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Animal trade plays an important role for the spread of infectious diseases in livestock populations. The central question of this work is how infectious diseases can potentially spread via trade in such a livestock population. We address this question by analyzing the underlying network of animal movements. In particular, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The considered pig trade dataset spans several years and is analyzed with respect to its potential to spread infectious diseases. Focusing on measurements of network-topological properties, we avoid the usage of external parameters, since these properties are independent of specific pathogens. They are on the contrary of great importance for understanding any general spreading process on this particular network. We analyze the system using different network models, which include varying amounts of information: (i) static network, (ii) network as a time series of uncorrelated snapshots, (iii) temporal network, where causality is explicitly taken into account. We find that a static network view captures many relevant aspects of the trade system, and premises can be classified into two clearly defined risk classes. Moreover, our results allow for an efficient allocation strategy for intervention measures using centrality measures. Data on trade volume do barely alter the results and is therefore of secondary importance. Although a static network description yields useful results, the temporal resolution of data plays an outstanding role for an in-depth understanding of spreading processes. This applies in particular for an accurate calculation of the maximum outbreak size.

Surveillance of infectious diseases in livestock is traditionally carried out at the farms, which are the typical units of epidemiological investigations and interventions. In Central and Western Europe, high-quality, long-term time series of animal transports have become available and this opens the possibility to new approaches like sentinel surveillance. By comparing a sentinel surveillance scheme based on markets to one based on farms, the primary aim of this paper is to identify the smallest set of sentinel holdings that would reliably and timely detect emergent disease outbreaks in Swiss cattle. Using a data-driven approach, we simulate the spread of infectious diseases according to the reported or available daily cattle transport data in Switzerland over a four year period. Investigating the efficiency of surveillance at either market or farm level, we find that the most efficient early warning surveillance system [the smallest set of sentinels that timely and reliably detect outbreaks (small outbreaks at detection, short detection delays)] would be based on the former, rather than the latter. We show that a detection probability of 86% can be achieved by monitoring all 137 markets in the network. Additional 250 farm sentinels—selected according to their risk—need to be placed under surveillance so that the probability of first hitting one of these farm sentinels is at least as high as the probability of first hitting a market. Combining all markets and 1000 farms with highest risk of infection, these two levels together will lead to a detection probability of 99%. We conclude that the design of animal surveillance systems greatly benefits from the use of the existing abundant and detailed animal transport data especially in the case of highly dynamic cattle transport networks. Sentinel surveillance approaches can be tailored to complement existing farm risk-based and syndromic surveillance approaches.

Understanding animal movements is an important factor for the development of meaningful surveillance and control programs, but also for the development of disease spread models. We analysed the Danish pig movement network using static and temporal network analysis tools to provide deeper insight in the connection between holdings dealing with pigs, such as breeding and multiplier herds, production herds, slaughterhouses or traders. Pig movements, which occurred between 1st January 2006 and 31st December 2015 in Denmark, were summarized to investigate temporal trends such as the number of active holdings, the number of registered movements and the number of pigs moved. To identify holdings and holding types with potentially higher risk for introduction or spread of diseases via pig movements, we determined loyalty patterns, annual network components and contact chains for the 24 registered holding types. The total number of active holdings as well as the number of pig movements decreased during the study period while the holding sizes increased. Around 60-90% of connections between two pig holdings were present in two consecutive years and around one third of the connections persisted within the considered time period. Weaner herds showed the highest level of in-loyalty, whereas we observed an intermediate level of in-loyalty for all breeding sites and for production herds. Boar stations, production herds and trade herds showed a high level of out-loyalty. Production herds constituted the highest proportion of holdings in the largest strongly connected component. All production sites showed low levels of in-going contact chains and we observed a high level of out-going contact chain for breeding and multiplier herds. Except for livestock auctions, all transit sites also showed low levels of out-going contact chains. Our results reflect the pyramidal structure of the underlying network. Based on the considered disease, the time frame for the calculation of network measurements needs to be adapted. Using these adapted values for loyalty and contact chains might help to identify holdings with high potential of spreading diseases and thus limit the outbreak size or support control or eradication of the considered pathogen.

To control African swine fever (ASF) efficiently, easily interpretable metrics of the outbreak dynamics are needed to plan and adapt the required measures. We found that the spread pattern of African Swine Fever cases in wild boar follows the mechanics of a diffusion process, at least in the early phase, for the cases that occurred in Germany. Following incursion into a previously unaffected area, infection disseminates locally within a naive and abundant wild boar population. Using real case data for Germany, we derive statistics about the time differences and distances between consecutive case reports. With the use of these statistics, we generate an ensemble of random walkers (continuous time random walks, CTRW) that resemble the properties of the observed outbreak pattern as one possible realization of all possible disease dissemination patterns. The trained random walker ensemble yields the diffusion constant, the affected area, and the outbreak velocity of early ASF spread in wild boar. These methods are easy to interpret, robust, and may be adapted for different regions. Therefore, diffusion metrics can be useful descriptors of early disease dynamics and help facilitate efficient control of African Swine Fever.

We present a contact-based model to study the spreading of epidemics by means of extending the dynamic message-passing approach to temporal networks. The shift in perspective from node- to edge-centric quantities enables accurate modeling of Markovian susceptible-infected-recovered outbreaks on time-varying trees, i.e., temporal networks with a loop-free underlying topology. On arbitrary graphs, the proposed contact-based model incorporates potential structural and temporal heterogeneities of the contact network and improves analytic estimations with respect to the individual-based (node-centric) approach at a low computational and conceptual cost. Within this new framework, we derive an analytical expression for the epidemic threshold on temporal networks and demonstrate the feasibility of this method on empirical data.

We extend the concept of accessibility in temporal networks to model infections with a finite infectious period such as the susceptible-infected-recovered (SIR) model. This approach is entirely based on elementary matrix operations and unifies the disease and network dynamics within one algebraic framework. We demonstrate the potential of this formalism for three examples of networks with high temporal resolution: networks of social contacts, sexual contacts, and livestock-trade. Our investigations provide a new methodological framework that can be used, for instance, to estimate the epidemic threshold, a quantity that determines disease parameters, for which a large-scale outbreak can be expected.

Many networks exhibit time-dependent topologies, where an edge only exists during a certain period of time. The first measurements of such networks are very recent so that a profound theoretical understanding is still lacking. In this work, we focus on the propagation properties of infectious diseases in time-dependent networks. In particular, we analyze a dataset containing livestock trade movements. The corresponding networks are known to be a major route for the spread of animal diseases. In this context chronology is crucial. A disease can only spread if the temporal sequence of trade contacts forms a chain of causality. Therefore, the identification of relevant nodes under time-varying network topologies is of great interest for the implementation of counteractions. We find that a time-aggregated approach might fail to identify epidemiologically relevant nodes. Hence, we explore the adaptability of the concept of centrality of nodes to temporal networks using a data-driven approach on the example of animal trade. We utilize the size of the in- and out-component of nodes as centrality measures. Both measures are refined to gain full awareness of the time-dependent topology and finite infectious periods. We show that the size of the components exhibit strong temporal heterogeneities. In particular, we find that the size of the components is overestimated in time-aggregated networks. For disease control, however, a risk assessment independent of time and specific disease properties is usually favored. We therefore explore the disease parameter range, in which a time-independent identification of central nodes remains possible. We find a ranking of nodes according to their component sizes reasonably stable for a wide range of infectious periods. Samples based on this ranking are robust enough against varying disease parameters and hence are promising tools for disease control.

Animal activity is an indicator for its welfare and manual observation is time and cost intensive. To this end, automatic detection and monitoring of live captive animals is of major importance for assessing animal activity, and, thereby, allowing for early recognition of changes indicative for diseases and animal welfare issues. We demonstrate that machine learning methods can provide a gap-less monitoring of red foxes in an experimental lab-setting, including a classification into activity patterns. Therefore, bounding boxes are used to measure fox movements, and, thus, the activity level of the animals. We use computer vision, being a non-invasive method for the automatic monitoring of foxes. More specifically, we train the existing algorithm ‘you only look once’ version 4 (YOLOv4) to detect foxes, and the trained classifier is applied to video data of an experiment involving foxes. As we show, computer evaluation outperforms other evaluation methods. Application of automatic detection of foxes can be used for detecting different movement patterns. These, in turn, can be used for animal behavioral analysis and, thus, animal welfare monitoring. Once established for a specific animal species, such systems could be used for animal monitoring in real-time under experimental conditions, or other areas of animal husbandry.

Livestock production systems are complex and evolve over time, affecting their adaptability to economic, political, and disease-related changes. In Europe, disease resilience is crucial due to threats like the African swine fever virus, which jeopardizes pork production stability. The European Union identifies farm production type as a key risk factor for disease spread, making it important to track changes in farm production types to assess disease risk. However, detailed production type data is often lacking in national databases. For Swiss pig farms, we used prediction and clustering algorithms to classify 9’687 − 11’247 trading farms between 2014 and 2019 by one of eleven production types. We then analyzed the pig trade network and stratified farm centrality measures (ICC and OCC) by production type. We found that 145 farms belonging to three production types have substantially higher ICC and OCC than other farms, suggesting that they could be the target of disease surveillance programs. Our predictions until 2025 show an increase both in overall pig trade network connectivity and in proportion of production types with high ICC and OCC, indicating that the structural changes in the Swiss pig production system may increase infectious disease exposure over time.

The behavior of animals is related to their health and welfare status. The latter plays a particular role in animal experiments, where continuous monitoring is essential for animal welfare. In this study, we focus on red foxes in an experimental setting and study their behavior. Although animal behavior is a complex concept, it can be described as a combination of body posture and activity. To measure body posture and activity, video monitoring can be used as a non-invasive and cost-efficient tool. While it is possible to analyze the video data resulting from the experiment manually, this method is time consuming and costly. We therefore use computer vision to detect and track the animals over several days. The detector is based on a neural network architecture. It is trained to detect red foxes and their body postures, i.e., ‘lying’, ‘sitting’, and ‘standing’. The trained algorithm has a mean average precision of 99.91%. The combination of activity and posture results in nearly continuous monitoring of animal behavior. Furthermore, the detector is suitable for real-time evaluation. In conclusion, evaluating the behavior of foxes in an experimental setting using computer vision is a powerful tool for cost-efficient real-time monitoring.