Bayesian analysis of animal movements related to factors at herd and between herd levels: Implications for disease spread modeling

A method to assess the influence of between herd distances, production types and herd sizes on patterns of between herd contacts is presented. It was applied on pig movement data from a central database of the Swedish Board of Agriculture. To determine the influence of these factors on the contact between holdings we used a Bayesian model and Markov chain Monte Carlo (MCMC) methods to estimate the posterior distribution of model parameters. The analysis showed that the contact pattern via animal movements is highly heterogeneous and influenced by all three factors, production type, herd size, and distance between holdings. Most production types showed a positive relationship between maximum capacity and the probability of both incoming and outgoing movements. In agreement with previous studies, holdings also differed in both the number of contacts as well as with what holding types contact occurred with. Also, the scale and shape of distance dependence in contact probability was shown to differ depending on the production types of holdings.To demonstrate how the methodology may be used for risk assessment, disease transmissions via animal movements were simulated with the model used for analysis of contacts, and parameterized by the analyzed posterior distribution. A Generalized Linear Model showed that herds with production types Sow pool center, Multiplying herd and Nucleus herd have higher risk of generating a large number of new infections. Multiplying herds are also expected to generate many long distance transmissions, while transmissions generated by Sow pool centers are confined to more local areas. We argue that the methodology presented may be a useful tool for improvement of risk assessment based on data found in central databases.     

The effectiveness of fallowing strategies in disease control in salmon aquaculture assessed with an SIS model

Salmon production is an important industry in Scotland, with an estimated retail value >￡1 billion. However, this salmon industry can be threatened by the invasion and spread of diseases. To reduce this risk, the industry is divided into management areas that are physically separated from each other. Pathogens can spread between farms by local processes such as water movement or by long-distance processes such as live fish movements. Here, network modelling was used to investigate the importance of transmission routes at these two scales. We used different disease transmission rates (β), where infected farms had the probability of 0.10, 0.25 or 0.50 per month to infect each contacted farm. Interacting farms were modelled in such a way that neighbours within a management area could infect each other, resulting in two contacts per farm per month. In addition, non-local transmission occurred at random. Salmon are input to marine sites where they are raised to harvest size, the site is then fallowed; in the model the effects of different fallowing strategies (synchronised, partial synchronised and unsynchronised fallowing at the management area level) on the emergence of diseases were investigated. Synchronised fallowing was highly effective at eradicating epidemics when transmission rate is low (β=0.10) even when long distance contacts were fairly common (up to 1.5farm(-1)month(-1)). However for higher transmission rates, long distance contacts have to be kept at much lower levels (0.15contactsmonth(-1) where β=0.25) when synchronised fallowing was applied. If fallowing was partially synchronised or unsynchronised then low rates of long-distance contact are required (0.75 or 0.15farm(-1)month(-1)) even if β=0.10. These results demonstrate the potential benefits of having epidemiologically isolated management areas and applying synchronised fallowing.     

Farm animal networks: unraveling the contact structure of the British sheep population

The spatial and temporal dynamics of many farm animal diseases depend both on disease specific parameters and on the underlying contact structure between farms. Whilst many models for farm animal diseases focus on obtaining and estimating disease transmission parameters, relatively little attention has been given to modelling the underlying network of contacts. In this paper, we present an initial analysis of two relations underlying the contact network of individual sheep breeds in Great Britain. The first relation is based on geographical proximity and the second is based on attendance at agricultural shows. These relations are combined to give a risk-potential network that is based on these two levels of interaction. The structure of each network is investigated using techniques developed in graph theory and social network analysis.     

A novel epidemiological model to better understand and predict the observed seasonal spread of Pestivirus in Pyrenean chamois populations

Seasonal variations in individual contacts give rise to a complex interplay between host demography and pathogen transmission. This is particularly true for wild populations, which highly depend on their natural habitat. These seasonal cycles induce variations in pathogen transmission. The seasonality of these biological processes should therefore be considered to better represent and predict pathogen spread. In this study, we sought to better understand how the seasonality of both the demography and social contacts of a mountain ungulate population impacts the spread of a pestivirus within, and the dynamics of, this population. We propose a mathematical model to represent this complex biological system. The pestivirus can be transmitted both horizontally through direct contact and vertically in utero. Vertical transmission leads to abortion or to the birth of persistently infected animals with a short life expectancy. Horizontal transmission involves a complex dynamics because of seasonal variations in contact among sexes and age classes. We performed a sensitivity analysis that identified transmission rates and disease-related mortality as key parameters. We then used data from a long-term demographic and epidemiological survey of the studied population to estimate these mostly unknown epidemiological parameters. Our model adequately represents the system dynamics, observations and model predictions showing similar seasonal patterns. We show that the virus has a significant impact on population dynamics, and that persistently infected animals play a major role in the epidemic dynamics. Modeling the seasonal dynamics allowed us to obtain realistic prediction and to identify key parameters of transmission.

Electronic supplementary material

The online version of this article (doi:10.1186/s13567-015-0218-8) contains supplementary material, which is available to authorized users.     

A novel method to identify herds with an increased probability of disease introduction due to animal trade

In the design of surveillance, there is often a desire to target high risk herds. Such risk-based approaches result in better allocation of resources and improve the performance of surveillance activities. For many contagious animal diseases, movement of live animals is a main route of transmission, and because of this, herds that purchase many live animals or have a large contact network due to trade can be seen as a high risk stratum of the population. This paper presents a new method to assess herd disease risk in animal movement networks. It is an improvement to current network measures that takes direction, temporal order, and also movement size and probability of disease into account. In the study, the method was used to calculate a probability of disease ratio (PDR) of herds in simulated datasets, and of real herds based on animal movement data from dairy herds included in a bulk milk survey for Coxiella burnetii. Known differences in probability of disease are easily incorporated in the calculations and the PDR was calculated while accounting for regional differences in probability of disease, and also by applying equal probability of disease throughout the population. Each herd's increased probability of disease due to purchase of animals was compared to both the average herd and herds within the same risk stratum. The results show that the PDR is able to capture the different circumstances related to disease prevalence and animal trade contact patterns. Comparison of results based on inclusion or exclusion of differences in risk also highlights how ignoring such differences can influence the ability to correctly identify high risk herds. The method shows a potential to be useful for risk-based surveillance, in the classification of herds in control programmes or to represent influential contacts in risk factor studies.     

Network modeling of BVD transmission

ABSTRACT: Endemic diseases of cattle, such as bovine viral diarrhea, have significant impact on production efficiency of food of animal origin with consequences for animal welfare and climate change reduction targets. Many modeling studies focus on the local scale, examining the on-farm dynamics of this infectious disease. However, insight into prevalence and control across a network of farms ultimately requires a network level approach. Here, we implement understanding of infection dynamics, gained through these detailed on-farm modeling studies, to produce a national scale model of bovine viral diarrhea virus transmission. The complex disease epidemiology and on-farm dynamics are approximated using SIS dynamics with each farm treated as a single unit. Using a top down approach, we estimate on-farm parameters associated with contraction and subsequent clearance from infection at herd level. We examine possible control strategies associated with animal movements between farms and find measures targeted at a small number of high-movement farms efficient for rapid and sustained prevalence reduction.     

Use of heterogeneous operation-specific contact parameters changes predictions for foot-and-mouth disease outbreaks in complex simulation models

The role of contact parameters in a complex spatial simulation model of foot-and-mouth disease spread was determined by comparing predictions of number of infected premises, epidemic duration, and relative infection risk for different production sectors between a model that included the Full, heterogeneous (differing by production type) type-specific information about animal, vehicle and personnel movement between premises, and models that used partial and homogeneous (similar across production types) weighted-mean or proxy parameter sets for contacts between premises of all types. The model was run using a dataset of known premises locations in a three-county area in the Central Valley of California and categorized into 13 premises types and six production sectors.Results from models run with homogeneous contact parameters were always different from those obtained from the Full model, demonstrating that model predictions are affected by heterogeneity in contact parameters. Models simplified by using weighted-mean parameters predicted fewer infected premises. Models that were simplified by using medium dairy farm or large swine operation proxy parameters predicted longer epidemics with more infected premises, while those using small beef operation proxy parameters predicted shorter epidemics with fewer infected premises. Simplified-parameter models underestimated the impact on the economically important dairy sector, while overestimating the impact on beef and backyard operations. Results establish a need for heterogeneous, operation-specific contact parameters in complex stochastic simulation models that must be weighed against the cost of obtaining and coding premises type-specific contact information.     

Small-world topology of UK racing: the potential for rapid spread of infectious agents

REASONS FOR PERFORMING STUDY: The topology of the network of contacts between individuals has important effects on infectious disease dynamics within a population. Here we examine for the first time a network of contacts between training yards that occurred through racing. OBJECTIVES: To explore the topology of this network and to consider the effects of the network on the potential for disease transmission. METHODS: Race data from one week was analysed. Contacts were defined as occurring between trainers that raced horses in the same race and hence one trainer could contact another trainer several times. A connection was said to exist between trainers who contacted each other at least once. The network of contacts and connections that occurred during the study period was reconstructed and analysed. RESULTS: All 466 trainers formed a single large network. The network of contacts had a short average path length and high clustering and was, therefore, characteristic of a 'small world network'. The probability distribution of the number of contacts was scale-free, whereas that for the number of connections followed a single-scale. The effect of the network would be to increase R0, such that an agent that would tend toward extinction in a homogenously mixing population may persist in the observed network. CONCLUSIONS: The observed small world network topology has important implication for the transmission and, therefore, the control of infectious agents in this population. POTENTIAL RELEVANCE: Effective disease control and surveillance must take account of the contact structure of the population. Further studies investigating other contact definitions and other populations are now required.     

Impact of regulatory perturbations to disease spread through cattle movements in Great Britain

During the past decade the British livestock industry has suffered from several major pathogen outbreaks, and a variety of regulatory and disease control measures have been applied to the movement of livestock with the express aim of mitigating the spread of infection. The Rapid Analysis and Detection of Animal-related Risks (RADAR) project, which has been collecting data on the movement of cattle since 1998, provides a relatively comprehensive record of how these policies have influenced the movement of cattle between animal holdings, markets, and slaughterhouses in Britain. Many previous studies have focused on the properties of the network that can be derived from these movements--treating farms as nodes and movements as directed (and potentially weighted) edges in the network. However, of far greater importance is how these policy changes have influenced the potential spread of infectious diseases. Here we use a stochastic fully individual-based model of cattle in Britain to assess how the epidemic potential has varied from 2000 to 2009 as the pattern of movements has changed in response to legislation and market forces. Our simulations show that the majority of policy changes lead to significant decreases in the epidemic potential (measured in multiple ways), but that this potential then increases through time as cattle farmers modify their behaviour in response. Our results suggest that the cattle industry is likely to experience boom-bust dynamics, with the actions that farmers take during epidemic-free periods to maximise their profitability likely to increase the potential for large-scale epidemics to occur.     

Influence of contact heterogeneity on TB reproduction ratio R0 in a free-living brushtail possum Trichosurus vulpecula population

Social network analyses were used to investigate contact patterns in a free-living possum Trichosurus vulpecula population and to estimate the influence of contact on R(0) for bovine tuberculosis (TB). Using data collected during a five-year capture-mark-recapture study of a free-living possum population, observed estimates of R(0) were computed and compared with R(0) computed from random networks of similar size that approximated a random mixing process. All networks displayed a heterogeneous pattern of contact with the average number of contacts per possum ranging from 20 to 26 per year. The networks consistently showed small-world and single-scale features. The mean estimates of R(0) for TB using the observed contact networks were 1.78, 1.53, 1.53, 1.51, and 1.52 times greater than the corresponding random networks (P <0.05). We estimate that TB would spread if an average of between 1.94 and 1.97 infective contacts occurred per year per infected possum, which is approximately half of that expected from a random network. These results have implications for the management of TB in New Zealand where the possum is the principal wildlife reservoir host of Mycobacterium bovis, the causal agent of bovine TB. This study argues the relevance of refining epidemiological models used to inform disease management policy to account for contact heterogeneity.     

Network analysis of Danish cattle industry trade patterns as an evaluation of risk potential for disease spread

Trade patterns of animal movements in a specific industry are complex and difficult to study because there are many stakeholders, premises that are heterogeneously spread over the country, and a highly dynamic flow of animals exists among them. The Danish cattle industry was defined as a network of animal movements and graph theory was used to analyse the movements of cattle within this network. A premise was defined as a farm, an abattoir or a market. These premises constituted the network nodes in the graph and the animal movements between them were the links. In this framework, each premise had a sub-network of other premises to which it was linked by these animal movements. If no movement of animals were registered for a specific farm, then the sub-network for that premise consisted of only that premise. Otherwise, the sub-network linked the premise of interest to all premises from which and to which animals were moved, as long as there was a path linking animal movements to that specific premise. This approach allowed visualization and analyses of four levels of organization that existed in Denmark animal registers: (1) the animal that was moved, (2) the movements of all animals between two premises, (3) the specific premise network, and (4) the overall industry network. When contagious animals are moved from one premise to another, then to a third and so forth, these movements create a path for potential transfer of pathogens. The paths within which pathogens are present identify the transmission risks. A network of animal movements should provide information about pathogen transmission and disease spread. The network of the Danish cattle industry network was a directed scale-free graph (the direction of a movement was known), with an in-degree power of 2 an out-degree power of 1.46, consisted of 29,999 nodes, and 130,265 movements during a 6-month period. The in clustering coefficient was calculated to be 0.52 for the inward direction (movement to), while it was 0.02 for the outward direction (movement from). In Denmark, the cattle movements between premises demonstrated a large degree of heterogeneity. This heterogeneity in movements between farms should be used to evaluate the risk potential of disease transmission for each premise and must be considered when modelling disease spread between premises. The objective of this research was to describe the network of animal movements and not just the animal movements per se.     

Models to capture the potential for disease transmission in domestic sheep flocks

Successful control of livestock diseases requires an understanding of how they spread amongst animals and between premises. Mathematical models can offer important insight into the dynamics of disease, especially when built upon experimental and/or field data. Here the dynamics of a range of epidemiological models are explored in order to determine which models perform best in capturing real-world heterogeneities at sufficient resolution. Individual based network models are considered together with one- and two-class compartmental models, for which the final epidemic size is calculated as a function of the probability of disease transmission occurring during a given physical contact between two individuals. For numerical results the special cases of a viral disease with a fast recovery rate (foot-and-mouth disease) and a bacterial disease with a slow recovery rate (brucellosis) amongst sheep are considered. Quantitative results from observational studies of physical contact amongst domestic sheep are applied and results from the differently structured flocks (ewes with newborn lambs, ewes with nearly weaned lambs and ewes only) compared. These indicate that the breeding cycle leads to significant changes in the expected basic reproduction ratio of diseases. The observed heterogeneity of contacts amongst animals is best captured by full network simulations, although simple compartmental models describe the key features of an outbreak but, as expected, often overestimate the speed of an outbreak. Here the weights of contacts are heterogeneous, with many low weight links. However, due to the well-connected nature of the networks, this has little effect and differences between models remain small. These results indicate that simple compartmental models can be a useful tool for modelling real-world flocks; their applicability will be greater still for more homogeneously mixed livestock, which could be promoted by higher intensity farming practices.     

Qualitative risk assessment in a data-scarce environment: a model to assess the impact of control measures on spread of African Swine Fever

In the absence of data, qualitative risk assessment frameworks have proved useful to assess risks associated with animal health diseases. As part of a scientific opinion for the European Commission (EC) on African Swine Fever (ASF), a working group of the European Food Safety Authority (EFSA) assessed the risk of ASF remaining endemic in Trans Caucasus Countries (TCC) and the Russian Federation (RF) and the risk of ASF becoming endemic in the EU if disease were introduced. The aim was to develop a tool to evaluate how current control or preventive measures mitigate the risk of spread and giving decision makers the means to review how strengthening of surveillance and control measures would mitigate the risk of disease spread. Based on a generic model outlining disease introduction, spread and endemicity in a region, the impact of risk mitigation measures on spread of disease was assessed for specific risk questions. The resulting hierarchical models consisted of key steps containing several sub-steps. For each step of the risk pathways risk estimates were determined by the expert group based on existing data or through expert opinion elicitation. Risk estimates were combined using two different combination matrices, one to combine estimates of independent steps and one to combine conditional probabilities. The qualitative risk assessment indicated a moderate risk that ASF will remain endemic in current affected areas in the TCC and RF and a high risk of spread to currently unaffected areas. If introduced into the EU, ASF is likely to be controlled effectively in the production sector with high or limited biosecurity. In the free range production sector, however, there is a moderate risk of ASF becoming endemic due to wild boar contact, non-compliance with animal movement bans, and difficult access to all individual pigs upon implementation of control measures. This study demonstrated the advantages of a systematic framework to assist an expert panel to carry out a risk assessment as it helped experts to disassociate steps in the risk pathway and to overcome preconceived notions of final risk estimates. The approach presented here shows how a qualitative risk assessment framework can address animal diseases with complexity in their spread and control measures and how transparency of the resulting estimates was achieved.     

The role of spatial mixing in the spread of foot-and-mouth disease

A model of epidemic dispersal (based on the assumption that susceptible cattle were homogeneously mixed over space, or non-spatial model) was compared to a partially spatially explicit and discrete model (the spatial model), which was composed of differential equations and used geo-coded data (Euclidean distances between county centroids). While the spatial model accounted for intra- and inter-county epidemic spread, the non-spatial model did not assess regional differences. A geo-coded dataset that resembled conditions favouring homogeneous mixing assumptions (based on the 2001 Uruguayan foot-and-mouth disease epidemic), was used for testing. Significant differences between models were observed in the average transmission rate between farms, both before and after a control policy (animal movement ban) was imposed. They also differed in terms of daily number of infected farms: the non-spatial model revealed a single epidemic peak (at, approximately, 25 epidemic days); while the spatial model revealed two epidemic peaks (at, approximately, 12 and 28 days, respectively). While the spatial model fitted well with the observed cumulative number of infected farms, the non-spatial model did not (P<0.01). In addition, the spatial model: (a) indicated an early intra-county reproductive number R of approximately 87 (falling to <1 within 25 days), and an inter-county R<1; (b) predicted that, if animal movement restrictions had begun 3 days before/after the estimated initiation of such policy, cases would have decreased/increased by 23 or 26%, respectively. Spatial factors (such as inter-farm distance and coverage of vaccination campaigns, absent in non-spatial models) may explain why partially explicit spatial models describe epidemic spread more accurately than non-spatial models even at early epidemic phases. Integration of geo-coded data into mathematical models is recommended.     

Description of empirical movement data from Canadian swine herds with an application to a disease spread simulation model

We report the methods and findings of a survey of Canadian swine producers summarizing farm-types at-risk of foreign animal disease (FAD) and the routine movement of animals, semen and workers among swine farms, as observed during a 42-day period. Of the 311 producers who returned completed questionnaires, 17% represented swine-herds with no swine or semen movement on or off the farm during the 42 days, 57% were sow herds or farrow-to-finish herds with limited movement onto the farm but movement off the farm, and 26% were swine-herds with movements on and off the farm. A substantial number of premises (>50% in some provinces) with swine also kept other animal species on the same premises. We applied the empirical movement data from the survey in a stochastic simulation model to estimate the number of herds infected and the basic regional distribution of infection that could be expected to occur if the FAD was not detected and routine movements were permitted to occur up to 42 days after infection with a FAD of a single randomly selected herd. Forty-five percent of the simulations did not involve spread beyond the index farm, whereas 34.8% involved spread among five or more farms after 42 days of routine movement.     

Modeling spatial and temporal transmission of foot-and-mouth disease in France: identification of high-risk areas

Foot-and-mouth disease is one of the most contagious diseases of animal livestock. We used statistical tools to explore the dynamics of epidemics and to evaluate the consequences of virus reintroduction in France. We developed a stochastic farm-based model adapted to the French farm structure from previous modeling works following the 2001 epidemic in the United Kingdom. This model depends upon the distance between the 280,000 French farms and on species type (e.g. cows and sheep) and it tracks each animal's farm status at any given day. Since data were only available at the town scale, the farm location and the number of animals in each farm were simulated over the surface area of each French town, as well as the number of mixed farms. Based on 200 simulations of the model, our results allowed for the study of local disease transmission, since it begins simulations once limitation of movement is put into place. On average, the same 50 randomly chosen initially infected farms would lead to 1,110 infected farms (610; 1,590) when two control strategies (culling within 0.5 km from an infected farm and vaccination within 3 km) are put into place. Regions with high densities of cows and sheep (e.g. Pays-de-la-Loire) are high-risk zones, confirming that the epidemic process depends upon the location and the type of initially infected farms (size, species type). The results of this model highlight the importance of Geographical Information Systems (GIS) to obtain more precise data concerning herds.     

Direct and indirect contacts between cattle farms in north-west England

Little is known regarding the types and frequencies of contact that exist between farms and which of these may act as pathogen transmission routes; however it is likely that farms demonstrate considerable heterogeneity in such contacts. In this cross-sectional study, we explored the direct and indirect contact types and frequencies that exist between cattle farms within a region, focusing on potential routes of pathogen transmission. The owners/managers of 56 farms located in a 10 km by 10 km study area in north-west England were administered an interview-based questionnaire between June and September 2005. Information was obtained relating to contact types and frequencies, including those involving animal movements, equipment sharing between farms and any contractors or companies visiting the farms.

The data was explored using hierarchical cluster analysis and network analysis. There was considerable variation between farms arising from different contact types. Some networks exhibited great connectivity, incorporating approximately 90% of the farms interviewed in a single component, whilst other networks were more fragmented, with multiple small components (sets of connected farms not linked with other farms). A range of factors influencing contact between farms were identified. For example, contiguous farms were more likely to be linked via other contacts, such as sharing of equipment and direct farm-to-farm animal movements (p < 0.001 and p = 0.02, respectively).

The frequency of contacts was also investigated; it is likely that the amount of contact a farm receives from a company or contractor and whether or not biosecurity is performed after contact would impact on disease transmission potential. We found considerable heterogeneity in contact frequency and that many company and contractor personnel undertook little biosecurity.

These findings lead to greater understanding of inter-farm contact and may aid development of appropriate biosecurity practices and control procedures, and inform mathematical modelling of infectious diseases.