The diffusion metrics of African swine fever in wild boar.

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.

Decoding the double trouble: A mathematical modelling of co-infection dynamics of SARS-CoV-2 and influenza-like illness.

After the detection of coronavirus disease 2019 (Covid-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, Hubei Province, China in late December, the cases of Covid-19 have spiralled out around the globe. Due to the clinical similarity of Covid-19 with other flulike syndromes, patients are assayed for other pathogens of influenza like illness. There have been reported cases of co-infection amongst patients with Covid-19. Bacteria for example Streptococcus pneumoniae, Staphylococcus aureus, Klebsiella pneumoniae, Mycoplasma pneumoniae, Chlamydia pneumonia, Legionella pneumophila etc and viruses such as influenza, coronavirus, rhinovirus/enterovirus, parainfluenza, metapneumovirus, influenza B virus etc are identified as co-pathogens. In our current effort, we develop and analysed a compartmental based Ordinary Differential Equation (ODE) type mathematical model to understand the co-infection dynamics of Covid-19 and other influenza type illness. In this work we have incorporated the saturated treatment rate to take account of the impact of limited treatment resources to control the possible Covid-19 cases. As results, we formulate the basic reproduction number of the model system. Finally, we have performed numerical simulations of the co-infection model to examine the solutions in different zones of parameter space.

Ticks on the Run: A Mathematical Model of Crimean-Congo Haemorrhagic Fever (CCHF)-Key Factors for Transmission.

Crimean-Congo haemorrhagic fever (CCHF) is a zoonotic disease caused by the Crimean-Congo hemorrhagic fever virus (CCHFV). Ticks of the genus Hyalomma are the main vectors and represent a reservoir for the virus. CCHF is maintained in nature in an endemic vertebrate-tick-vertebrate cycle. The disease is prevalent in wide geographical areas including Asia, Africa, South-Eastern Europe and the Middle East. It is of great importance for the public health given its occasionally high case/fatality ratio of CCHFV in humans. Climate change and the detection of possible CCHFV vectors in Central Europe suggest that the establishment of the transmission in Central Europe may be possible in future. We have developed a compartment-based nonlinear Ordinary Differential Equation (ODE) system to model the disease transmission cycle including blood sucking ticks, livestock and human. Sensitivity analysis of the basic reproduction number R0 shows that decreasing the tick survival time is an efficient method to control the disease. The model supports us in understanding the influence of different model parameters on the spread of CCHFV. Tick-to-tick transmission through co-feeding and the CCHFV circulation through transstadial and transovarial transmission are important factors to sustain the disease cycle. The proposed model dynamics are calibrated through an empirical multi-country analysis and multidimensional plot reveals that the disease-parameter sets of different countries burdened with CCHF are different. This information may help decision makers to select efficient control strategies.

Modelling control strategies against classical swine fever: Influence of traders and markets using static and temporal networks in Ecuador.

Pig farming in Ecuador represents an important economic and cultural sector, challenged by classical swine fever (CSF). Recently, the National Veterinary Service (NVS), has dedicated its efforts to control the disease by implementing pig identification, mandatory vaccination against CSF and movement control. Our objective was to characterise pig premises according to risk criteria, to model the effect of movement restriction strategies and to consider the temporal evolution of the network. Social network analysis (SNA), SIRS (susceptible, infected, recovered, susceptible) network modelling and temporal analysis were used. The network contained 751,003 shipments and 6 million pigs from 2017 to 2019. Participating premises consisted of 144,118 backyard farms, 138 industrial farms, 21,337 traders and 51 markets. The 10 most influential markets, in the Andean highlands, received between 500 and 4600 pigs each week. The 10 most influential traders made about 3 shipments with 17 pigs per week. Simulations without control strategy resulted in an average CSF prevalence of 14.4 %; targeted movement restriction reduced the prevalence to 7.2 %, while with random movement restriction it was 13 %. Targeting the top 10 national traders and markets and one of the high-risk premises in every parish was one of the best strategies with the surveillance infrastructure available, highlighting its major influence and epidemiological importance in the network. When comparing the static network with its temporal counterpart, causal fidelity (c = 0.62) showed a 38 % overestimation in the number of transmission paths, also traversing the network required 4.39 steps, lasting approximately 233 days. In conclusion, NVS surveillance strategies could be more efficient by targeting the most at-risk premises, and in particular, taking into account the temporal information would make the risk assessment much more precise. This information could contribute to implement risk-based surveillance reducing the time to eradicate CSF and other infectious animal diseases.

Computer Vision for Detection of Body Posture and Behavior of Red Foxes.

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.

A Temporal Network Model for Livestock Trade Systems.

The movements of animals between farms and other livestock holdings for trading activities form a complex livestock trade network. These movements play an important role in the spread of infectious diseases among premises. For studying the disease spreading among animal holdings, it is of great importance to understand the structure and dynamics of the trade system. In this paper, we propose a temporal network model for animal trade systems. Furthermore, a novel measure of node centrality important for disease spreading is introduced. The experimental results show that the model can reasonably well describe these spreading-related properties of the network and it can generate crucial data for research in the field of the livestock trade system.

Application of YOLOv4 for Detection and Motion Monitoring of Red Foxes.

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.

Early warning of infectious disease outbreaks on cattle-transport networks.

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.

Corrigendum: Hierarchical Structures in Livestock Trade Networks-A Stochastic Block Model of the German Cattle Trade Network.

[This corrects the article DOI: 10.3389/fvets.2020.00281.].

Hierarchical Structures in Livestock Trade Networks-A Stochastic Block Model of the German Cattle Trade Network.

Trade of cattle between farms forms a complex trade network. We investigate partitions of this network for cattle trade in Germany. These partitions are groups of farms with similar properties and they are inferred directly from the trade pattern between farms. We make use of a rather new method known as stochastic block modeling (SBM) in order to divide the network into smaller units. SBM turns out to outperform the more established community detection method in the context of disease control in terms of trade restriction. Moreover, SBM is also superior to geographical based trade restrictions and could be a promising approach for disease control.

Locally temperature - driven mathematical model of West Nile virus spread in Germany.

West Nile virus (WNV) is an arthropod-borne virus (arbovirus) transmitted by the bites of infected mosquitoes. WNV can also infect horses and humans, where it may cause serious illness and can be fatal. Birds are the natural reservoir, and humans, equines and probably other mammals are dead-end hosts. In 2018, WNV occurred for the first time in Germany, affecting birds and horses. Seroconversion of an exposed veterinarian has also been reported. It is therefore of importance to evaluate the circumstances, under which WNV may establish in Germany as a whole or in particular favourable regions. In our current work, we formulate a dynamic model to describe the spreading process of West Nile virus in the presence of migratory birds. To investigate the possible role of migratory birds in the dissemination of WNV in Germany, we include the recurring presence of migratory birds through a mechanistic ordinary differential equations (ODE) model system. We also perform a sensitivity analysis of the infection curves. Seasonal impacts are also taken into consideration. As result, we present an analytical expression for the basic reproduction number R0. We find that after introducing WNV into Germany, R0 will be above the critical value in many regions of the country. Furthermore, we observe that in the south of Germany, the disease reoccurs in the following season after the introduction. We include a potential distribution map associated with WNV cases in Germany to illustrate our findings in a spatial scale.

Implications of Cattle Trade for the Spread and Control of Infectious Diseases in Slovenia.

The objectives of this study were to gain insight into the structure of the cattle trade network in Slovenia and to evaluate the potential for infectious disease spread through movements. The study considered cattle movements between different types of premises that occurred between August 1, 2011 and July 31, 2016 with the exclusion of the movements to the end nodes (e.g., slaughterhouses). In the first part, we performed a static network analysis on monthly and yearly snapshots of the network. These time scales reflect our interest in slowly spreading pathogens; namely Mycobacterium avium subsp. paratuberculosis (MAP), which causes paratuberculosis, a worldwide economically important disease. The results showed consistency in the network measures over time; nevertheless, it was evident that year to year contacts between premises were changing. The importance of individual premises for the network connectedness was highly heterogeneous and the most influential premises in the network were collection centers, mountain pastures, and pastures. Compared to random node removal, targeted removal informed by ranking based on local network measures from previous years was substantially more effective in network disassociation. Inclusion of the latest movement data improved the results. In the second part, we simulated disease spread using a Susceptible-Infectious (SI) model on the temporal network. The SI model was based on the empirically estimated true prevalence of paratuberculosis in Slovenia and four scenarios for probabilities of transmission. Different probabilities were realized by the generation of new networks with the corresponding proportion of contacts which were randomly selected from the original network. These diluted networks served as substrates for simulation of MAP spread. The probability of transmission had a significant influence on the velocity of disease spread through the network. The peaks in daily incidence rates of infected herds were observed at the end of the grazing period. Our results suggest that network analysis may provide support in the optimization of paratuberculosis surveillance and intervention in Slovenia. The approach of simulating disease spread on a diluted network may also be used to model other transmission pathways between herds.

Automatic classification of farms and traders in the pig production chain.

The trade in live pigs is an essential risk factor in the spread of animal diseases. Traders play a key role in the trade network, as they are logistics hubs and responsible for large animal movements. In order to implement targeted control measures in case of a disease outbreak, it is hence strongly advisable to use information about the holding type in the pig production chain. However, in many datasets the types of the producing farms or the fact whether the agent is a trader are unknown. In this paper we introduce two indices that can be used to identify the position of a producing farm in the pig production chain and more importantly, identify traders. This was realized partially through a novel dynamic programming algorithm. Analyzing the pig trade network in Germany from 2005 to 2007, we demonstrate that our algorithm is very sensitive in detecting traders. Since the methodology can easily be applied to trade networks in other countries with similar infrastructure and legislation, we anticipate its use for augmenting the datasets in further network analyses and targeting control measures. For further usage, we have developed an R package which can be found in the supplementary material to this manuscript.

Network analysis of pig movements: Loyalty patterns and contact chains of different holding types in Denmark.

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.

Impact of Network Activity on the Spread of Infectious Diseases through the German Pig Trade Network.

The trade of livestock is an important and growing economic sector, but it is also a major factor in the spread of diseases. The spreading of diseases in a trade network is likely to be influenced by how often existing trade connections are active. The activity α is defined as the mean frequency of occurrences of existing trade links, thus 0 < α ≤ 1. The observed German pig trade network had an activity of α = 0.11, thus each existing trade connection between two farms was, on average, active at about 10% of the time during the observation period 2008-2009. The aim of this study is to analyze how changes in the activity level of the German pig trade network influence the probability of disease outbreaks, size, and duration of epidemics for different disease transmission probabilities. Thus, we want to investigate the question, whether it makes a difference for a hypothetical spread of an animal disease to transport many animals at the same time or few animals at many times. A SIR model was used to simulate the spread of a disease within the German pig trade network. Our results show that for transmission probabilities <1, the outbreak probability increases in the case of a decreased frequency of animal transports, peaking range of α from 0.05 to 0.1. However, for the final outbreak size, we find that a threshold exists such that finite outbreaks occur only above a critical value of α, which is ~0.1, and therefore in proximity of the observed activity level. Thus, although the outbreak probability increased when decreasing α, these outbreaks affect only a small number of farms. The duration of the epidemic peaks at an activity level in the range of α = 0.2-0.3. Additionally, the results of our simulations show that even small changes in the activity level of the German pig trade network would have dramatic effects on outbreak probability, outbreak size, and epidemic duration. Thus, we can conclude and recommend that the network activity is an important aspect, which should be taken into account when modeling the spread of diseases within trade networks.

Disease Spread through Animal Movements: A Static and Temporal Network Analysis of Pig Trade in Germany.

BACKGROUND: 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. METHODOLOGY: 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. FINDINGS: 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.

Infections on Temporal Networks--A Matrix-Based Approach.

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.

On the robustness of in- and out-components in a temporal network.

BACKGROUND: 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. METHODOLOGY/FINDINGS: 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. CONCLUSIONS: 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.

Unfolding accessibility provides a macroscopic approach to temporal networks.

An accessibility graph of a network contains a link wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding paths of growing length (unfolding), we obtain information about the distribution of shortest path durations and characteristic time scales in temporal networks. Moreover, we define causal fidelity to measure the goodness of their static representation. The practicability of our proposed methods is demonstrated for three examples: networks of social contacts, livestock trade, and sexual contacts.

Spread of infectious diseases in directed and modular metapopulation networks.

We consider epidemics in metapopulations on different network topologies. Recent work on epidemics on networks has focused on epidemics of humans. In this work we present a model for epidemics on directed networks, which are found, for example, in the livestock trade. We show that the direction of edges and the modular structure of networks have an impact on the outbreak size and the time of the outbreak peak. In some circumstances, the outbreak size in directed networks can even be larger than in undirected systems. The results presented here could be useful for decision-making processes in directed modular systems.