A mechanistic model captures livestock trading, disease dynamics, and compensatory behaviour in response to control measures.

Trade is a complex, multi-faceted process that can contribute to the spread and persistence of disease. We here develop novel mechanistic models of supply. Our model is framed within a livestock trading system, where farms form and end trade partnerships with rates dependent on current demand, with these trade partnerships facilitating trade between partners. With these time-varying, stock dependent partnership and trade dynamics, our trading model goes beyond current state of the art modelling approaches. By studying instantaneous shocks to farm-level supply and demand we show that behavioural responses of farms lead to trading systems that are highly resistant to shocks with only temporary disturbances to trade observed. Individual adaptation in response to permanent alterations to trading propensities, such that animal flows are maintained, illustrates the ability for farms to find new avenues of trade, minimising disruptions imposed by such alterations to trade that common modelling approaches cannot adequately capture. In the context of endemic disease control, we show that these adaptations hinder the potential beneficial reductions in prevalence such changes to trading propensities have previously been shown to confer. Assessing the impact of a common disease control measure, post-movement batch testing, highlights the ability for our model to measure the stress on multiple components of trade imposed by such control measures and also highlights the temporary and, in some cases, the permanent disturbances to trade that post-movement testing has on the trading system.

When and why direct transmission models can be used for environmentally persistent pathogens.

Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen's characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models' mean outputs diverge, with distinct predictions of outbreak size and duration.

Survival of Mycobacterium avium subspecies paratuberculosis in retail pasteurised milk.

A survey of retail purchased semi-skimmed pasteurised milk (n = 368) for Mycobacterium avium subspecies paratuberculosis (MAP) was conducted between May 2014 and June 2015 across the midlands of England using the Phage-PCR assay. Overall, 10.3% of the total samples collected contained viable MAP cells, confirming that pasteurisation is not capable of fully eliminating human exposure to viable MAP through milk. Comparison of the results gained using the Phage-PCR assay with the results of surveys using either culture or direct PCR suggest that the phage-PCR assay is able to detect lower numbers of cells, resulting in an increase in the number of MAP-positive samples detected. Comparison of viable count and levels of MAP detected in bulk milk samples suggest that MAP is not primarily introduced into the milk by faecal contamination but rather are shed directly into the milk within the udder. In addition results detected an asymmetric distribution of MAP exists in the milk matrix prior to somatic cell lysis, indicating that the bacterial cells in naturally contaminated milk are clustered together and may primarily be located within somatic cells. These latter two results lead to the hypothesis that intracellular MAP within the somatic cells may be protected against heat inactivation during pasteurisation, accounting for the presence of low levels of MAP detected in retail milk.

Using Combined Diagnostic Test Results to Hindcast Trends of Infection from Cross-Sectional Data.

Infectious disease surveillance is key to limiting the consequences from infectious pathogens and maintaining animal and public health. Following the detection of a disease outbreak, a response in proportion to the severity of the outbreak is required. It is thus critical to obtain accurate information concerning the origin of the outbreak and its forward trajectory. However, there is often a lack of situational awareness that may lead to over- or under-reaction. There is a widening range of tests available for detecting pathogens, with typically different temporal characteristics, e.g. in terms of when peak test response occurs relative to time of exposure. We have developed a statistical framework that combines response level data from multiple diagnostic tests and is able to 'hindcast' (infer the historical trend of) an infectious disease epidemic. Assuming diagnostic test data from a cross-sectional sample of individuals infected with a pathogen during an outbreak, we use a Bayesian Markov Chain Monte Carlo (MCMC) approach to estimate time of exposure, and the overall epidemic trend in the population prior to the time of sampling. We evaluate the performance of this statistical framework on simulated data from epidemic trend curves and show that we can recover the parameter values of those trends. We also apply the framework to epidemic trend curves taken from two historical outbreaks: a bluetongue outbreak in cattle, and a whooping cough outbreak in humans. Together, these results show that hindcasting can estimate the time since infection for individuals and provide accurate estimates of epidemic trends, and can be used to distinguish whether an outbreak is increasing or past its peak. We conclude that if temporal characteristics of diagnostics are known, it is possible to recover epidemic trends of both human and animal pathogens from cross-sectional data collected at a single point in time.

Accounting for uncertainty in model-based prevalence estimation: paratuberculosis control in dairy herds.

BACKGROUND: A common approach to the application of epidemiological models is to determine a single (point estimate) parameterisation using the information available in the literature. However, in many cases there is considerable uncertainty about parameter values, reflecting both the incomplete nature of current knowledge and natural variation, for example between farms. Furthermore model outcomes may be highly sensitive to different parameter values. Paratuberculosis is an infection for which many of the key parameter values are poorly understood and highly variable, and for such infections there is a need to develop and apply statistical techniques which make maximal use of available data. RESULTS: A technique based on Latin hypercube sampling combined with a novel reweighting method was developed which enables parameter uncertainty and variability to be incorporated into a model-based framework for estimation of prevalence. The method was evaluated by applying it to a simulation of paratuberculosis in dairy herds which combines a continuous time stochastic algorithm with model features such as within herd variability in disease development and shedding, which have not been previously explored in paratuberculosis models. Generated sample parameter combinations were assigned a weight, determined by quantifying the model's resultant ability to reproduce prevalence data. Once these weights are generated the model can be used to evaluate other scenarios such as control options. To illustrate the utility of this approach these reweighted model outputs were used to compare standard test and cull control strategies both individually and in combination with simple husbandry practices that aim to reduce infection rates. CONCLUSIONS: The technique developed has been shown to be applicable to a complex model incorporating realistic control options. For models where parameters are not well known or subject to significant variability, the reweighting scheme allowed estimated distributions of parameter values to be combined with additional sources of information, such as that available from prevalence distributions, resulting in outputs which implicitly handle variation and uncertainty. This methodology allows for more robust predictions from modelling approaches by allowing for parameter uncertainty and combining different sources of information, and is thus expected to be useful in application to a large number of disease systems.

Generative models of network dynamics provide insight into the effects of trade on endemic livestock disease.

We develop and apply analytically tractable generative models of livestock movements at national scale. These go beyond current models through mechanistic modelling of heterogeneous trade partnership network dynamics and the trade events that occur on them. Linking resulting animal movements to disease transmission between farms yields analytical expressions for the basic reproduction number R 0. We show how these novel modelling tools enable systems approaches to disease control, using R 0 to explore impacts of changes in trading practices on between-farm prevalence levels. Using the Scottish cattle trade network as a case study, we show our approach captures critical complexities of real-world trade networks at the national scale for a broad range of endemic diseases. Changes in trading patterns that minimize disruption to business by maintaining in-flow of animals for each individual farm reduce R 0, with the largest reductions for diseases that are most challenging to eradicate. Incentivizing high-risk farms to adopt such changes exploits 'scale-free' properties of the system and is likely to be particularly effective in reducing national livestock disease burden and incursion risk. Encouragingly, gains made by such targeted modification of trade practices scale much more favourably than comparably targeted improvements to more commonly adopted farm-level biosecurity.

When to kill a cull: factors affecting the success of culling wildlife for disease control.

Culling wildlife to control disease can lead to both decreases and increases in disease levels, with apparently conflicting responses observed, even for the same wildlife-disease system. There is therefore a pressing need to understand how culling design and implementation influence culling's potential to achieve disease control. We address this gap in understanding using a spatial metapopulation model representing wildlife living in distinct groups with density-dependent dispersal and framed on the badger-bovine tuberculosis (bTB) system. We show that if population reduction is too low, or too few groups are targeted, a 'perturbation effect' is observed, whereby culling leads to increased movement and disease spread. We also demonstrate the importance of culling across appropriate time scales, with otherwise successful control strategies leading to increased disease if they are not implemented for long enough. These results potentially explain a number of observations of the dynamics of both successful and unsuccessful attempts to control TB in badgers including the Randomized Badger Culling Trial in the UK, and we highlight their policy implications. Additionally, for parametrizations reflecting a broad range of wildlife-disease systems, we characterize 'Goldilocks zones', where, for a restricted combination of culling intensity, coverage and duration, the disease can be reduced without driving hosts to extinction.

Effects of host social hierarchy on disease persistence.

The effects of social hierarchy on population dynamics and epidemiology are examined through a model which contains a number of fundamental features of hierarchical systems, but is simple enough to allow analytical insight. In order to allow for differences in birth rates, contact rates and movement rates among different sets of individuals the population is first divided into subgroups representing levels in the hierarchy. Movement, representing dominance challenges, is allowed between any two levels, giving a completely connected network. The model includes hierarchical effects by introducing a set of dominance parameters which affect birth rates in each social level and movement rates between social levels, dependent upon their rank. Although natural hierarchies vary greatly in form, the skewing of contact patterns, introduced here through non-uniform dominance parameters, has marked effects on the spread of disease. A simple homogeneous mixing differential equation model of a disease with SI dynamics in a population subject to simple birth and death process is presented and it is shown that the hierarchical model tends to this as certain parameter regions are approached. Outside of these parameter regions correlations within the system give rise to deviations from the simple theory. A Gaussian moment closure scheme is developed which extends the homogeneous model in order to take account of correlations arising from the hierarchical structure, and it is shown that the results are in reasonable agreement with simulations across a range of parameters. This approach helps to elucidate the origin of hierarchical effects and shows that it may be straightforward to relate the correlations in the model to measurable quantities which could be used to determine the importance of hierarchical corrections. Overall, hierarchical effects decrease the levels of disease present in a given population compared to a homogeneous unstructured model, but show higher levels of disease than structured models with no hierarchy. The separation between these three models is greatest when the rate of dominance challenges is low, reducing mixing, and when the disease prevalence is low. This suggests that these effects will often need to be considered in models being used to examine the impact of control strategies where the low disease prevalence behaviour of a model is critical.

Climate-driven tipping-points could lead to sudden, high-intensity parasite outbreaks.

Parasitic nematodes represent one of the most pervasive and significant challenges to grazing livestock, and their intensity and distribution are strongly influenced by climate. Parasite levels and species composition have already shifted under climate change, with nematode parasite intensity frequently low in newly colonized areas, but sudden large-scale outbreaks are becoming increasingly common. These outbreaks compromise both food security and animal welfare, yet there is a paucity of predictions on how climate change will influence livestock parasites. This study aims to assess how climate change can affect parasite risk. Using a process-based approach, we determine how changes in temperature-sensitive elements of outbreaks influence parasite dynamics, to explore the potential for climate change to influence livestock helminth infections. We show that changes in temperate-sensitive parameters can result in nonlinear responses in outbreak dynamics, leading to distinct 'tipping-points' in nematode parasite burdens. Through applying two mechanistic models, of varying complexity, our approach demonstrates that these nonlinear responses are robust to the inclusion of a number of realistic processes that are present in livestock systems. Our study demonstrates that small changes in climatic conditions around critical thresholds may result in dramatic changes in parasite burdens.

Demographic processes drive increases in wildlife disease following population reduction.

Population reduction is often used as a control strategy when managing infectious diseases in wildlife populations in order to reduce host density below a critical threshold. However, population reduction can disrupt existing social and demographic structures leading to changes in observed host behaviour that may result in enhanced disease transmission. Such effects have been observed in several disease systems, notably badgers and bovine tuberculosis. Here we characterise the fundamental properties of disease systems for which such effects undermine the disease control benefits of population reduction. By quantifying the size of response to population reduction in terms of enhanced transmission within a generic non-spatial model, the properties of disease systems in which such effects reduce or even reverse the disease control benefits of population reduction are identified. If population reduction is not sufficiently severe, then enhanced transmission can lead to the counter intuitive perturbation effect, whereby disease levels increase or persist where they would otherwise die out. Perturbation effects are largest for systems with low levels of disease, e.g. low levels of endemicity or emerging disease. Analysis of a stochastic spatial meta-population model of demography and disease dynamics leads to qualitatively similar conclusions. Moreover, enhanced transmission itself is found to arise as an emergent property of density dependent dispersal in such systems. This spatial analysis also shows that, below some threshold, population reduction can rapidly increase the area affected by disease, potentially expanding risks to sympatric species. Our results suggest that the impact of population reduction on social and demographic structures is likely to undermine disease control in many systems, and in severe cases leads to the perturbation effect. Social and demographic mechanisms that enhance transmission following population reduction should therefore be routinely considered when designing control programmes.

Modelling parasite transmission in a grazing system: the importance of host behaviour and immunity.

Parasitic helminths present one of the most pervasive challenges to grazing herbivores. Many macro-parasite transmission models focus on host physiological defence strategies, omitting more complex interactions between hosts and their environments. This work represents the first model that integrates both the behavioural and physiological elements of gastro-intestinal nematode transmission dynamics in a managed grazing system. A spatially explicit, individual-based, stochastic model is developed, that incorporates both the hosts' immunological responses to parasitism, and key grazing behaviours including faecal avoidance. The results demonstrate that grazing behaviour affects both the timing and intensity of parasite outbreaks, through generating spatial heterogeneity in parasite risk and nutritional resources, and changing the timing of exposure to the parasites' free-living stages. The influence of grazing behaviour varies with the host-parasite combination, dependent on the development times of different parasite species and variations in host immune response. Our outputs include the counterintuitive finding that under certain conditions perceived parasite avoidance behaviours (faecal avoidance) can increase parasite risk, for certain host-parasite combinations. Through incorporating the two-way interaction between infection dynamics and grazing behaviour, the potential benefits of parasite-induced anorexia are also demonstrated. Hosts with phenotypic plasticity in grazing behaviour, that make grazing decisions dependent on current parasite burden, can reduce infection with minimal loss of intake over the grazing season. This paper explores how both host behaviours and immunity influence macro-parasite transmission in a spatially and temporally heterogeneous environment. The magnitude and timing of parasite outbreaks is influenced by host immunity and behaviour, and the interactions between them; the incorporation of both regulatory processes is required to fully understand transmission dynamics. Understanding of both physiological and behavioural defence strategies will aid the development of novel approaches for control.

Livestock Helminths in a Changing Climate: Approaches and Restrictions to Meaningful Predictions.

Climate change is a driving force for livestock parasite risk. This is especially true for helminths including the nematodes Haemonchus contortus, Teladorsagia circumcincta, Nematodirus battus, and the trematode Fasciola hepatica, since survival and development of free-living stages is chiefly affected by temperature and moisture. The paucity of long term predictions of helminth risk under climate change has driven us to explore optimal modelling approaches and identify current bottlenecks to generating meaningful predictions. We classify approaches as correlative or mechanistic, exploring their strengths and limitations. Climate is one aspect of a complex system and, at the farm level, husbandry has a dominant influence on helminth transmission. Continuing environmental change will necessitate the adoption of mitigation and adaptation strategies in husbandry. Long term predictive models need to have the architecture to incorporate these changes. Ultimately, an optimal modelling approach is likely to combine mechanistic processes and physiological thresholds with correlative bioclimatic modelling, incorporating changes in livestock husbandry and disease control. Irrespective of approach, the principal limitation to parasite predictions is the availability of active surveillance data and empirical data on physiological responses to climate variables. By combining improved empirical data and refined models with a broad view of the livestock system, robust projections of helminth risk can be developed.

Routes of intraspecies transmission of Mycobacterium avium subsp. paratuberculosis in rabbits (Oryctolagus cuniculus): a field study.

Rabbits have been increasingly linked to the persistence of paratuberculosis (Johne's disease) in domestic ruminants in the United Kingdom. The aims of this study were to determine the routes of intraspecies transmission of Mycobacterium avium subspecies paratuberculosis (MAP) in rabbits and to estimate the probability of transmission via each route, in order to gain understanding of the dynamics of MAP in this host. Rabbits were sampled from two sites where MAP had previously been isolated from the livestock and rabbit populations. No pathology was noted in any animals, but the overall prevalence of MAP in rabbits was high at both sites studied, 39.7% and 23.0%, respectively. MAP was isolated from the testes, uterus, placenta, fetuses, and milk. This is the first time that the bacterium has been isolated from any of these tissues in a nonruminant wildlife species. These results suggest that transmission may occur vertically, pseudovertically, and horizontally. Vertical, i.e., transplacental, and/or pseudo-vertical, i.e., through the ingestion of contaminated milk and/or feces, transmission occurred in 14% of offspring entering the population at 1 month of age. As infection via these routes is only possible from infected adult females, this equates to a probability of infection via this route of 0.326. Probability of infection via horizontal transmission (including interspecies transmission) occurred at up to 0.037 per month. The presence of these routes of transmission within natural rabbit populations will contribute to the maintenance of MAP infections within such populations and, therefore, the environment.