Mathematical modelling of the foot and mouth disease epidemic of 2001: strengths and weaknesses

Network analysis of pig movement data as an epidemiological tool: an Austrian case study

Animal movements represent a major risk for the spread of infectious diseases in the domestic swine population. In this study, we adopted methods from social network analysis to explore pig trades in Austria. We used a dataset of daily records of swine movements covering the period 2015-2021. We analyzed the topology of the network and its structural changes over time, including seasonal and long-term variations in the pig production activities. Finally, we studied the temporal dynamics of the network community structure. Our findings show that the Austrian pig production was dominated by small-sized farms while spatial farm density was heterogeneous. The network exhibited a scale-free topology but was very sparse, suggesting a moderate impact of infectious disease outbreaks. However, two regions (Upper Austria and Styria) may present a higher structural vulnerability. The network also showed very high assortativity between holdings from the same federal state. Dynamic community detection revealed a stable behavior of the clusters. Yet trade communities did not correspond to sub-national administrative divisions and may be an alternative zoning approach to managing infectious diseases. Knowledge about the topology, contact patterns, and temporal dynamics of the pig trade network can support optimized risk-based disease control and surveillance strategies.

Modeling nation-wide U.S. swine movement networks at the resolution of the individual premises

The spread of infectious livestock diseases is a major cause for concern in modern agricultural systems. In the dynamics of the transmission of such diseases, movements of livestock between herds play an important role. When constructing mathematical models used for activities such as forecasting epidemic development, evaluating mitigation strategies, or determining important targets for disease surveillance, including between-premises shipments is often a necessity. In the United States (U.S.), livestock shipment data is not routinely collected, and when it is, it is not readily available and mostly concerned with between-state shipments. To bridge this gap in knowledge and provide insight into the complete livestock shipment network structure, we have developed the U.S. Animal Movement Model (USAMM). Previously, USAMM has only existed for cattle shipments, but here we present a version for domestic swine. This new version of USAMM consists of a Bayesian model fit to premises demography, county-level livestock industry variables, and two limited data sets of between-state swine movements. The model scales up the data to simulate nation-wide networks of both within- and between-state shipments at the level of individual premises. Here we describe this shipment model in detail and subsequently explore its usefulness with a rudimentary predictive model of the prevalence of porcine epidemic diarrhea virus (PEDv) across the U.S. Additionally, in order to promote further research on livestock disease and other topics involving the movements of swine in the U.S., we also make 250 synthetic premises-level swine shipment networks with complete coverage of the entire conterminous U.S. freely available to the research community as a useful surrogate for the absent shipment data.

Integrative modelling for One Health: pattern, process and participation

This paper argues for an integrative modelling approach for understanding zoonoses disease dynamics, combining process, pattern and participatory models. Each type of modelling provides important insights, but all are limited. Combining these in a '3P' approach offers the opportunity for a productive conversation between modelling efforts, contributing to a 'One Health' agenda. The aim is not to come up with a composite model, but seek synergies between perspectives, encouraging cross-disciplinary interactions. We illustrate our argument with cases from Africa, and in particular from our work on Ebola virus and Lassa fever virus. Combining process-based compartmental models with macroecological data offers a spatial perspective on potential disease impacts. However, without insights from the ground, the 'black box' of transmission dynamics, so crucial to model assumptions, may not be fully understood. We show how participatory modelling and ethnographic research of Ebola and Lassa fever can reveal social roles, unsafe practices, mobility and movement and temporal changes in livelihoods. Together with longer-term dynamics of change in societies and ecologies, all can be important in explaining disease transmission, and provide important complementary insights to other modelling efforts. An integrative modelling approach therefore can offer help to improve disease control efforts and public health responses.This article is part of the themed issue 'One Health for a changing world: zoonoses, ecosystems and human well-being'.

Ensemble modelling and structured decision-making to support Emergency Disease Management

Epidemiological models in animal health are commonly used as decision-support tools to understand the impact of various control actions on infection spread in susceptible populations. Different models contain different assumptions and parameterizations, and policy decisions might be improved by considering outputs from multiple models. However, a transparent decision-support framework to integrate outputs from multiple models is nascent in epidemiology. Ensemble modelling and structured decision-making integrate the outputs of multiple models, compare policy actions and support policy decision-making. We briefly review the epidemiological application of ensemble modelling and structured decision-making and illustrate the potential of these methods using foot and mouth disease (FMD) models. In case study one, we apply structured decision-making to compare five possible control actions across three FMD models and show which control actions and outbreak costs are robustly supported and which are impacted by model uncertainty. In case study two, we develop a methodology for weighting the outputs of different models and show how different weighting schemes may impact the choice of control action. Using these case studies, we broadly illustrate the potential of ensemble modelling and structured decision-making in epidemiology to provide better information for decision-making and outline necessary development of these methods for their further application.

Spatial and Functional Organization of Pig Trade in Different European Production Systems: Implications for Disease Prevention and Control

Understanding the complexity of live pig trade organization is a key factor to predict and control major infectious diseases, such as classical swine fever (CSF) or African swine fever (ASF). Whereas the organization of pig trade has been described in several European countries with indoor commercial production systems, little information is available on this organization in other systems, such as outdoor or small-scale systems. The objective of this study was to describe and compare the spatial and functional organization of live pig trade in different European countries and different production systems. Data on premise characteristics and pig movements between premises were collected during 2011 from Bulgaria, France, Italy, and Spain, which swine industry is representative of most of the production systems in Europe (i.e., commercial vs. small-scale and outdoor vs. indoor). Trade communities were identified in each country using the Walktrap algorithm. Several descriptive and network metrics were generated at country and community levels. Pig trade organization showed heterogeneous spatial and functional organization. Trade communities mostly composed of indoor commercial premises were identified in western France, northern Italy, northern Spain, and north-western Bulgaria. They covered large distances, overlapped in space, demonstrated both scale-free and small-world properties, with a role of trade operators and multipliers as key premises. Trade communities involving outdoor commercial premises were identified in western Spain, south-western and central France. They were more spatially clustered, demonstrated scale-free properties, with multipliers as key premises. Small-scale communities involved the majority of premises in Bulgaria and in central and Southern Italy. They were spatially clustered and had scale-free properties, with key premises usually being commercial production premises. These results indicate that a disease might spread very differently according to the production system and that key premises could be targeted to more cost-effectively control diseases. This study provides useful epidemiological information and parameters that could be used to design risk-based surveillance strategies or to more accurately model the risk of introduction or spread of devastating swine diseases, such as ASF, CSF, or foot-and-mouth disease.

Prediction of province-level outbreaks of foot-and-mouth disease in Iran using a zero-inflated negative binomial model

To identify events that could predict province-level frequency of foot-and-mouth disease (FMD) outbreaks in Iran, 5707 outbreaks reported from April 1995 to March 2002 were studied. A zero-inflated negative binomial model was used to estimate the probability of a 'no-outbreak' status and the number of outbreaks in a province, using the number of previous occurrences of FMD for the same or adjacent provinces and season as covariates. For each province, the probability of observing no outbreak was negatively associated with the number of outbreaks in the same province in the previous month (odds ratio [OR]=0.06, 95% confidence interval [CI]: 0.01, 0.30) and in 'the second previous month' (OR=0.10, 95% CI: 0.02, 0.51), the total number of outbreaks in the second previous month in adjacent provinces (OR=0.57, 95% CI: 0.36, 0.91) and the season (winter [OR=0.18, 95% CI: 0.06, 0.55] and spring [OR=0.27, 95% CI: 0.09, 0.81], compared with summer). The expected number of outbreaks in a province was positively associated with number of outbreaks in the same province in previous month (coefficient [coef]=0.74, 95% CI: 0.66, 0.82) and in the second previous month (coef=0.23, 95% CI: 0.16, 0.31), total number of outbreaks in adjacent provinces in the previous month (coef=0.32, 95% CI: 0.22, 0.41) and season (fall [coef=0.20, 95% CI: 0.07, 0.33] and spring [coef=0.18, 95% CI: 0.05, 0.31], compared to summer); however, number of outbreaks was negatively associated with the total number of outbreaks in adjacent provinces in the second previous month (coef=-0.19, 95% CI: -0.28, -0.09). The findings indicate that the probability of an outbreak (and the expected number of outbreaks if any) may be predicted based on previous province information, which could help decision-makers allocate resources more efficiently for province-level disease control measures. Further, the study illustrates use of zero inflated negative binomial model to study diseases occurrence where disease is infrequently observed.

Uncertainties in the governance of animal disease: an interdisciplinary framework for analysis

Uncertainty is an inherent feature of strategies to contain animal disease. In this paper, an interdisciplinary framework for representing strategies of containment, and analysing how uncertainties are embedded and propagated through them, is developed and illustrated. Analysis centres on persistent, periodic and emerging disease threats, with a particular focus on cryptosporidiosis, foot and mouth disease and avian influenza. Uncertainty is shown to be produced at strategic, tactical and operational levels of containment, and across the different arenas of disease prevention, anticipation and alleviation. The paper argues for more critically reflexive assessments of uncertainty in containment policy and practice. An interdisciplinary approach has an important contribution to make, but is absent from current real-world containment policy.

Transmission models and management of lymphatic filariasis elimination

The planning and evaluation of parasitic control programmes are complicated by the many interacting population dynamic and programmatic factors that determine infection trends under different control options. A key need is quantification about the status of the parasite system state at any one given timepoint and the dynamic change brought upon that state as an intervention program proceeds. Here, we focus on the control and elimination of the vector-borne disease, lymphatic filariasis, to show how mathematical models of parasite transmission can provide a quantitative framework for aiding the design of parasite elimination and monitoring programs by their ability to support (1) conducting rational analysis and definition of endpoints for different programmatic aims or objectives, including transmission endpoints for disease elimination, (2) undertaking strategic analysis to aid the optimal design of intervention programs to meet set endpoints under different endemic settings and (3) providing support for performing informed evaluations of ongoing programs, including aiding the formation of timely adaptive management strategies to correct for any observed deficiencies in program effectiveness. The results also highlight how the use of a model-based framework will be critical to addressing the impacts of ecological complexities, heterogeneities and uncertainties on effective parasite management and thereby guiding the development of strategies to resolve and overcome such real-world complexities. In particular, we underscore how this approach can provide a link between ecological science and policy by revealing novel tools and measures to appraise and enhance the biological controllability or eradicability of parasitic diseases. We conclude by emphasizing an urgent need to develop and apply flexible adaptive management frameworks informed by mathematical models that are based on learning and reducing uncertainty using monitoring data, apply phased or sequential decision-making to address extant uncertainty and focus on developing ecologically resilient management strategies, in ongoing efforts to control or eliminate filariasis and other parasitic diseases in resource-poor communities.

Transmission risks and control of foot-and-mouth disease in The Netherlands: spatial patterns

In 2001 the epidemics of foot-and-mouth disease virus (FMDV) in Great Britain, The Netherlands and France have shown how fast FMDV may spread between farms. The massive socio-economic impact of these epidemics and the intervention measures taken demonstrate the need for quantitative assessments of the efficacy of candidate intervention strategies. Here we use a mathematical model to describe the spatial transmission of FMDV in The Netherlands and use the Dutch 2001 outbreak data to estimate model parameters. We assess the effect of ring culling strategies using a novel and fast approach producing risk maps, and discuss its consequences for ring vaccination. These risk maps identify both the geographical areas of low risk, where a given intervention strategy is likely to achieve epidemic control within only two or three farm-to-farm infection generations, and high-risk areas, where control is likely to take (much) longer. Our results indicate that certain densely populated livestock areas in the Netherlands remain high-risk areas even for strategies that extend EU minimum measures with culling or vaccination within a ring radius of several kilometres. Depending on an economic assessment, area-wide vaccination might be judged appropriate once an FMDV outbreak would have been confirmed in or close to such a high-density area. The modeling approach developed here could be readily applied to outbreak data for other diseases and in other countries.

A review of network analysis terminology and its application to foot-and-mouth disease modelling and policy development

Livestock movements are important in spreading infectious diseases and many countries have developed regulations that require farmers to report livestock movements to authorities. This has led to the availability of large amounts of data for analysis and inclusion in computer simulation models developed to support policy formulation. Social network analysis has become increasingly popular to study and characterize the networks resulting from the movement of livestock from farm-to-farm and through other types of livestock operations. Network analysis is a powerful tool that allows one to study the relationships created among these operations, providing information on the role that they play in acquiring and spreading infectious diseases, information that is not readily available from more traditional livestock movement studies. Recent advances in the study of real-world complex networks are now being applied to veterinary epidemiology and infectious disease modelling and control. A review of the principles of network analysis and of the relevance of various complex network theories to infectious disease modelling and control is presented in this paper.

Advances in biosecurity to 2010 and beyond: towards integrated detection, analysis and response to exotic pest invasions

In order to limit the number and impact of exotic pest invasions, leading-edge technologies must be embraced and embedded within integrated national and international biosecurity systems. Outlined here are recent advances in the detection of exotic pests, and prospects for the early recognition of disease. Applications of new tools are described, using our understanding of the genomes of pathogens and vectors. In addition, the role of mathematical and simulation models to aid both biosecurity planning, and decision making in the face of an epidemic, are discussed, and recent attempts to unify epidemiology and evolutionary dynamics are outlined. Given the importance of emerging diseases and zoonoses, the need to align human and veterinary surveillance within fully integrated systems is underlined.

Transmission parameters of the 2001 foot and mouth epidemic in Great Britain

Despite intensive ongoing research, key aspects of the spatial-temporal evolution of the 2001 foot and mouth disease (FMD) epidemic in Great Britain (GB) remain unexplained. Here we develop a Markov Chain Monte Carlo (MCMC) method for estimating epidemiological parameters of the 2001 outbreak for a range of simple transmission models. We make the simplifying assumption that infectious farms were completely observed in 2001, equivalent to assuming that farms that were proactively culled but not diagnosed with FMD were not infectious, even if some were infected. We estimate how transmission parameters varied through time, highlighting the impact of the control measures on the progression of the epidemic. We demonstrate statistically significant evidence for assortative contact patterns between animals of the same species. Predictive risk maps of the transmission potential in different geographic areas of GB are presented for the fitted models.

The role of ecological theory in microbial ecology

Microbial ecology is currently undergoing a revolution, with repercussions spreading throughout microbiology, ecology and ecosystem science. The rapid accumulation of molecular data is uncovering vast diversity, abundant uncultivated microbial groups and novel microbial functions. This accumulation of data requires the application of theory to provide organization, structure, mechanistic insight and, ultimately, predictive power that is of practical value, but the application of theory in microbial ecology is currently very limited. Here we argue that the full potential of the ongoing revolution will not be realized if research is not directed and driven by theory, and that the generality of established ecological theory must be tested using microbial systems.

Mathematical models and lymphatic filariasis control: endpoints and optimal interventions

The current global initiative to eliminate lymphatic filariasis is a major renewed commitment to reduce or eliminate the burden of one of the major helminth infections from resource-poor communities of the world. Mathematical models of filariasis transmission can serve as an effective tool for guiding the scientific development and management of successful community-level intervention programmes by acting as analytical frameworks for integrating knowledge regarding parasite transmission dynamics with programmatic factors. However, the power of these tools for supporting control interventions will be realized fully only if researchers address the current uncertainties and gaps in data and knowledge of filarial population dynamics and the effectiveness of currently proposed filariasis intervention options.

Modelling the spread of foot-and-mouth disease in Australia

Preparedness for an incursion of an exotic animal disease is of key importance to government, industry, producers and the Australian community. An important aspect of Australia's preparedness for a possible incursion of foot-and-mouth disease is investigation into the likely effectiveness and cost-efficiency of eradication strategies when applied to different regional outbreak scenarios. Disease modelling is a tool that can be used to study diseases such as foot-and-mouth disease to better understand potential disease spread and control under different conditions. The Australian Government Department of Agriculture, Fisheries and Forestry has been involved with epidemiologic simulation modelling for more than 10 years, and has developed a sophisticated spatial model for foot-and-mouth disease (AusSpread) that operates within a geographic information system framework. The model accommodates real farm boundary or point-location data, as well as synthesised data based on agricultural census and land use information. The model also allows for interactions between herds or flocks of different animal species and production type, and considers the role that such interactions are likely to play in the epidemiology of a regional outbreak of foot-and-mouth disease. The user can choose mitigations and eradication strategies from those that are currently described in Australia's veterinary emergency plan. The model also allows the user to evaluate the impact of constraints on the availability of resources for mitigations or eradication measures. Outputs include a range of maps and tabulated outbreak statistics describing the geographic extent of the outbreak and its duration, the numbers of affected, slaughtered, and, as relevant, vaccinated herds or flocks, and the cost of control and eradication. Cost-related outputs are based on budgets of the value of stock and the cost of mitigations, each of which can be varied by the user. These outputs are a valuable resource to assist with policy development and disease management.

Models of foot-and-mouth disease

During the 2001 foot-and-mouth disease outbreak in the UK, three very different models were used in an attempt to predict the disease dynamics and inform control measures. This was one of the first times that models had been used during an epidemic to support the decision-making process. It is probable that models will play a pivotal role in any future livestock epidemics, and it is therefore important that decision makers, veterinarians and farmers understand the uses and limitations of models. This review describes the utility of models in general before focusing on the three foot-and-mouth disease models used in 2001. Finally, the future of modelling is discussed, analysing the advances needed if models are to be successfully applied during any subsequent epidemics.

A review of foot-and-mouth disease with special consideration for the clinical and epidemiological factors relevant to predictive modelling of the disease

Modelling the epidemiology of foot-and-mouth disease (FMD) has been undertaken since the early 1970s. We review here clinical factors and modelling procedures that have been used in the past, differentiating between those that have proved to be more relevant in controlling FMD epidemics, and those that have showed less significance. During the 2001 UK FMD epidemic, many previously developed FMD models were available for consideration and use. Accurate epidemiological models can become useful tools for determining relevant control policies for different scenarios and, conversely, inaccurate models may become an abuse for disease control. Inaccuracy presents two opposing difficulties. Firstly, too much control (in terms of animal slaughter for 2001) would negatively impact the farming community for many subsequent years, whilst too little control would permit an epidemic to persist. Accuracy however, presents the optimal permutation of control measures that could be implemented for a given set of conditions, and is a prerequisite to boosting public confidence in the use of epidemiological models for future epidemics.

Epidemiological investigations of the 2001 foot-and-mouth disease outbreak in Argentina

A total of 2126 herds, an attack rate of 0.82 per cent, were affected during an epidemic of foot-and-mouth disease in Argentina in 2001. The spatial and temporal distribution of the epidemic was investigated using nearest-neighbour and spatial scan tests and by estimating the frequency distributions of the times to intervention, and distances and times between outbreaks. The outbreaks were clustered and associated significantly (P<0.01) with herd density; 94 per cent were located in the Pampeana region, where the cattle population is concentrated, which had an attack rate of 1.4 per cent. The clustering results suggested that the virus had spread locally between outbreaks. Most of the outbreaks were separated by one day and the maximum distance between outbreaks was almost 2000 km, indicating that the infection spread rapidly over large distances. The index outbreak was detected more than 15 days after the primary outbreak, and restrictions on the movement of cattle were probably not enforced until about one month after infection occurred. As in other major epidemics, the period between the first outbreaks and the effective application of control strategies was probably crucial in determining the progress of the epidemic.

Using conservation of pattern to estimate spatial parameters from a single snapshot

Rapid reaction in the face of an epidemic is a key element in effective and efficient control; this is especially important when the disease has severe public health or economic consequences. Determining an appropriate level of response requires rapid estimation of the rate of spread of infection from limited disease distribution data. Generally, the techniques used to estimate such spatial parameters require detailed spatial data at multiple time points; such data are often time-consuming and expensive to collect. Here we present an alternative approach that is computationally efficient and only requires spatial data from a single time point, hence saving valuable time at the start of the epidemic. By assuming that fundamental spatial statistics are near equilibrium, parameters can be estimated by minimizing the expected rate of change of these statistics, hence conserving the general spatial pattern. Although applicable to both ecological and epidemiological data, here we focus on disease data from computer simulations and real epidemics to show that this method produces reliable results that could be used in practical situations.