming infected and likelihood of transmitting

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infection to other farms) may be different depending on a herd’s management factors. These

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include whether the herd engages primarily in selling or buying cattle, and the origin of the latter.

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Characterizing patterns of cattle movements before a disease outbreak occurs is thus critical to

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identifying which herds have the highest risk of infection and which would be most likely to

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transmit an infection to others. Furthermore, the identification of high risk herds, based on cattle

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movements, do not exclude the role of wildlife for disease spread after it is present, but highlight

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the importance of cattle movements as the primary source for disease introduction in a disease

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free area (Mintiens et al., 2008; Natale et al., 2009).

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Network analysis, a methodology arising from the social sciences with recent

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applications to the spread of human and animal infectious diseases, has proven to be an useful

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tool in understanding the structure of contacts within and between animal populations as well as

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the role of high risk herds in the transmission of infectious diseases in livestock (Bigras-Poulin et

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al., 2006; Dubé et al., 2008; Volkova et al., 2010). In a network analysis framework, a population

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is described in terms of a set of nodes and the edges that describe the interactions between them.

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In the case of describing the spread of bTB between cattle premises (e.g. herds, sale yards, fairs,

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etc), nodes represent cattle premises, where an edge between two herds represents the movement

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of animals from one premise to another and a potential pathway for disease introduction. A

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variety of measures have been developed to characterize network features, including measures of

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connectedness, clustering, and distance, as well as the specific role of individual nodes in the

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network, including measures of importance or centrality (Wasserman and Faust, 1994). Certain

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network measures have been linked with the risk of infection, such as in-degree, the number of

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incoming connections to a node; while others have been associated with both the risk of infection

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and also of transmitting disease to other nodes in the network, such as betweenness centrality

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(Frössling et al., 2012; Keeling and Eames, 2005; Pastor-Satorras and Vespignani, 2001).

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Given the association of livestock movements with outbreaks of bTB (Gilbert et al.,

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2005), the objectives of this study were (1) to characterize cattle movements in the region of a

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past bTB outbreak and (2) to identify herds with a higher risk of becoming infected and/or of

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infecting other herds based on known risk factors related with cattle movements and network

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analysis parameters. The ultimate goal was to develop a risk-based surveillance framework for

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bTB, in order to identify in which herds to focus surveillance resources to minimize disease

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burden and reduce the cost of disease control. We made use of cattle movement data collected

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following a recent bTB outbreak in Minnesota. Bovine tuberculosis was first detected in 2005 in

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cattle in northwestern Minnesota through slaughter surveillance. By 2009, 12 cattle herds were

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found to be infected with bTB. Almost all herds in the outbreak could be linked to an infected

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herd through cattle movements (Shaw, 2008). Bovine tuberculosis was contained in a smaller

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area in northwestern Minnesota classified as modified accredited (MA) (Carstensen and

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Doncarlos, 2011), corresponding to a prevalence inferior to 0.1% in cattle (USDA-APHIS,

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2005). In 2011, the state was declared bTB free. From January 2008 to 2011, cattle movements

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within the MA region were recorded electronically as part of an eradication program.

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The USDA recently issued a document outlining a new approach to bTB surveillance.

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This included the development of targeted approaches, with the objective of responding to the 5      Page 5 of 41

new challenges posed by this disease. Of greater importance are the following: most cases

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detected at slaughter are imported animals (mostly from Mexico), the risk for wildlife reservoirs

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to emerge, and the greater cost of disease control and eradication due to increased herd size and

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long distance cattle movements across the country (USDA-APHIS-VS, 2009c).

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The objectives of this analysis are supported by the hypothesis that the assumption of

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randomness does not hold in infectious disease transmission due to the heterogeneity of the

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populations and their contacts. In our study, the focus is on the heterogeneity of cattle

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movements between herds, where each herd contributes differently to the overall risk of disease

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transmission (Keeling and Eames, 2005; Woolhouse et al., 2005). Furthermore, the longitudinal

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component of the current data set allows the estimation of network parameters across several

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years and evaluation of the influence of the most prominent nodes of the network of cattle

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movements.

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2. Material and Methods

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2.1. Data collection

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Data on cattle movements for the bTB MA zone, from 2008 through 2011, were obtained

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from the Minnesota Board of Animal Health (MNBAH). Due to Minnesota’s split-state status

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over this time period, all cattle movements to and from farms in the MA zone were recorded

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through animal movement certificates and radio frequency identification (RFID) tagging of

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individual animals. The MNBAH has made these data available as a part of the electronic

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Generic Database (software made available to states by USDA-APHIS). The RFID tag data

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reflects all individual animal movements, including within-herd movements (i.e. within the same

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owner but between different locations), between-herd movements, to and from sale yards, to

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slaughter facilities, and to and from county or state fairs. 6      Page 6 of 41

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2.2. Study population The bTB MA zone was located in the interface between four counties in northwestern

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Minnesota: Beltrami, Lake of the Woods, Marshall and Roseau. Cattle operations in this area are

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predominantly beef farms (versus dairy farms) (Table 1).

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2.3. Inclusion criteria

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We included all cattle movements entering, exiting, and within the MA zone that had a

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complete movement record in our analysis. For cattle movements within the MA zone or

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between the MA zone and the rest of Minnesota, we excluded cattle movements for which either

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the origin or destination farm could not be identified from our data. For movements entering or

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exiting the MA zone with origins or destinations outside the state of Minnesota, we did not

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exclude any movement, as long as the state of origin or receipt of the movement was available.

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One farmer may own or manage multiple premises; as cattle might move seasonally to different

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locations depending on availability of feed. Since we were only interested in movements

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between distinct operations, movements to and from premises operated by the same farmer were

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combined into one cattle farm, since it corresponded to the same cattle herd.

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2.4. Analysis and definitions

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From the cattle movement data, we constructed a network reflecting the structure of cattle

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movement between premises. In the network, each cattle operation (private farm, sale yard or

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other) is represented by a node and edges (connections) represent the movement of cattle from

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one node to another. We constructed a directed network to account for the fact that cattle

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movements are not reciprocal; where some cattle operations may serve primarily as suppliers,

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with many out-going connections, while other operations may predominantly import cattle, with

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many in-coming connections. We constructed separate networks for each of the four years in the 7      Page 7 of 41

study period, reflecting the specific cattle movements of any given year. We also constructed an

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aggregate cattle movement network, which reflects the cattle movements over the entire four-

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year period. The network of cattle movements was analyzed as both a valued network, to account

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for the strength of relationship between nodes (i.e. multiple movements between the same nodes

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were considered) and also as dichotomous network (only accounting for one movement between

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the same nodes) (Wasserman and Faust, 1994).

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We analyzed each cattle movement network using UCINET®, a software package for

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network analysis (Borgatti et al., 2002). We characterized each network in terms of standard

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network features, including the network’s overall density, mean degree, and betweenness

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centrality index (for definitions, see Table 3) (Bonacich 1987; Freeman et al. 1991; Wasserman

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and Faust 1994; Martínez-López et al. 2009). We also constructed a degree distribution of the

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overall degree as well as of in-degree and out-degree separately to evaluate proportion of nodes

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involved in the majority of movements and cattle moved (Woolhouse et al., 2005). Spearman

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correlations were calculated to evaluate the association between centrality parameters for

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incoming and outgoing movements.

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We considered “influential” nodes in the network to be those nodes with high degree

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(Dubé et al., 2010; Mansley et al., 2003; Mclaws and Ribble, 2007; Robinson and Christley,

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2007). For each of these important nodes, we constructed ego-centric networks, which represent

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the network of direct links (i.e. only one step in distance), incoming or outgoing, for one node of

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interest. The objective was to identify in detail which nodes were receiving cattle from these

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more central nodes. Network graphs were constructed in order to visualize the main characteristics of the

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network of cattle movements, particularly influential nodes and type of movements (incoming or 8      Page 8 of 41

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outgoing). However, spatial location was not considered in the figures in order to avoid

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identifying individual farm locations within the area involved. After characterizing the network features of cattle movements, we proposed a risk-score

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for private farms designed to reflect the risk of bTB infection based on a farm’s role and position

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in the network. Such a score could be used in developing targeted surveillance strategies to

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improve the efficiency and timeliness of bTB detection in the region. We based the risk-score on

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the number of cattle movements, the number of cattle in each movement and the movement

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characteristics that affect risk, which was informed by published literature (summarized in Table

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4).

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The risk-score was calculated at the movement level, and then summarized at the farm

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level on an annual basis to account for year-specific differences. The final risk-score was the

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Total Risk Score (TRS) over the four-year period. To account for parameter uncertainty,

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regarding the risk associated with origin of movements, we randomly sampled parameter values

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from Pert distributions and calculated the resulting mean risk score and the associated 25th and

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75th percentiles over 10,000 samples (Table 5). The risk score incorporates not only the

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heterogeneity in the number of contacts and the number of cattle in each contact, but also the

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origin of the cattle moved, which is known to affect risk of disease introduction. Therefore, each

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movement counted once, a risk was associated with the origin of each movement, and the

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number of animals in each movement was considered by applying an ordinal weight, where

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larger movements (>100) had a greater weight, when compared to medium (11-100 cattle) and

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small size movements (n≤10). The former (origin) was stochastic, while the latter (size) was

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deterministic. The reason for this decision was based on the uncertainty regarding the level of

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risk associated with movements originated from sale yards and from other states, as no studies

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have been performed in the US to estimate these parameters. The weights applied to each

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movement, accordingly to number of cattle, were based on the data distribution, since there is no

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perfect cutoff and the main purpose of this variable was to magnify or maintain the risk

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associated with the movement. The model was built in Microsoft Excel® using ModelRisk®

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(Vose software, Gent Belgium), an add-in software for risk analysis. The parameter values for

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the Pert distributions for risk associated with import movements (i.e. movements from out-of-

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state) and movements from sale yards were based on published literature (Table 4) and

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confirmed by expert opinion. The Pert distribution is usually used to model expert opinion when

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information regarding the parameters is difficult to infer from published literature, and only

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requires estimates of the minimum, most likely and maximum values for the parameter (Vose,

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2008). In the current study, parameters were first inferred from the published literature and

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expert opinion from the University of Minnesota and the Minnesota Board of Animal Health was

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used to confirm the parameters chosen. Farms were ranked based on the TRS and divided into

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high, medium, and low risk groups based on a combination of the TRS, the interquartile range

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and the cumulative risk. Farms in the high risk group had the highest score, the larger

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interquartile range indicating a greater level of uncertainty, and comprised 80% of the

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cumulative risk; the medium risk group was responsible for the remaining cumulative risk (i.e.

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20%) with a smaller inter-quartile range; and the low risk group corresponded to the farms with

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no incoming movements. Pearson correlations were calculated between the risk scores for each

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year and confidence intervals were calculated by bootstrapping the standard the error. The model

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was built in Microsoft Excel® using ModelRisk® (Vose software, Gent Belgium), add-in software

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for risk analysis.

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each farm in each year, and the TRS.

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3. Results

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3.1. Descriptive analysis with trends by year and month

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The equations in Table 5 explain the calculation of the risk score for each movement to

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From 2008 through 2011, 3,467 movements (~99% of movements available) satisfied the

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inclusion criteria, representing a total of 46,717 cattle moved, and 559 premises, including

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private farms, sale yards, slaughter facilities and county or state fairs (Table 2).

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The number of movements of cattle entering, exiting, and within the MA zone peaked in

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January and December each year, although a significant number of cattle movements occurred at

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other times of year (Figure 1). The number of cattle moved was maximal in the same months

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(January and December), but exhibited a stronger seasonal trend, reaching a minimum in the

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summer months (Figure 2).

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3.2. Network analysis of the complete network and by year.

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The networks representing the structure of cattle movements in the bTB MA zone, both

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on an annual basis and over the entire four-year period, were characterized by having far fewer

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edges (i.e. movements) present in the network compared to the total number of possible edges, as

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reflected in a low density and a high fragmentation (Table 6). Furthermore, the nodes connected

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to a given node were unlikely to be connected themselves (low clustering coefficient). Most

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nodes were not along the shortest path between other nodes (low betweeness index) and since the

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network had low density, most of nodes were unable to reach other nodes in the network (low

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closeness index). These two parameters indicated that the network “power” was concentrated in a

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very small number of nodes. In the network figures (Figures 3a, 3b) is possible to identify the

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presence of two main hubs in the network, which corresponded to two sale yards located in

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northern Minnesota just outside the bTB MA area with a huge number of incoming connections

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(Figure 3a). Aside from these two hubs, it’s also possible to verify that the majority of nodes in

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the network had more outgoing movements than incoming movements (Figure 3b) and most

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movements were within the bTB MA area or within MN. The longitudinal component of the data

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showed very little variation between years for the network parameters (Table 6).

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outgoing movements was extremely high (Table 7).

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3.3. Degree distribution

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In the current network, the correlation among parameters related to incoming and

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The degree distribution showed that 20% of the nodes with highest degree account for

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90% of the movements and 86% of the cattle being moved. Again the two main sale yards were

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the dominant influence on these results (Figure 4).

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When evaluating only the private farms within the bTB area, most farms had low in-

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degree (Figure 5a) and out-degree (Figure 5b). Most farms had more outgoing movements,

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reflecting the management practices of the study area, where cow-calf beef operations prevail

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(Figure 5b), and a large number had no incoming movements.

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3.4. Sale yards

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The network had 12 sale yards and 7 were located within Minnesota. From the sale yards

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in MN, 2 had a central role in the network of cattle movements to and from the bTB area.

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Overall, 61% of the total number of cattle moved and 64% of the total number of movements

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went through these 2 sale yards (Table 8). The ego-networks, incorporating nodes that send and

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receive directly to and from both sale yards, included 45% and 47% of total number of nodes for

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sale yard 1 and 2, respectively (Table 8). Both sale yards had a greater number of incoming cattle

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than outgoing cattle, in part as cattle sold to farms outside of the bTB MA area are not accounted

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for.

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3.5. Risk score for private farms within the bTB area From our cut-off values, the higher risk group included 14% (n=50) of the farms, the

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medium risk group included 46% (n=169) of farms, and the low risk group consisted of farms

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with a null risk score and had 40% (n=149) of the total number of farms. The correlation

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between the risk score for the years with more data, 2009 and 2010 was 0.44 (95% CI [0.236;

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0.670]), and the strongest correlation was between years 2010 and 2011, with 0.62 (95% CI

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[0.496; 0.729]).

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3.5.1. Evaluation of the impact of farms in the high risk group

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Once infected, not all herds at high risk for infection are equally important to disease

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transmission. Figure 7 differentiates among farms with a high probability of infection, based on

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the risk score, and those that may have a higher or lower impact on disease transmission based

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on out-degree or flow betweenness centrality. With out-degree, there was more spread of the

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results, since more farms had out-going movements, which impacted the network locally, i.e. to

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their immediate connections, after excluding movements to slaughter plants. Concerning flow

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betweenness, since it is a parameter that measures connectivity to the whole network, fewer

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farms had the potential for widespread impact in the overall network. Furthermore, the farms

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with the highest risk of infection within the high risk group did not have the higher values for

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out-degree and flow betweenness (Figure 7).

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4. Discussion

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In this analysis, we developed a potential approach to targeted surveillance by

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incorporating network analysis parameter (in-degree) and known risk factors for bTB associated 13      Page 13 of 41

with cattle movements. This analysis was only possible since complete cattle movement data was

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available, which to the authors knowledge constitutes a unique situation in the US. The ability to

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score farms and to identify those at high risk for disease introduction could greatly improve the

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effectiveness of disease surveillance by detecting disease more quickly while reducing cost. This

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is assumed, since disease is more likely to be introduced in the high risk farms, where

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surveillance would be enhanced.

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The method developed here has limitations, particularly the absence of estimates for the

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parameters used in the risk model in disease free scenarios, such as the Minnesota situation.

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However, using current established knowledge on bTB risk factors for disease introduction into a

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disease-free area adds confidence to our assumptions (Gilbert et al., 2005; Gopal et al., 2006;

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Ramírez-Villaescusa et al., 2010; USDA-APHIS-VS, 2009b).

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The current dataset had the advantage of incorporating 4 years of data, allowing for a

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longitudinal analysis of network features and farm risk scores. This is particularly important

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when dealing with a disease with a long latent period such as bTB, where risk behaviors in one

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year can still influence the population four years later. However, the completeness of the data

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was not consistent over the entire observational period, with fewer movements recorded in early

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2008 and late 2011 than during other times. Since cattle movements were self-reported by farm

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owners, adherence may have been low at the beginning of the mandatory reporting period and

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enforcement of this mandatory reporting likely declined once the status of the MA bTB area

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changed to bTB free in 2011. These observations highlight some of the problems of relying on

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self-reported cattle movements, as these may not reflect what in fact occurs in the field. This can

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be improved by education and by clear policy measures that reward those who adhere to the rules

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and penalize violators.

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The application of network analysis to understand the heterogeneous structure of contacts

321 

in a population has been extremely important in identifying the high risk players, or

323 

“superspreaders”, that play a key role in the spread of infection (Dubé et al., 2008; Frössling et

324 

al., 2012; Keeling and Eames, 2005; Woolhouse et al., 2005). For example, we know from

325 

disease modeling in scale-free networks, where the degree distribution follows a power-law (i.e.

326 

few nodes have more connections versus a random distribution of connections), that nodes with

327 

the highest degree are more likely to become infected and, once infected, to rapidly spread

328 

disease throughout the network (Newman, 2001; Pastor-Satorras and Vespignani, 2001).

329 

However, the vast majority of these conclusions have been based on analyses of undirected

330 

networks, where nodes may both infect and be infected by their direct contacts. In contrast, cattle

331 

movements are inherently and importantly directed, making the distinction between risk of

332 

infection and risk of transmission essential. Each of these types of risk can only be assessed

333 

using a directed network approach. We used in-degree as the primary parameter indicator of risk

334 

for disease introduction, as centrality measures relating to incoming movements were all highly

335 

correlated. This high correlation between degree and Bonacich Power, for both incoming and

336 

outgoing movements can be explained by the strong influence of two sale yards, with the

337 

majority of movements being performed either to or from these facilities. In other words, those

338 

nodes that have more movements are also more likely to have movements to or from those

339 

highly influential nodes, thus resulting in very little difference between both parameters

340 

(Bonacich, 2007). Outgoing movements were more variable, so we assessed the risk of disease

341 

transmission through an analysis of both out-degree and more complex parameters such as flow

342 

betweenness centrality (Borgatti, 2005; Freeman et al., 1991). Both the in-degree and out-degree

343 

are local measures in the network, calculated based on immediate edges to each node. On the

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15      Page 15 of 41

other hand, centrality measures such as flow betweenness centrality, evaluate the role of each

345 

node in the overall network. Unlike the more commonly used measure, betweenness centrality,

346 

which only considers geodesic paths between nodes, flow betweenness centrality considers all

347 

possible paths between two nodes and can account for different strengths of connections (e.g.,

348 

differences in the number of cattle moving from one premise to another). Nodes with a higher

349 

flow-betweenness have a higher influence in the network’s overall connectivity, which

350 

extrapolated for risk of disease transmission could be interpreted as an increased risk of

351 

transmission if infected.

us

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344 

Analyzing the directed movements of cattle between premises has allowed us to observe

353 

important differences in import and export behaviors. The distribution of in-degree of premises

354 

in the MA bTB region is highly skewed, as expected, approaching the characteristics of a power

355 

law distribution, where a few actors incorporate most of the activity of the study population

356 

(Keeling and Eames, 2005; Woolhouse et al., 2005). However, we did not see this trend to the

357 

same extent in out-degree connections, which is likely related to the types of cattle production

358 

system in the MA bTB area. This area has a predominance of beef cow-calf operations, with

359 

most herds shipping calves after weaning and few behaving as buyers, and many of the private

360 

farms having no incoming movements at all throughout the 4 years.

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352 

One of the primary findings in the movement data for the MA bTB area was the highly

361  362 

influential role of two sale yards that acted as hubs in the network and connected many different

363 

farms together through cattle movements. Both sale yards had a higher number of incoming

364 

movements. This difference, between incoming and outgoing movements, was much greater in

365 

the case of sale yard 2, reflecting differences in sale yard operations: sale yard 1 dealt more with

366 

young stock, while sale yard 2 managed more cull cattle (i.e. to be sold for slaughter), which 16      Page 16 of 41

were less likely to be sold to other farms in the bTB MA area. Because beef cow-calf herds were

368 

the predominant cattle operation type in the bTB MA area, many more farms sent cattle to sale

369 

yards than imported from them. This regional feature shows the ability of the sale yards in

370 

dispersing cattle with diverse origins, and potentially disease as well, across a broad area.

ip t

367 

Sale yards or animal markets and their role in disease spread have been studied

371 

previously in other circumstances and have been found to be extremely important factors in

373 

disease transmission (Ferguson et al. 2001; Gibbens et al. 2001). In an analysis of foot-and-

374 

mouth disease (FMD) outbreaks, in non-endemic areas, from 1992 to 2003, authors concluded

375 

that the primary factor contributing to a large outbreak size was an FMD-infected animal going

376 

through a market (Mclaws and Ribble, 2007). A descriptive investigation of the initial spread of

377 

the 2001 UK FMD outbreak also highlighted the pivotal role of a sale yard in disease spread

378 

(Mansley et al., 2003). Anecdotally, after the 2005 Minnesota bTB outbreak began, official

379 

veterinarians identified cattle from over 20 states in sale yard 1 while performing animal-level

380 

testing. Furthermore, movements from markets have been identified as a risk factor for bTB

381 

infection at a herd level (Johnston et al., 2005; Ramírez-Villaescusa et al., 2010). Although FMD

382 

and bTB are very different diseases, the former highly infectious while the latter is a chronic

383 

disease with a long latent period, sale yards play an important role in facilitating mixing between

384 

cattle from many different areas, increasing the potential for disease transmission.

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372 

The centrality of sale yards in the current network analysis highlights the importance of

385  386 

keeping thorough records of animals moving through these holdings. Such records are extremely

387 

informative in the event of an outbreak disease investigation. Until an agreement is reached to

388 

implement a comprehensive national cattle identification system in the US, with mandatory

389 

tracking of cattle movements, tracking movements to and from sale yards constitutes one 17      Page 17 of 41

potential targeted disease surveillance measure that could be very effective when facing a disease

391 

emergency. This is particular important when considering the fact that sale yards tend to include

392 

movements that cover longer distances, working as bridges between otherwise geographically

393 

isolated areas, increasing the risk for a more widespread outbreak (Dubé et al., 2009). Changing

394 

the organization of sale yards could also mitigate the risk of disease spread, such as segregating

395 

cattle originating from areas with different levels of risk for disease from each other.

cr

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390 

Among private farms, low values of overall flow betweenness, as with low density,

397 

confirm the low level of connection of this network of cattle movements and the minimum

398 

impact caused by any of the farms, if infected, in the overall network. Very likely, disease would

399 

spread slowly and would affect a small number of farms. The network analysis presented here

400 

sheds light in understanding what potentially happened in the bTB outbreak in MN, where only

401 

12 farms were infected during a 5 year period after disease was introduced. The risk for spread

402 

will increase if an additional host emerges in the wildlife population, creating additional routes

403 

for disease propagation (Miller and Sweeney, 2013).

te

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396 

Studies investigating the risk of disease attributable to cattle movements are limited and

Ac ce p

404  405 

in general rely on data collected in bTB endemic areas. However, risk factors such as cattle

406 

movements, and more specifically movements from sale yards or from areas known to be

407 

infected, have been shown to be highly influential on bTB positivity at the herd level (Gilbert et

408 

al., 2005; Goodchild and Clifton-Hadley, 2001; Johnston et al., 2005; Ramírez-Villaescusa et al.,

409 

2010). In support of these conclusions, 90% of the purchased cattle in the index herd of the 2005

410 

bTB Minnesota outbreak originated from out-of-state. This is in contrast to the other bTB case

411 

herds, in which only 3% of bought cattle originated from outside Minnesota (USDA-APHIS-VS,

412 

2009b). 18      Page 18 of 41

The risk score for targeting surveillance for bTB does not exclude the standard slaughter

413 

surveillance applied to every animal. The goal is to implement higher levels of surveillance

415 

expressed by more field testing or increased submission of tissues from slaughter, for farms

416 

identified as high risk. This targeting aims to increase the surveillance system sensitivity.

417 

Furthermore, the identification of such farms and the higher level of surveillance implemented,

418 

including the identification incoming and outgoing contacts, would allow a faster response when

419 

performing contact tracing (Keeling and Eames, 2005). The main objective is to perform targeted

420 

surveillance on farms that are more likely to become infected with bTB and consequentially

421 

mitigate bTB spread into the overall cattle population and potentially to wildlife populations. The

422 

number of farms to test will depend on availability of resources, but instead of based on a

423 

random selection process it could be based on a risk score. Targeting education to high risk

424 

farms before a disease incursion in order to improve response to an outbreak has also been

425 

proposed (Dubé et al., 2009).

te

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414 

Though we considered individual movements between premises, we ignored the specific

427 

timing of these movements. The order in which movements occur over time is important, as any

428 

exports occurring from an uninfected herd prior to the importation of an infected animal have no

429 

potential for disease transmission. The ordering of movements is particularly important when

430 

performing trace back investigations after an outbreak, where the specific chain of infection must

431 

be identified (Dubé et al., 2008; Frössling et al., 2012; Nöremark et al., 2011). However, for this

432 

analysis, which aimed to identify the high risk farms for disease introduction into a disease-free

433 

area, this variable was less critical, since we addressed the first movement of a potential chain of

434 

movements to follow.

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19      Page 19 of 41

This evaluation of the impact of high risk farms in the network of cattle movements

435 

shows the potential of using network parameters to quantify risk and target surveillance.

437 

However, an analysis based on cattle movements alone does not necessarily capture all

438 

transmission pathways for bTB. For example, animals in neighboring farms may come into

439 

contact with each other at fence lines, with potential for bTB transmission. While the risk score

440 

does not incorporate proximity to high risk farms, in an outbreak situation, farms with fence line

441 

contact to high risk farms would be immediately included in a protection surveillance zone (OIE,

442 

2012). The presence of bTB-susceptible wildlife, such as white-tail deer, may also facilitate

443 

unmeasured contact between farms (Knust et al., 2011). Wildlife may move freely through

444 

farmland and come into contact with animals from different herds, facilitating disease spread. As

445 

control and eradication are even more difficult in wildlife populations, once infected these

446 

populations may become maintenance hosts (Haydon et al., 2002). Thus, when assessing the

447 

potential impact of high risk farms in the network, incorporating their potential for interacting

448 

with white-tail deer is necessary. Empirical studies of the behavior of deer and other relevant

449 

wildlife in the farm landscape are needed in order to properly account for wildlife mediated

450 

contact between farms in the network and risk models.

Ac ce p

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436 

Network analysis is a widely used tool in veterinary epidemiology, however very few

451  452 

papers have used it to inform disease surveillance in a practical way (Frössling et al., 2012;

453 

Nöremark et al., 2011). The current model, although limited in its application in a specific area in

454 

Minnesota, can serve as a basis to be applied in similar circumstances to other regions. In

455 

addition, the model is simple in its application and the data collection is feasible, and could

456 

therefore be implemented by animal health agencies. The objectives of animal health

457 

surveillance can be greatly improved by using targeted approaches, particularly in areas that are 20      Page 20 of 41

disease-free in order to act more effectively and minimize the high costs associated with

459 

investigating and controlling disease outbreaks. For this to be possible it is essential that

460 

registration of cattle movements should be made mandatory, and enforced by state and federal

461 

agencies.

462 

Acknowledgments

ip t

458 

This project was supported by a grant from the University of Minnesota Academic

cr

463 

Health Center Faculty Research Development Program. We greatly acknowledge the Minnesota

465 

Board of Animal Health and its director, Dr. Bill Hartman, for the data sharing and willingness

466 

to collaborate.

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467 

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References

470  471 

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Bigras-Poulin, M., Thompson, R. a, Chriel, M., Mortensen, S., Greiner, M., 2006. Network analysis of Danish cattle industry trade patterns as an evaluation of risk potential for disease spread. Prev. Vet. Med. 76, 11–39.

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Bonacich, P., 1987. Power and Centrality: A Family of Measures. Am. J. Sociol. 92, 1170–1182.

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Bonacich, P., 2007. Some unique properties of eigenvector centrality. Soc. Networks 29, 555– 564.

478 

Borgatti, S.P., 2005. Centrality and network flow. Soc. Networks 27, 55–71.

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Borgatti, S.P., Everett, M.G., Freeman, L.C., 2002. UCINET for Windows: software for social network analysis.

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Carstensen, M., Doncarlos, M.W., 2011. Preventing the establishment of a wildlife disease reservoir: a case study of bovine tuberculosis in wild deer in Minnesota, USA. Vet. Med. Int. 2011, 413240.

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Dubé, C., Ribble, C., Kelton, D., 2010. An analysis of the movement of dairy cattle through 2 large livestock markets in the province of Ontario, Canada. Can. Vet. J. 51, 1254–60.

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Dubé, C., Ribble, C., Kelton, D., McNab, B., 2008. Comparing network analysis measures to determine potential epidemic size of highly contagious exotic diseases in fragmented monthly networks of dairy cattle movements in Ontario, Canada. Transbound. Emerg. Dis. 55, 382–92.

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Dubé, C., Ribble, C., Kelton, D., McNab, B., 2009. A review of network analysis terminology and its application to foot-and-mouth disease modelling and policy development. Transbound. Emerg. Dis. 56, 73–85.

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Ferguson, N.M., Donnelly, C. a, Anderson, R.M., 2001. The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions. Science 292, 1155–60.

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Fischer, E. a J., van Roermund, H.J.W., Hemerik, L., van Asseldonk, M. a P.M., de Jong, M.C.M., 2005. Evaluation of surveillance strategies for bovine tuberculosis (Mycobacterium bovis) using an individual based epidemiological model. Prev. Vet. Med. 67, 283–301.

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Freeman, L.C., Borgatti, S.P., White, D.R., 1991. Centrality in valued graphs: A measure of betweenness based on network flow. Soc. Networks 13, 141–154.

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Frössling, J., Ohlson, A., Björkman, C., Håkansson, N., Nöremark, M., 2012. Application of network analysis parameters in risk-based surveillance - Examples based on cattle trade data and bovine infections in Sweden. Prev. Vet. Med.

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Gibbens, J.C., Sharpe, C.E., Wilesmith, J.W., Mansley, L.M., Michalopoulou, E., Ryan, J.B., Hudson, M., 2001. Descriptive epidemiology of the 2001 foot-and-mouth disease epidemic in Great Britain: the first five months. Vet. Rec. 149, 729–43.

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Gilbert, M., Mitchell, a, Bourn, D., Mawdsley, J., Clifton-Hadley, R., Wint, W., 2005. Cattle movements and bovine tuberculosis in Great Britain. Nature 435, 491–6.

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Goodchild, A.V.., Clifton-Hadley, R.S., 2001. Cattle to cattle transmission of Mycobacterium bovis. Tuberculosis 81, 23–41.

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Gopal, R., Goodchild, A., Hewinson, G., Domenech, R.D.R., 2006. Introduction of bovine tuberculosis to north-east England by bought-in cattle. Vet. Rec. 165–271.

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Haydon, D.T., Cleaveland, S., Taylor, L.H., Laurenson, M.K., 2002. Identifying reservoirs of infection: a conceptual and practical challenge. Emerg. Infect. Dis. 8, 1468–73.

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Johnston, W.T., Gettinby, G., Cox, D.R., Donnelly, C. a, Bourne, J., Clifton-Hadley, R., Le Fevre, a M., McInerney, J.P., Mitchell, a, Morrison, W.I., Woodroffe, R., 2005. Herd-level

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risk factors associated with tuberculosis breakdowns among cattle herds in England before the 2001 foot-and-mouth disease epidemic. Biol. Lett. 1, 53–6.

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Keeling, M.J., Eames, K.T.D., 2005. Networks and epidemic models. J. R. Soc. Interface 2, 295– 307.

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Knust, B.M., Wolf, P.C., Wells, S.J., 2011. Characterization of the risk of deer-cattle interactions in Minnesota by use of an on-farm environmental assessment tool. Am. J. Vet. Res. 72, 924–931.

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Mansley, L.M., Dunlop, P.J., Whiteside, S.M., Smith, R.G.H., 2003. Early dissemination of footand-mouth disease virus through sheep marketing in February 2001. Vet. Rec. 153, 43–50.

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Martínez-López, B., Perez, A.M., Sánchez-Vizcaíno, J.M., 2009. Social network analysis. Review of general concepts and use in preventive veterinary medicine. Transbound. Emerg. Dis. 56, 109–20.

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Mclaws, M., Ribble, C., 2007. Description of recent foot and mouth disease outbreaks in nonendemic areas: Exploring the relationship between early detection and epidemic size. Can. Vet. J. 48, 1051–1062.

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Miller, R.S., Sweeney, S.J., 2013. Mycobacterium bovis (bovine tuberculosis) infection in North American wildlife: current status and opportunities for mitigation of risks of further infection in wildlife populations. Epidemiol. Infect. 1–14.

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Mintiens, K., Méroc, E., Faes, C., Abrahantes, J.C., Hendrickx, G., Staubach, C., Gerbier, G., Elbers, a R.W., Aerts, M., De Clercq, K., 2008. Impact of human interventions on the spread of bluetongue virus serotype 8 during the 2006 epidemic in north-western Europe. Prev. Vet. Med. 87, 145–61.

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National Research Council, 1994. Livestock Disease Eradication: Evaluation of the Cooperative State-Federal Bovine Tuberculosis Eradication Program. National Academy Press, Washington D.C.

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Newman, M., 2001. Clustering and preferential attachment in growing networks. Phys. Rev. E 64, 1–4.

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Nöremark, M., Håkansson, N., Lewerin, S.S., Lindberg, A., Jonsson, A., 2011. Network analysis of cattle and pig movements in Sweden: measures relevant for disease control and risk based surveillance. Prev. Vet. Med. 99, 78–90.

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Ramírez-Villaescusa, a M., Medley, G.F., Mason, S., Green, L.E., 2010. Risk factors for herd breakdown with bovine tuberculosis in 148 cattle herds in the south west of England. Prev. Vet. Med. 95, 224–30.

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Robinson, S.E., Christley, R.M., 2007. Exploring the role of auction markets in cattle movements within Great Britain. Prev. Vet. Med. 81, 21–37.

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USDA-APHIS-VS, 2009a. Analysis of Bovine Tuberculosis Surveillance in Accredited Free States, Tuberculosis. Fort Collins, CO.

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Vose, D., 2008. Risk analysis: quantitative guide, 3rd ed. Wiley & Sons, Incorporated, John, West Sussex, UK.

575  576 

Wasserman, S., Faust, K., 1994. Social Network Analysis: methods and applications, 1st edit. ed. Cambridge University Press, New York, NY.

577  578  579 

Woolhouse, M.E.J., Shaw, D.J., Matthews, L., Liu, W.-C., Mellor, D.J., Thomas, M.R., 2005. Epidemiological implications of the contact network structure for cattle farms and the 20-80 rule. Biol. Lett. 1, 350–2.

580 

Figure captions

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24      Page 24 of 41

Figure 1 – Number1 of cattle movements in the MN bovine tuberculosis Modified Accredited

582 

area by month, with each series representing a year.

583 

Figure 2 – Number1 of cattle moved in the MN bovine tuberculosis Modified Accredited by

584 

month, with each series representing a year.

585 

Figure 3 – Network graphs for all the cattle movements between 2008 and 2011 in the MN

586 

bovine tuberculosis Modified Accredited area. Shapes represent type of node: ● - private farms,

587 

◊ – sale yards, ■ – other and ▲ – slaughter facilities. Colors represent location: white – outside

588 

MN (other state or Canada), black – MN outside bTB area and grey – bTB area. Nodes are sized

589 

by a) in-degree for a valued network and b) by out-degree for a valued network. Location of

590 

nodes in the graph is random and not related with geographic location.

591 

Figure 4 – Distribution of the proportion of movements and proportion of cattle moved in

592 

relation to the total for the upper 20% of nodes with higher in and out-degree (defined as high

593 

risk).

594 

Figure 5 – Histograms with the distributions of in-degree (a) and out-degree (b) for the binary

595 

network for private farms (n=367) within the bovine tuberculosis Modified Accredited area.

596 

Figure 6 – Histogram with total risk score and interquartile range (25th to 75thth percentile) of

597 

the Total Risk Score after 10000 iterations for private farms within the bovine tuberculosis

598 

Modified Accredited area. Dashed lines indicate thresholds for targeted surveillance based on

599 

combination of the cumulative proportion of the Total Risk Score and variability of the

600 

interquartile range.                                                                  

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581 

25      Page 25 of 41

601 

Figure 7 –Scatter plot with 3-dimensions with Total Risk Score (after 10000 iterations) by flow

602 

betweenness and out-degree for a valued network for herds in the bovine tuberculosis Modified

603 

Accredited area, including only herds in the high risk category from the risk score model.

ip t

Table 1 – Farm characteristics in the MN counties included in the bTB area1. Total cattle/total Beef cattle/ Dairy cattle/ County Average size of farms total farms total farms 2 farm (km ) (n/n) (n/n) (n/n) 1.27 19,706/261 9,975/228 975/15 Beltrami 1.74 4,000/49 1800/46 200/Lake of the Woods3 2.62 11,668/167 5,160/143 1,823/7 Marshall 2.02 17,948/249 8,009/211 1,422/22 Roseau 1.91 53,332/726 24,944/628 4,420/44 Overall 1 604  Data obtained for the 2007 Agriculture Census form the USDA-NASS.

Rank of total cattle2

606  607 

2

Position in the ranking of total cattle for counties in MN.

3

Lake of the Woods did not have information, from the 2007 Census, for total farms and also for

M

605 

an

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cr

43 61 49

the rank.

d

608 

te

609 

Ac ce p

610  611  612  613  614  615  616  617  618 

26      Page 26 of 41

619  620 

622 

cr

Table 2 – Summary of cattle movement data included in the network analysis Years 2009

302

386

594

1,025

8,702

14,140

Number of premises

Number of movements Number of cattle

Overall

2011

375

280

559

1,168

680

3,467

14,181

9,694

46,717

te

d

623 

M

with movements

2010

an

2008

us

Items

ip t

621 

624 

Ac ce p

625  626  627  628  629  630  631  632  633 

27      Page 27 of 41

634  635 

Table 3 – Network parameters calculated and its description and equation. Description Contacts that occur between pairs of nodes as a fraction of the total number of contacts that could occur

Density (D)1

Formula

us

Parameter

cr

637 

ip t

636 

Probability that two nodes connected to another same node are connected between them

Fragmentation (F)3

Proportion of pairs of nodes that are not connected as a fraction of the total number of contacts that could occur

Degree (d)4

total number of contacts (i.e. cattle movements) for each node

te

d

M

an

Clustering coefficient (CC)2

Mean Degree5

Mean degree of the network

Number of times a node is on the shortest path (geodesic path) that connects two other nodes.

Ac ce p

Betweenness centrality (CB)6

Flow betweenness Centrality (CF)7

Betweenness centralization index (NBc)8 Closeness centrality (CC)9

Closeness centralization index (NCc)10

Number of times a node is between all paths that connect two other nodes. Overall level of betweenness centrality for the network

How close a node is connected to all the other nodes in the network Overall level of closeness centrality for the network

28      Page 28 of 41

Bonacich Power (ci)11

644  645  646  647  648  649  650  651  652 

ip t

cr

neighbors of node i; ki = degree of node i. 3

rij = 0 if nodes i and j are not connected or rij = 1 if nodes i and j are connected.

4

Degree was also calculated for only incoming movements = in degree (di) and only outgoing

us

643 

N = nodes in the network; ejz = number of connections between nodes j and z, which are

an

642 

2

movements = out-degree (do); ℓi – total number of movements for node i. 5

d(ni) = the number of movement for each node, g = total number of nodes in the network. Mean

M

641 

gxg matrix.

degree was also calculated for both in degree (di) and out degree (do). 6

sjk(ni) = number of shortest paths through node i; sjk = total number of shortest paths.

7

This parameter was normalized, i.e. for each node i the flow that passes through i divided by

d

640 

L - the number of contacts in the network; g (g-1) - the total number of possible contacts on a

te

639 

1

the total flow that does not include node i. 8

CB(n*) = highest value of betweenness centrality in the network; CB(ni) = value of betweenness

Ac ce p

638 

Centrality is defined not only by degree but also by how central are the nodes with which the node is connected.

centrality for each node; g = total number of nodes in the network. 9

Closeness was calculated also for both out-contacts (out closeness) and in contacts (in-

653 

closeness); d(ni, nj) – length of shortest path between nodes i and j (if does not exist maximum

654 

distance possible is assumed).

655  656 

10

CC(n*) – highest value of closeness centrality in the network; Cc(ni) = value of closeness

centrality for each node; g = total number of nodes in the network.

29      Page 29 of 41

657 

11

Rij = adjacency matrix ; α = normalizes the parameter ; β = increases centrality if positive or

658 

decreases it if negative. Needs to be smaller than the reciprocal of the largest eigenvalue of the

659 

adjacency matrix - β < 1/λ.

661  662 

Cattle bought from markets

Author Ramírez-Villaescusa et al., 2010

Parameter value/description1 OR=1.95; 95% CI (1.05, 3.63)

Johnston et al., 2005

OR = 3.26, 95% CI (1.71, 6.21)

an

Variable

us

Table 4 – References used to estimate parameters for risk score model.

cr

ip t

660 

Johnston et al., 2005

OR = 1.93, 95% CI (1.03, 3.60)

Bought-in cows

Reilly and Courtenay, 2007

OR = 22.5; 95% CI (4.0, 124.9)

Purchased cattle

Goodchild and Clifton-Hadley, 2001

Majority outbreaks were associated with purchased cattle

Marangon et al., 1998

OR = 5.79; (1.80, 18.61)

Cattle bought from infected herds

d

30 out of 31 herd level outbreaks were associated to cattle movements Wide range of source operations was associated with bTB infection

Munroe et al., 1999

OR = 48.8; 95% CI (9.7, 245.2)

Gilbert et al., 2005a

Main predictor for infection

Index herd in MN had 90% of purchased animals from out-of-state 1 All parameters values/descriptions reflect risk for bTB infection at the herd level.

Out of state movements 663 

Gopal et al., 2006

Ac ce p

Range of source operations

Gopal et al., 2006

te

In-coming movements

M

Cattle bought from farm sales

664 

USDA, 2009

665  666  667  30      Page 30 of 41

668  669  670 

ip t

671  672 

cr

673 

us

674 

Ac ce p

te

d

M

an

Table 5 – Summary of risk model variables and parameters at the movement level to characterize herds within the bTB MA area by risk of introduction. Variables Parameters Definition Model Inputs One incoming Incoming movement for each farm 1 In-degree1 movement Increased risk for farms with Not a movement 0 Import movements from out-of state versus from out-of-state Movement farms with no movements from out-of A movement from (IM)2 Pert(5, 10,15) state out-of-state Not a movement Increased risk for farms with 0 movements from sale yards versus from a sale yard Sale Yards farms with no movements from sale (SY)2 A movement from a Pert(3, 5, 7) yards sale yard Number of ≤10 cattle 1 cattle in Increased risk for farms with 11-100 cattle 2 each movements with more cattle movement >100 cattle 3 (W)3 Equation 1) Equation 2) Risk score4 Equation 3)

675  676  677  678  679 

1

Total incoming movements for each farm.

2

Risk associated with Import movements (IM) and movements from Sale Yard (SY), were

modeled using PERT distributions. 3

Number of cattle in each movement (W) was applied as a weight to the risk score and was

divided in three categories with respective weights. 31      Page 31 of 41

680 

4

Equation 1 refers to the risk score for each incoming movement (RSi) that includes the

following variables: 1 - to account for each movement, which when summed corresponds to the

682 

in-degree for each farm; SY - movement from a sale yard; IM - import movement with origin

683 

outside of MN and W - weight accounting for number of cattle in the movement (1 = movement

684 

with ≤10 cattle, 2 = movement with 11 to 100 cattle and 3 = Movement with > 100 cattle).

685 

Equation 2 sums the individual incoming movement risk scores from equation 1 at farm level for

686 

each year of the study (RSjk). Equation 3 sums the risk scores from each year in order to obtain

687 

the total risk score (TRS) for each farm in the full period of the study.

us

cr

ip t

681 

0. 5

Fragmentation (%)

99.3

Cluster coefficient (%)

8.0

Average in-degree (range)

Average out-degree (range)

0. 4

0. 6

0. 4

89.5

85.6

86.4

77.0

8.5

10.4

10.8

14.6

1.427 (0 - 133)

1.672 (0 - 182)

1.709 (0 - 156)

1.543 (0 - 120)

2.257 (0 - 261)

1.427 (0 - 8)

1.672 (0 - 19)

1.709 (0 - 18)

1.543 (0 - 17)

2.257 (0 - 32)

Ac ce p

Density (%)

d

0. 5

te

Parameters

M

an

Table 6 – Summary of network parameters by year of movements and overall after dichotomizing the matrix1. Years Overall 2008 2009 2010 2011

Betweenness network 0.10 6.28 8.90 9.50 12.67 centralization Index (%) Closeness network in-centralization 0.71 1.44 1.32 1.29 0.64 Index (%) 1 688  The parameters were calculated for a binary network, considering only one movement between 689 

a pair of nodes even if multiple movements occurred. 32      Page 32 of 41

690  691  692 

ip t

693  694 

cr

695 

us

696  697 

an

698 

0.91

In-Bonacich Power2

0.91

1

Out-degree

0.05

Out-Bonacich Power2

0.05

0.67

0.58

0.05

0.04

0.70

0.61

0.05

1

0.92

0.62

0.56

0.04

0.04

0.92

1

0.56

0.49

0.67

0.70

0.62

0.56

1

0.80

Ac ce p

Betweenness

0.04

d

1

te

In-degree

M

Table 7 – Spearman rank correlation between centrality measures calculated for the complete network dichotomized1 to compare incoming and outgoing parameters. In-Bonacich Out-Bonacich Flow In-degree Out-degree Betweenness 2 2 Power Power Betweenness

Flow 0.58 0.61 0.56 0.49 0.80 Betweenness 1 699  All the network parameters were calculated based on a binary network, with the exception of 700  701 

1

flow betweenness that was calculated for a valued network. 2

Centrality is defined not only by degree but also by how central are the nodes with which the

702 

node is connected (i.e. when comparing two nodes with the value 1 for in-degree, a node with

703 

low degree connected with a node with high degree will have a higher Bonacich Power

704 

compared with a node with high degree connected with a node with low degree). 33      Page 33 of 41

705  706  707 

ip t

708  709 

cr

710 

us

711  712 

an

713 

M

Table 8 – Summary of number of movements and cattle moved for the two primary sale yards included in the network of cattle movements (valued network1) for the MN bTB Modified Accredited area. Incoming Outgoing Nodes Nodes In-degree Out-degree cattle cattle receiving sending 75

Sale yard 2

1,230

89

Total

2,055

164

2,037

29

248

20,872

342

32

261

28,559

2,379

61

509

Network that accounts for all movements of cattle between the same premise, adding strength to each tie.

716 

Ac ce p

714  715 

1

7,727

d

825

te

Sale yard 1

34      Page 34 of 41

160 140 120 100

ip t

2008

80

2009 2010

cr

60 40 20

2011

us

Number of Movements

180

an

0

Month

M

716  717 

1

718 

data-collection starting in 2008 and ending in 2011.

d

Data corresponds to the number of reported movements to the Minnesota Board of Animal Health, with

te

719 

Ac ce p

720 

35      Page 35 of 41

3000

ip t

2000 2008

1500

2009

1000

cr

Number of cattle

2500

2011

us

500

2010

an

0

Month

M

721  722 

1

723 

data-collection starting in 2008 and ending in 2011.

d

Data corresponds to the number of reported movements to the Minnesota Board of Animal Health, with

te

724  725 

Ac ce p

726  727  728  729 

36      Page 36 of 41

ip t cr us

730 

a)

b)

an

731  732 

M

733  734 

d

735 

Ac ce p

te

736 

37      Page 37 of 41

100%

“High risk” in-degree

90%

86%

“High risk” out-degree

80% 67%

64%

ip t

70% 60%

cr

50% 40% 30%

us

Proprtion of the total (%)

90%

20%

an

10% 0% Number of movements

Number of cattle

M

Category 737 

d

738 

te

739  740 

Ac ce p

741  742  743  744  745  746  747  748  749 

   38      Page 38 of 41

100

a)

 

753 

 

2

3 4 5 In-degree

6

7

757 

 

758 

 

M

 

 

d

756 

 

te

 

0 1 2 3 4 5 6 7 8 9 10 11 12 18 Out-degree

9

754  755 

ip t

0 1

cr

752 

40

us

 

b)

60

an

751 

80

20 0

750 

Frequency

Frequency

120

160 140 120 100 80 60 40 20 0

Ac ce p

759  760 

39      Page 39 of 41

140

120%

120

100%

HIGH RISK

ip t

LOW RISK 80%

cr

80

60

us

Total Risk Score

100

MEDIUM RISK

Cumulative proportion of the Total Risk Score (%)

Total risk score Cumulative risk score % Interquartile range

an

40

M

20

0 1

21

41

61

81

60%

40%

20%

0%

101 121 141 161 181 201 221 241 261 281 301 321 341 361

Rank of farms from the BTb area

d

761 

te

762                                                                                          

Ac ce p

763  764  765  766 

40      Page 40 of 41

ip t cr us an

767 

Ac ce p

te

d

M

768 

 

41      Page 41 of 41