Validation of the risk assessment analysis.

<p>(<i>A</i>), (<i>B</i>): Probability distributions of the risk ratio <i>ν</i> for the cattle trade network and the sexual contact network, respectively. Red lines are computed on training sets (2007–08 for cattle and s2-s3 for sexual contacts). The dashed lines peaking around 1 represent a null model based on reshuffling the infection statuses, i.e. randomly permuting the attribute <i>“actually being infected”</i> among the nodes for which risk assessment is performed. (<i>C</i>), (<i>D</i>): Probability distributions of the predictive power <i>ω</i> for the cattle trade network and the sexual contact network, respectively.</p

Memory driven dynamical model: model properties and validation of the risk assessment analysis.

<p>(<i>A</i>): Probability distributions of the node in-degree, in the low (<i>p</i>_<i>α</i> = 0.3) and high memory (<i>p</i>_<i>α</i> = 0.7) regimes. The slope of the distributions does not depend on <i>p</i>_<i>α</i>, and it is forced by the exponent <i>γ</i> of the <i>β</i>_<i>in</i> distribution (dashed line). (<i>B</i>): Probability distributions of the loyalty, in the low and high memory regimes. Distributions are color-coded as in panel (<i>a</i>). (<i>C</i>): Probability distributions of the risk ratio <i>ν</i>, in the low and high memory regimes. Lines represent the median values obtained from 50 realizations of the model; darker and lighter shaded areas represent the 50% and 95% confidence intervals. (<i>D</i>): Probability distributions of the predictive power <i>ω</i>, in the low and high memory regimes. Medians and confidence intervals are presented as in panel (<i>C</i>). Distributions are color-coded as in panel (<i>A</i>).</p

List of variables and their description.

<p>List of variables and their description.</p

Infection potentials and loyalty transitions.

<p>(<i>A</i>), (<i>B</i>): Probability distributions of the infections potentials for loyal (<i>π</i>_<i>L</i>, green) and disloyal nodes (<i>π</i>_<i>D</i>, orange), for the cattle trade network and the sexual contact network, respectively. Loyalty is set with a threshold <i>ϵ</i> = 0.1. Dashed lines show the fit with a Landau+exponential model (see Material and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004152#sec009" target="_blank">Methods</a>). (<i>C</i>), (<i>D</i>): Loyalty transition probabilities between loyal statuses (<i>T</i>_<i>LL</i>(<i>k</i>), green) and disloyal statuses (<i>T</i>_<i>DD</i>(<i>k</i>), orange) as functions of the degree <i>k</i> of the node, for the cattle trade network and the sexual contact network, respectively. Dashed lines represent the logarithmic models: <i>T</i>_<i>DD</i>(<i>k</i>) = 0.78−0.11log <i>k</i>, and <i>T</i>_<i>LL</i>(<i>k</i>) = 0.63+0.06log <i>k</i> for the cattle trade network; <i>T</i>_<i>DD</i>(<i>k</i>) = 0.94−0.10log <i>k</i>, and <i>T</i>_<i>LL</i>(<i>k</i>) = 0.25+0.17log <i>k</i> for the sexual contact network. Transition probabilities are computed as frequencies in the datasets under study. The error bars here represent one binomial standard deviation from these frequencies. In (<i>C</i>) the error bars are smaller than the size of the points. A single pair of configurations is considered here as example; the behavior observed is the same for all the pair of configurations.</p

The division of layer farms in Israel into groups at low and high-risk of infection with <i>Salmonella</i> serovars Enteritidis and/or Typhimurium as a result of between-farm transmission.

Base map from the Wolfram Knowledgebase and OpenStreetMap, which is made available under the Open Database License.</p

The division of layer farms in Israel into groups at low and high-risk of infection with <i>Salmonella</i> serovar Typhimurium as a result of between-farm transmission.

Base map from the Wolfram Knowledgebase and OpenStreetMap, which is made available under the Open Database License.</p

The influence of the predetermined upper limit for the length of the sampling interval on the yearly number of sampling events for risk-based surveillance programmes targeting <i>Salmonella</i> serovars Enteritidis, Typhimurium or both.

The influence of the predetermined upper limit for the length of the sampling interval on the yearly number of sampling events for risk-based surveillance programmes targeting Salmonella serovars Enteritidis, Typhimurium or both.</p

Characteristics of the optimised risk-based surveillance programmes for <i>Salmonella</i> serovars Enteritidis and/or Typhimurium for pullet and layer farms in Israel.

Characteristics of the optimised risk-based surveillance programmes for Salmonella serovars Enteritidis and/or Typhimurium for pullet and layer farms in Israel.</p

The yearly number of sampling events for the risk-based surveillance programme as a function of the local farm density (in a circular area of 300 m around a given farm), that was used to divide layer farms in Israel into groups with a low and a high risk of between-farm transmission of <i>Salmonella</i> Typhimurium.

The yearly number of sampling events for the risk-based surveillance programme as a function of the local farm density (in a circular area of 300 m around a given farm), that was used to divide layer farms in Israel into groups with a low and a high risk of between-farm transmission of Salmonella Typhimurium.</p

S1 Appendix -

Human salmonellosis cases are often caused by Salmonella serovars Enteritidis and Typhimurium and associated with the consumption of eggs and egg products. Many countries therefore implemented general surveillance programmes on pullet and layer farms. The identification of risk factors for Salmonella infection may be used to improve the performance of these surveillance programmes. The aims of this study were therefore to determine 1) whether local farm density is a risk factor for the infection of pullet and layer farms by Salmonella Enteritidis and Typhimurium and 2) whether the sampling effort of surveillance programmes can be reduced by accounting for this risk factor, while still providing sufficient control of these serovars. We assessed the importance of local farm density as a risk factor by fitting transmission kernels to Israeli surveillance data during the period from June 2017 to April 2019. The analysis shows that the risk of infection by serovars Enteritidis and Typhimurium significantly increased if infected farms were present within a radius of approximately 4 km and 0.3 km, respectively. We subsequently optimized a surveillance programme that subdivided layer farms into low and high risk groups based on the local farm density with and allowed the sampling frequency to vary between these groups. In this design, the pullet farms were always sampled one week prior to pullet distribution. Our analysis shows that the risk-based surveillance programme is able to keep the between-farm R0 of serovars Enteritidis and Typhimurium below 1 for all pullet and layer farms, while reducing the sampling effort by 32% compared to the currently implemented surveillance programme in Israel. The results of our study therefore indicate that local farm density is an important risk factor for infection of pullet and layer farms by Salmonella Enteritidis and Typhimurium and can be used to improve the performance of surveillance programmes.</div