Epidemic predictions in an imperfect world: modelling disease spread with partial data

A foot and mouth disease ranking of risk using cattle transportation

Foot-and-mouth disease (FMD) is a highly infectious condition that affects domestic and wild cloven-hoofed animals. This disease has substantial economic consequences. Livestock movement is one of the primary causes of disease dissemination. The centrality properties of the livestock mobilization transportation network provide valuable information for surveillance and control of FMD. However, the same transportation network can be described by different centrality descriptions, making it challenging to prioritize the most vulnerable nodes in the transportation network. This work considers the construction of a single network risk ranking, which helps prioritize disease control measurements. Results show that the proposed ranking constructed on 2016 livestock mobilization data may predict an actual outbreak reported in the Cesar (Colombia) region in 2018, with a performance measured by the area under the receiver operating characteristic curve of 0.91. This result constitutes the first quantitative evidence of the predictive capacity of livestock transportation to target FMD outbreaks. This approach may help decision-makers devise strategies to control and prevent FMD.

Cattle transport network predicts endemic and epidemic foot-and-mouth disease risk on farms in Turkey

The structure of contact networks affects the likelihood of disease spread at the population scale and the risk of infection at any given node. Though this has been well characterized for both theoretical and empirical networks for the spread of epidemics on completely susceptible networks, the long-term impact of network structure on risk of infection with an endemic pathogen, where nodes can be infected more than once, has been less well characterized. Here, we analyze detailed records of the transportation of cattle among farms in Turkey to characterize the global and local attributes of the directed—weighted shipments network between 2007-2012. We then study the correlations between network properties and the likelihood of infection with, or exposure to, foot-and-mouth disease (FMD) over the same time period using recorded outbreaks. The shipments network shows a complex combination of features (local and global) that have not been previously reported in other networks of shipments; i.e. small-worldness, scale-freeness, modular structure, among others. We find that nodes that were either infected or at high risk of infection with FMD (within one link from an infected farm) had disproportionately higher degree, were more central (eigenvector centrality and coreness), and were more likely to be net recipients of shipments compared to those that were always more than 2 links away from an infected farm. High in-degree (i.e. many shipments received) was the best univariate predictor of infection. Low in-coreness (i.e. peripheral nodes) was the best univariate predictor of nodes always more than 2 links away from an infected farm. These results are robust across the three different serotypes of FMD observed in Turkey and during periods of low-endemic prevalence and high-prevalence outbreaks.

Contact network epidemiology has been extensively used in the context of infectious diseases, primarily focusing on epidemic diseases. In this paper we use detailed recorded data about cattle exchange between farms in Turkey from 2007 to 2012, to build, analyze and characterize the directed-weighted complex network of shipments of cattle. Additionally, using outbreaks data about recorded cases of foot-and-mouth disease (FMD) in Turkey, we assess the correlation between the “farm’s” position in the network (importance) and the risk of being infected with FMD, which has been endemic in Turkey for a long time. We find some network measures that are more likely to identify high-risk and low-risk farms (in-degree and in-coreness, respectively) when proposing strategies for surveillance or containment of an infectious disease.

Quantifying changes in the British cattle movement network

The modelling of disease spread is crucial to the farming industry and policy makers. In some of these industries, excellent data exist on animal movements, along with the networks that these movements create, and allow researchers to model spread of disease (both epidemic and endemic). The Cattle Tracing System is an online recording system for cattle births, deaths and between-herd movements in the United Kingdom and is an excellent resource for any researchers interested in networks or modelling infectious disease spread through the UK cattle system. Data exist that cover many years, and it can be useful to know how much change is occurring in a network, to help judge the merit of using historical data within a modelling context. This article uses the data to construct weighted directed monthly movement networks for two distinct periods of time, 2004-2006 and 2015-2017, to quantify by how much the underlying structure of the network has changed. Substantial changes in network structure may influence policy-makers directly or may influence models built upon the network data, and these in turn could impact policy-makers and their assessment of risk. We examined 13 network metrics, ranging from general descriptive metrics such as total number of nodes with movements and total movements, through to metrics to describe the network (e.g., Giant weakly and strongly connected components) and metrics calculated per node (betweenness, degree and strength). Mixed effect models show that there is a statistically significant effect of the period (2004-2006 vs 2015-2017) in the values of nine of the 13 network metrics. For example median total degree decreased by 19%. In addition to examining networks for two time periods, two updates of the data were examined to determine by how much the movement data stored for 2004-2006 had been cleansed between updates. Examination of these updates shows that there are small decreases in problem movements (such as animals leaving slaughterhouses) and therefore evidence of historical data being improved between updates. In combination with the significant effect of period on many of the network metrics, the modification of data between updates provides further evidence that the most recent available data should be used for network modelling. This will ensure that the most representative descriptions of the network are available to provide accurate modelling results to best inform policy makers.

Challenges and opportunities for using national animal datasets to support foot-and-mouth disease control

National level databases of animal numbers, locations and movements provide the essential foundations for disease preparedness, outbreak investigations and control activities. These activities are particularly important for managing and mitigating the risks of high-impact transboundary animal disease outbreaks such as foot-and-mouth disease (FMD), which can significantly affect international trade access and domestic food security. In countries where livestock production systems are heavily subsidized by the government, producers are often required to provide detailed animal movement and demographic data as a condition of business. In the remaining countries, it can be difficult to maintain these types of databases and impossible to estimate the extent of missing or inaccurate information due to the absence of gold standard datasets for comparison. Consequently, competent authorities are often required to make decisions about disease preparedness and control based on available data, which may result in suboptimal outcomes for their livestock industries. It is important to understand the limitations of poor data quality as well as the range of methods that have been developed to compensate in both disease-free and endemic situations. Using FMD as a case example, this review first discusses the different activities that competent authorities use farm-level animal population data for to support (1) preparedness activities in disease-free countries, (2) response activities during an acute outbreak in a disease-free country, and (3) eradication and control activities in an endemic country. We then discuss (4) data requirements needed to support epidemiological investigations, surveillance, and disease spread modelling both in disease-free and endemic countries.

Beyond ranking nodes: Predicting epidemic outbreak sizes by network centralities

Identifying important nodes for disease spreading is a central topic in network epidemiology. We investigate how well the position of a node, characterized by standard network measures, can predict its epidemiological importance in any graph of a given number of nodes. This is in contrast to other studies that deal with the easier prediction problem of ranking nodes by their epidemic importance in given graphs. As a benchmark for epidemic importance, we calculate the exact expected outbreak size given a node as the source. We study exhaustively all graphs of a given size, so do not restrict ourselves to certain generative models for graphs, nor to graph data sets. Due to the large number of possible nonisomorphic graphs of a fixed size, we are limited to ten-node graphs. We find that combinations of two or more centralities are predictive (R2 scores of 0.91 or higher) even for the most difficult parameter values of the epidemic simulation. Typically, these successful combinations include one normalized spectral centrality (such as PageRank or Katz centrality) and one measure that is sensitive to the number of edges in the graph.

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

Spatially explicit livestock disease models require demographic data for individual farms or premises. In the U.S., demographic data are only available aggregated at county or coarser scales, so disease models must rely on assumptions about how individual premises are distributed within counties. Here, we addressed the importance of realistic assumptions for this purpose. We compared modeling of foot and mouth disease (FMD) outbreaks using simple randomization of locations to premises configurations predicted by the Farm Location and Agricultural Production Simulator (FLAPS), which infers location based on features such as topography, land-cover, climate, and roads. We focused on three premises-level Susceptible-Exposed-Infectious-Removed models available from the literature, all using the same kernel approach but with different parameterizations and functional forms. By computing the basic reproductive number of the infection (R₀) for both FLAPS and randomized configurations, we investigated how spatial locations and clustering of premises affects outbreak predictions. Further, we performed stochastic simulations to evaluate if identified differences were consistent for later stages of an outbreak. Using Ripley’s K to quantify clustering, we found that FLAPS configurations were substantially more clustered at the scales relevant for the implemented models, leading to a higher frequency of nearby premises compared to randomized configurations. As a result, R₀ was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R₀ and simulations exhibited substantial spatial heterogeneity in terms of differences between configurations. Thus, using realistic assumptions when de-aggregating locations based on available data can have a pronounced effect on epidemiological predictions, affecting if, where, and to what extent FMD may invade the population. We conclude that methods such as FLAPS should be preferred over randomization approaches.

When modeling the spread of infectious livestock diseases such as foot-and-mouth disease (FMD), the distance between premises is an important aspect. In the U.S., locations of premises are not available, forcing modelers to make assumptions about their coordinates. Such assumptions can be more or less crude and will impact the conclusions drawn from the model. To investigate the impact of such assumptions, we modeled outbreaks of FMD within the cattle population of the U.S. under two assumptions about premises locations. Their position was either randomly distributed within counties or informed by a state-of-the-art method developed specifically to simulate realistic locations of agricultural operations. We found that the higher degree of spatial clustering of premises associated with more realistic assumptions about locations leads to a substantially higher risk of outbreaks. Our results also show that the amount with which the risk is under-estimated by randomizing locations is unevenly distributed across the landscape. Together, these findings show a clear support for using informed methods to determine the spatial locations of premises and highlight the importance of spatial clustering when modeling FMD-like diseases.

The Role of Movement Restrictions in Limiting the Economic Impact of Livestock Infections

Movements are essential for the economic success of the livestock industry. These movements however bring the risk of long-range spread of infection, potentially bringing infection to previously disease-free areas where subsequent localised transmission can be devastating. Mechanistic predictive models usually consider controls that minimize the number of livestock affected without considering other costs of an ongoing epidemic. However, it is more appropriate to consider the economic burden, as movement restrictions have major consequences for the economic revenue of farms. Using mechanistic models of foot-and-mouth disease (FMD), bluetongue virus (BTV) and bovine tuberculosis (bTB) in the UK, we contrast the economically optimal control strategies for these diseases. We show that for FMD, the optimal strategy is to ban movements in a small radius around infected farms; the balance between disease control and maintaining 'business as usual' varies between regions. For BTV and bTB, we find that the cost of any movement ban is more than the epidemiological benefits due to the low within-farm prevalence and slow rate of disease spread. This work suggests that movement controls need to be carefully matched to the epidemiological and economic consequences of the disease, and optimal movement bans are often far shorter than existing policy.

Machine Learning Model for Imbalanced Cholera Dataset in Tanzania

Cholera epidemic remains a public threat throughout history, affecting vulnerable population living with unreliable water and substandard sanitary conditions. Various studies have observed that the occurrence of cholera has strong linkage with environmental factors such as climate change and geographical location. Climate change has been strongly linked to the seasonal occurrence and widespread of cholera through the creation of weather patterns that favor the disease's transmission, infection, and the growth of Vibrio cholerae, which cause the disease. Over the past decades, there have been great achievements in developing epidemic models for the proper prediction of cholera. However, the integration of weather variables and use of machine learning techniques have not been explicitly deployed in modeling cholera epidemics in Tanzania due to the challenges that come with its datasets such as imbalanced data and missing information. This paper explores the use of machine learning techniques to model cholera epidemics with linkage to seasonal weather changes while overcoming the data imbalance problem. Adaptive Synthetic Sampling Approach (ADASYN) and Principal Component Analysis (PCA) were used to the restore sampling balance and dimensional of the dataset. In addition, sensitivity, specificity, and balanced-accuracy metrics were used to evaluate the performance of the seven models. Based on the results of the Wilcoxon sign-rank test and features of the models, XGBoost classifier was selected to be the best model for the study. Overall results improved our understanding of the significant roles of machine learning strategies in health-care data. However, the study could not be treated as a time series problem due to the data collection bias. The study recommends a review of health-care systems in order to facilitate quality data collection and deployment of machine learning techniques.

Why sold, not culled? Analysing farm and animal characteristics associated with livestock selling practices

Livestock disease simulation models that incorporate animal movements often assume (1) that farmers' livestock trading practices remain consistent over time in future, (2) that animals sold to other farms are chosen randomly from a herd, and (3) that the animals' fate on the destination farm is not influenced by their past production and movement histories. The objective of this study was to assess the extent to which these assumptions are violated in the real world using records from a national database in New Zealand that captures both milk production and movement data for individual dairy cattle. All individual animal milk test records from 2006 through 2010 were extracted from the database and processed to generate different animal and herd level variables including cow demographics, previous movement history, milk volume, and milk composition (somatic cell counts (SCC), protein percentage, and fat percentage). Various statistical models were used to explore factors associated with farms' selling practice and characteristics of animals being sold. The results showed farms' livestock selling practices were highly influenced by both external factors such as market milk price and internal factors such as previous year's cow mortality and how long farms had been in business. Higher milk price increased both the number of cows being sold and the number of farms selling cows. Compared with cows that remained in the herd at the end of lactation, cows sold to other farms had lower fat and protein percentages, but similar milk volumes and SCCs. Cows that had been sold more often in the past were more likely to be sold after controlling for the effects of age. Overall, these findings highlight the potential need for disease simulation models to account for dynamics in selling practices and animal characteristics when determining which animals will be sold to other herds.

Spatio-temporal patterns and characteristics of swine shipments in the U.S. based on Interstate Certificates of Veterinary Inspection

Domestic swine production in the United States is a critical economic and food security industry, yet there is currently no large-scale quantitative assessment of swine shipments available to support risk assessments. In this study, we provide a national-level characterization of the swine industry by quantifying the demographic (i.e. age, sex) patterns, spatio-temporal patterns, and the production diversity within swine shipments. We characterize annual networks of swine shipments using a 30% stratified sample of Interstate Certificates of Veterinary Inspection (ICVI), which are required for the interstate movement of agricultural animals. We used ICVIs in 2010 and 2011 from eight states that represent 36% of swine operations and 63% of the U.S. swine industry. Our analyses reflect an integrated and spatially structured industry with high levels of spatial heterogeneity. Most shipments carried young swine for feeding or breeding purposes and carried a median of 330 head (range: 1–6,500). Geographically, most shipments went to and were shipped from Iowa, Minnesota, and Nebraska. This work, therefore, suggests that although the swine industry is variable in terms of its size and type of swine, counties in states historically known for breeding and feeding operations are consistently more central to the shipment network.

Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15

Real-time forecasts based on mathematical models can inform critical decision-making during infectious disease outbreaks. Yet, epidemic forecasts are rarely evaluated during or after the event, and there is little guidance on the best metrics for assessment. Here, we propose an evaluation approach that disentangles different components of forecasting ability using metrics that separately assess the calibration, sharpness and bias of forecasts. This makes it possible to assess not just how close a forecast was to reality but also how well uncertainty has been quantified. We used this approach to analyse the performance of weekly forecasts we generated in real time for Western Area, Sierra Leone, during the 2013-16 Ebola epidemic in West Africa. We investigated a range of forecast model variants based on the model fits generated at the time with a semi-mechanistic model, and found that good probabilistic calibration was achievable at short time horizons of one or two weeks ahead but model predictions were increasingly unreliable at longer forecasting horizons. This suggests that forecasts may have been of good enough quality to inform decision making based on predictions a few weeks ahead of time but not longer, reflecting the high level of uncertainty in the processes driving the trajectory of the epidemic. Comparing forecasts based on the semi-mechanistic model to simpler null models showed that the best semi-mechanistic model variant performed better than the null models with respect to probabilistic calibration, and that this would have been identified from the earliest stages of the outbreak. As forecasts become a routine part of the toolkit in public health, standards for evaluation of performance will be important for assessing quality and improving credibility of mathematical models, and for elucidating difficulties and trade-offs when aiming to make the most useful and reliable forecasts.

Invited review: Big Data in precision dairy farming

Insight into current scientific applications of Big Data in the precision dairy farming area may help us to understand the inflated expectations around Big Data. The objective of this invited review paper is to give that scientific background and determine whether Big Data has overcome the peak of inflated expectations. A conceptual model was created, and a literature search in Scopus resulted in 1442 scientific peer reviewed papers. After thorough screening on relevance and classification by the authors, 142 papers remained for further analysis. The area of precision dairy farming (with classes in the primary chain (dairy farm, feed, breed, health, food, retail, consumer) and levels for object of interest (animal, farm, network)), the Big Data-V area (with categories on Volume, Velocity, Variety and other V’s) and the data analytics area (with categories in analysis methods (supervised learning, unsupervised learning, semi-supervised classification, reinforcement learning) and data characteristics (time-series, streaming, sequence, graph, spatial, multimedia)) were analysed. The animal sublevel, with 83% of the papers, exceeds the farm sublevel and network sublevel. Within the animal sublevel, topics within the dairy farm level prevailed with 58% over the health level (33%). Within the Big Data category, the Volume category was most favoured with 59% of the papers, followed by 37% of papers that included the Variety category. None of the papers included the Velocity category. Supervised learning, representing 87% of the papers, exceeds unsupervised learning (12%). Within supervised learning, 64% of the papers dealt with classification issues and exceeds the regression methods (36%). Time-series were used in 61% of the papers and were mostly dealing with animal-based farm data. Multimedia data appeared in a greater number of recent papers. Based on these results, it can be concluded that Big Data is a relevant topic of research within the precision dairy farming area, but that the full potential of Big Data in this precision dairy farming area is not utilised yet. However, the present authors expect the full potential of Big Data, within the precision dairy farming area, will be reached when multiple Big Data characteristics (Volume, Variety and other V’s) and sources (animal, groups, farms and chain parts) are used simultaneously, adding value to operational and strategic decision.

Global Spread of Hemorrhagic Fever Viruses: Predicting Pandemics

As successive epidemics have swept the world, the scientific community has quickly learned from them about the emergence and transmission of communicable diseases. Epidemics usually occur when health systems are unprepared. During an unexpected epidemic, health authorities engage in damage control, fear drives action, and the desire to understand the threat is greatest. As humanity recovers, policy-makers seek scientific expertise to improve their "preparedness" to face future events.Global spread of disease is exemplified by the spread of yellow fever from Africa to the Americas, by the spread of dengue fever through transcontinental migration of mosquitos, by the relentless influenza virus pandemics, and, most recently, by the unexpected emergence of Ebola virus, spread by motorbike and long haul carriers. Other pathogens that are remarkable for their epidemic expansions include the arenavirus hemorrhagic fevers and hantavirus diseases carried by rodents over great geographic distances and the arthropod-borne viruses (West Nile, chikungunya and Zika) enabled by ecology and vector adaptations. Did we learn from the past epidemics? Are we prepared for the worst?The ultimate goal is to develop a resilient global health infrastructure. Besides acquiring treatments, vaccines, and other preventive medicine, bio-surveillance is critical to preventing disease emergence and to counteracting its spread. So far, only the western hemisphere has a large and established monitoring system; however, diseases continue to emerge sporadically, in particular in Southeast Asia and South America, illuminating the imperfections of our surveillance. Epidemics destabilize fragile governments, ravage the most vulnerable populations, and threaten the global community.Pandemic risk calculations employ new technologies like computerized maintenance of geographical and historical datasets, Geographic Information Systems (GIS), Next Generation sequencing, and Metagenomics to trace the molecular changes in pathogens during their emergence, and mathematical models to assess risk. Predictions help to pinpoint the hot spots of emergence, the populations at risk, and the pathogens under genetic evolution. Preparedness anticipates the risks, the needs of the population, the capacities of infrastructure, the sources of emergency funding, and finally, the international partnerships needed to manage a disaster before it occurs. At present, the world is in an intermediate phase of trying to reduce health disparities despite exponential population growth, political conflicts, migration, global trade, urbanization, and major environmental changes due to global warming. For the sake of humanity, we must focus on developing the necessary capacities for health surveillance, epidemic preparedness, and pandemic response.

Epidemics on dynamic networks

In many populations, the patterns of potentially infectious contacts are transients that can be described as a network with dynamic links. The relative timescales of link and contagion dynamics and the characteristics that drive their tempos can lead to important differences to the static case. Here, we propose some essential nomenclature for their analysis, and then review the relevant literature. We describe recent advances in they apply to infection processes, considering all of the methods used to record, measure and analyse them, and their implications for disease transmission. Finally, we outline some key challenges and opportunities in the field.

Dynamic network measures reveal the impact of cattle markets and alpine summering on the risk of epidemic outbreaks in the Swiss cattle population

BACKGROUND

Livestock herds are interconnected with each other via an intricate network of transports of animals which represents a potential substrate for the spread of epidemic diseases. We analysed four years (2012-2015) of daily bovine transports to assess the risk of disease transmission and identify times and locations where monitoring would be most effective. Specifically, we investigated how the seasonal dynamics of transport networks, driven by the alpine summering and traditional cattle markets, affect the risk of epidemic outbreaks.

RESULTS

We found strong and consistent seasonal variation in several structural network measures as well as in measures for outbreak risk. Analysis of the consequences of excluding markets, dealers and alpine pastures from the network shows that markets contribute much more to the overall outbreak risk than alpine summering. Static descriptors of monthly transport networks were poor predictors of outbreak risk emanating from individual holdings; a dynamic measure, which takes the temporal structure of the network into account, gave better risk estimates. A stochastic simulation suggests that targeted surveillance based on this dynamic network allows a higher detection rate and smaller outbreak size at detection than compared to other sampling schemes.

CONCLUSIONS

Dynamic measures based on time-stamped data-the outgoing contact chain-can give better risk estimates and could help to improve surveillance schemes. Using this measure we find evidence that even in a country with intense summering practice, markets continue being the prime risk factor for the spread of contagious diseases.

Towards the description of livestock mobility in Sahelian Africa: Some results from a survey in Mauritania

Understanding spatio-temporal patterns of host mobility is a key factor to prevent and control animal and human diseases. This is utterly important in low-income countries, where animal disease epidemics have strong socio-economic impacts. In this article we analyzed a livestock mobility database, whose data have been collected by the Centre National d'Elevage et de Recherches Vétérinaires (CNERV) Mauritania, to describe its patterns and temporal evolution. Data were collected through phone and face-to-face interviews in almost all the regions in Mauritania over a period of roughly two weeks during June 2015. The analysis has shown the existence of two mobility patterns throughout the year: the first related to routine movements from January to August; the second strictly connected to the religious festivity of Tabaski that in 2014 occurred at the beginning of October. These mobility patterns are different in terms of animals involved (fewer cattle and dromedaries are traded around Tabaski), the means of transportation (the volume of animals moved by truck raises around Tabaski) and destinations (most of the animals are traded nationally around Tabaski). Due to the differences between these two periods, public health officers, researchers and other stakeholders should take account of the time of the year when implementing vaccination campaigns or creating surveillance networks.

Model-guided suggestions for targeted surveillance based on cattle shipments in the U.S

Risk-based sampling is an essential component of livestock health surveillance because it targets resources towards sub-populations with a higher risk of infection. Risk-based surveillance in U.S. livestock is limited because the locations of high-risk herds are often unknown and data to identify high-risk herds based on shipments are often unavailable. In this study, we use a novel, data-driven network model for the shipments of cattle in the U.S. (the U.S. Animal Movement Model, USAMM) to provide surveillance suggestions for cattle imported into the U.S. from Mexico. We describe the volume and locations where cattle are imported and analyze their predicted shipment patterns to identify counties that are most likely to receive shipments of imported cattle. Our results suggest that most imported cattle are sent to relatively few counties. Surveillance at 10 counties is predicted to sample 22-34% of imported cattle while surveillance at 50 counties is predicted to sample 43%-61% of imported cattle. These findings are based on the assumption that USAMM accurately describes the shipments of imported cattle because their shipments are not tracked separately from the remainder of the U.S. herd. However, we analyze two additional datasets - Interstate Certificates of Veterinary Inspection and brand inspection data - to ensure that the characteristics of potential post-import shipments do not change on an annual scale and are not dependent on the dataset informing our analyses. Overall, these results highlight the utility of USAMM to inform targeted surveillance strategies when complete shipment information is unavailable.

Market analyses of livestock trade networks to inform the prevention of joint economic and epidemiological risks

Conventional epidemiological studies of infections spreading through trade networks, e.g. via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic–epidemiological risks in networks underlying pathogen propagation and trade.

Challenges and priorities for modelling livestock health and pathogens in the context of climate change

Climate change has the potential to impair livestock health, with consequences for animal welfare, productivity, greenhouse gas emissions, and human livelihoods and health. Modelling has an important role in assessing the impacts of climate change on livestock systems and the efficacy of potential adaptation strategies, to support decision making for more efficient, resilient and sustainable production. However, a coherent set of challenges and research priorities for modelling livestock health and pathogens under climate change has not previously been available. To identify such challenges and priorities, researchers from across Europe were engaged in a horizon-scanning study, involving workshop and questionnaire based exercises and focussed literature reviews. Eighteen key challenges were identified and grouped into six categories based on subject-specific and capacity building requirements. Across a number of challenges, the need for inventories relating model types to different applications (e.g. the pathogen species, region, scale of focus and purpose to which they can be applied) was identified, in order to identify gaps in capability in relation to the impacts of climate change on animal health. The need for collaboration and learning across disciplines was highlighted in several challenges, e.g. to better understand and model complex ecological interactions between pathogens, vectors, wildlife hosts and livestock in the context of climate change. Collaboration between socio-economic and biophysical disciplines was seen as important for better engagement with stakeholders and for improved modelling of the costs and benefits of poor livestock health. The need for more comprehensive validation of empirical relationships, for harmonising terminology and measurements, and for building capacity for under-researched nations, systems and health problems indicated the importance of joined up approaches across nations. The challenges and priorities identified can help focus the development of modelling capacity and future research structures in this vital field. Well-funded networks capable of managing the long-term development of shared resources are required in order to create a cohesive modelling community equipped to tackle the complex challenges of climate change.

Sample size considerations for livestock movement network data

The movement of animals between farms contributes to infectious disease spread in production animal populations, and is increasingly investigated with social network analysis methods. Tangible outcomes of this work include the identification of high-risk premises for targeting surveillance or control programs. However, knowledge of the effect of sampling or incomplete network enumeration on these studies is limited. In this study, a simulation algorithm is presented that provides an estimate of required sampling proportions based on predicted network size, density and degree value distribution. The algorithm may be applied a priori to ensure network analyses based on sampled or incomplete data provide population estimates of known precision. Results demonstrate that, for network degree measures, sample size requirements vary with sampling method. The repeatability of the algorithm output under constant network and sampling criteria was found to be consistent for networks with at least 1000 nodes (in this case, farms). Where simulated networks can be constructed to closely mimic the true network in a target population, this algorithm provides a straightforward approach to determining sample size under a given sampling procedure for a network measure of interest. It can be used to tailor study designs of known precision, for investigating specific livestock movement networks and their impact on disease dissemination within populations.