Accuracy of models for the 2001 foot-and-mouth epidemic

Inferring transmission routes for foot-and-mouth disease virus within a cattle herd using approximate Bayesian computation

To control an outbreak of an infectious disease it is essential to understand the different routes of transmission and how they contribute to the overall spread of the pathogen. With this information, policy makers can choose the most efficient methods of detection and control during an outbreak. Here we assess the contributions of direct contact and environmental contamination to the transmission of foot-and-mouth disease virus (FMDV) in a cattle herd using an individual-based model that includes both routes. Model parameters are inferred using approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC) applied to data from transmission experiments and the 2007 epidemic in Great Britain. This demonstrates that the parameters derived from transmission experiments are applicable to outbreaks in the field, at least for closely related strains. Under the assumptions made in the model we show that environmental transmission likely contributes a majority of infections within a herd during an outbreak, although there is a lot of variation between simulated outbreaks. The accumulation of environmental contamination not only causes infections within a farm, but also has the potential to spread between farms via fomites. We also demonstrate the importance and effectiveness of rapid detection of infected farms in reducing transmission between farms, whether via direct contact or the environment.

Modeling target-density-based cull strategies to contain foot-and-mouth disease outbreaks

Total ring depopulation is sometimes used as a management strategy for emerging infectious diseases in livestock, which raises ethical concerns regarding the potential slaughter of large numbers of healthy animals. We evaluated a farm-density-based ring culling strategy to control foot-and-mouth disease (FMD) in the United Kingdom (UK), which may allow for some farms within rings around infected premises (IPs) to escape depopulation. We simulated this reduced farm density, or "target density", strategy using a spatially-explicit, stochastic, state-transition algorithm. We modeled FMD spread in four counties in the UK that have different farm demographics, using 740,000 simulations in a full-factorial analysis of epidemic impact measures (i.e., culled animals, culled farms, and epidemic length) and cull strategy parameters (i.e., target farm density, daily farm cull capacity, and cull radius). All of the cull strategy parameters listed above were drivers of epidemic impact. Our simulated target density strategy was usually more effective at combatting FMD compared with traditional total ring depopulation when considering mean culled animals and culled farms and was especially effective when daily farm cull capacity was low. The differences in epidemic impact measures among the counties are likely driven by farm demography, especially differences in cattle and farm density. To prevent over-culling and the associated economic, organizational, ethical, and psychological impacts, the target density strategy may be worth considering in decision-making processes for future control of FMD and other diseases.

Incorporating heterogeneity in farmer disease control behaviour into a livestock disease transmission model

Human behaviour is critical to effective responses to livestock disease outbreaks, especially with respect to vaccination uptake. Traditionally, mathematical models used to inform this behaviour have not taken heterogeneity in farmer behaviour into account. We address this by exploring how heterogeneity in farmers vaccination behaviour can be incorporated to inform mathematical models. We developed and used a graphical user interface to elicit farmers (n = 60) vaccination decisions to an unfolding fast-spreading epidemic and linked this to their psychosocial and behavioural profiles. We identified, via cluster analysis, robust patterns of heterogeneity in vaccination behaviour. By incorporating these vaccination behavioural groupings into a mathematical model for a fast-spreading livestock infection, using computational simulation we explored how the inclusion of heterogeneity in farmer disease control behaviour may impact epidemiological and economic focused outcomes. When assuming homogeneity in farmer behaviour versus configurations informed by the psychosocial profile cluster estimates, the modelled scenarios revealed a disconnect in projected distributions and threshold statistics across outbreak size, outbreak duration and economic metrics.

The Importance of Livestock Demography and Infrastructure in Driving Foot and Mouth Disease Dynamics

Transboundary animal diseases, such as foot and mouth disease (FMD) pose a significant and ongoing threat to global food security. Such diseases can produce large, spatially complex outbreaks. Mathematical models are often used to understand the spatio-temporal dynamics and create response plans for possible disease introductions. Model assumptions regarding transmission behavior of premises and movement patterns of livestock directly impact our understanding of the ecological drivers of outbreaks and how to best control them. Here, we investigate the impact that these assumptions have on model predictions of FMD outbreaks in the U.S. using models of livestock shipment networks and disease spread. We explore the impact of changing assumptions about premises transmission behavior, both by including within-herd dynamics, and by accounting for premises type and increasing the accuracy of shipment predictions. We find that the impact these assumptions have on outbreak predictions is less than the impact of the underlying livestock demography, but that they are important for investigating some response objectives, such as the impact on trade. These results suggest that demography is a key ecological driver of outbreaks and is critical for making robust predictions but that understanding management objectives is also important when making choices about model assumptions.

Comparing the efficacy of control strategies for infectious disease outbreaks using field and simulation studies

Diseases characterized by long distance inoculum dispersal (LDD) are among the fastest spreading epidemics in both natural and managed landscapes. Management of such epidemics is extremely challenging because of asymptomatic infection extending at large spatial scales and frequent escape from the newly established disease sources. We compared the efficacy of area- and timing-based disease management strategies in artificially initiated field epidemics of wheat stripe rust and complemented with simulations from an updated version of the spatially explicit model EPIMUL, using model parameters relevant to field epidemics. The model was further used to expand the number of epidemic mitigations beyond that feasible to incorporate in the field. The field experiment was conducted for 2 years in two locations having different climatic conditions. Culling and protection treatments were applied at different times after epidemic initiation and to different spatial extents surrounding the outbreaks. In each experiment, treatments were replicated four times in plots 33.5 m long and 1.52 m wide with a 0.76 × 0.76 m inoculated focus centered within each plot. Disease gradients were assessed along the center lines of the plots at 1.52 m intervals both upwind and downwind from the focus. Both field and simulation results indicated that control measures applied over the entire population were highly effective in suppressing the epidemics by more than 99% but may not always be logistically and economically feasible at large spatial scales. Comparison between the variable sized treatment areas and application timings suggested that implementing contiguous premises (CP) cull at 1 day after first sporulation in the outbreak focus reduced rust by 52% and 60% in Corvallis and Madras, respectively. However, altering the cull size did not significantly affect the disease epidemic development, which suggested that early timing had a greater influence in suppressing the epidemics than did increased area of application. However, sufficiently large, treated areas may compensate for a delay in application timing to some extent. Results from these replicated treatments may help to devise appropriate management strategies for other LDD pathogens.

A model exploration of carrier and movement transmission as potential explanatory causes for the persistence of foot-and-mouth disease in endemic regions

Foot-and-mouth disease (FMD) is a virulent and economically important disease of livestock, still endemic in many areas of Asia and sub-Saharan Africa. Transmission from persistently infected livestock, also known as carriers, has been proposed as a mechanism to support the persistence of FMD in endemic regions. However, whether carrier livestock can infect susceptible animals is controversial; recovered virus is infectious and there are claims of field transmission, but it remains undemonstrated experimentally. Alternate hypotheses for persistence include the movement of livestock within and between regions, and fomite contamination of the environment. Using a stochastic compartmental ordinary differential equation (ODE) model, we investigate the minimum rates of carrier transmission necessary to contribute to the maintenance of FMD in a region, and compare this to the alternate mechanism of persistence through cattle shipments. We find that carrier transmission can theoretically support persistence even at transmission rates much lower than the highest realistic rates previously proposed, and that the parameters with the most effect on the feasibility of carrier-mediated persistence are the average duration of both the carrier phase and natural immunity. However, shipment-mediated persistence remains a viable alternate mechanism for persistence without carrier transmission.

Causes of delayed outbreak responses and their impacts on epidemic spread

Livestock diseases have devastating consequences economically, socially and politically across the globe. In certain systems, pathogens remain viable after host death, which enables residual transmissions from infected carcasses. Rapid culling and carcass disposal are well-established strategies for stamping out an outbreak and limiting its impact; however, wait-times for these procedures, i.e. response delays, are typically farm-specific and time-varying due to logistical constraints. Failing to incorporate variable response delays in epidemiological models may understate outbreak projections and mislead management decisions. We revisited the 2001 foot-and-mouth epidemic in the United Kingdom and sought to understand how misrepresented response delays can influence model predictions. Survival analysis identified farm size and control demand as key factors that impeded timely culling and disposal activities on individual farms. Using these factors in the context of an existing policy to predict local variation in response times significantly affected predictions at the national scale. Models that assumed fixed, timely responses grossly underestimated epidemic severity and its long-term consequences. As a result, this study demonstrates how general inclusion of response dynamics and recognition of partial controllability of interventions can help inform management priorities during epidemics of livestock diseases.

Mycoplasma bovis outbreak in New Zealand cattle: An assessment of transmission trends using surveillance data

Mycoplasma bovis most likely infected New Zealand cattle in the latter half of 2015. Infection was detected in mid-2017 after which control activities were implemented. An official eradication programme commenced in mid-2018, which is ongoing. We examined farm-level tracing and surveillance data to describe the outbreak, analyse transmission trends and make inference on progress towards eradication. Results indicate that cattle movements were the primary means of spread. Although case farms were distributed throughout both islands of New Zealand, most animal movements off infected farms did not result in newly infected farms, indicating Mycoplasma bovis is not highly transmissible between farms. To describe and analyse outbreak trends, we undertook a standard descriptive outbreak investigation, including construction of an epidemic curve and calculation of estimated dissemination ratios. We then employed three empirical models-a non-linear growth model, time series model and branching process model based on time-varying effective reproduction numbers-to further analyse transmission trends and provide short-term forecasts of farm-level incidence. Our analyses suggest that Mycoplasma bovis transmission in New Zealand has declined and progress towards eradication has been made. Few incident cases were forecast for the period between 8 September and 17 December 2019. To date, no case farms with an estimated infection date assigned to this period have been detected; however, case detection is ongoing, and these results need to be interpreted cautiously considering model validation and other important contextual information on performance of the eradication programme, such as the time between infection, detection and implementation of movement controls on case farms.

Challenges to the Application of Spatially Explicit Stochastic Simulation Models for Foot-and-Mouth Disease Control in Endemic Settings: A Systematic Review

Simulation modeling has become common for estimating the spread of highly contagious animal diseases. Several models have been developed to mimic the spread of foot-and-mouth disease (FMD) in specific regions or countries, conduct risk assessment, analyze outbreaks using historical data or hypothetical scenarios, assist in policy decisions during epidemics, formulate preparedness plans, and evaluate economic impacts. Majority of the available FMD simulation models were designed for and applied in disease-free countries, while there has been limited use of such models in FMD endemic countries. This paper's objective was to report the findings from a study conducted to review the existing published original research literature on spatially explicit stochastic simulation (SESS) models of FMD spread, focusing on assessing these models for their potential use in endemic settings. The goal was to identify the specific components of endemic FMD needed to adapt these SESS models for their potential application in FMD endemic settings. This systematic review followed the PRISMA guidelines, and three databases were searched, which resulted in 1176 citations. Eighty citations finally met the inclusion criteria and were included in the qualitative synthesis, identifying nine unique SESS models. These SESS models were assessed for their potential application in endemic settings. The assessed SESS models can be adapted for use in FMD endemic countries by modifying the underlying code to include multiple cocirculating serotypes, routine prophylactic vaccination (RPV), and livestock population dynamics to more realistically mimic the endemic characteristics of FMD. The application of SESS models in endemic settings will help evaluate strategies for FMD control, which will improve livestock health, provide economic gains for producers, help alleviate poverty and hunger, and will complement efforts to achieve the Sustainable Development Goals.

Parallels, differences and lessons: a comparison of the management of foot-and-mouth disease and COVID-19 using UK 2001/2020 as points of reference

Foot-and-mouth disease (FMD) is an extremely infectious viral infection of cloven-hoofed animals which is highly challenging to control and can give rise to national animal health crises, especially if there is a lack of pre-existing immunity due to the emergence of new strains or following incursions into disease-free regions. The 2001 FMD epidemic in the UK was on a scale that initially overwhelmed the national veterinary services and was eventually controlled by livestock lockdown and slaughter on an unprecedented scale. In 2020, the rapid emergence of COVID-19 has led to a human pandemic unparalleled in living memory. The enormous logistics of multi-agency control efforts for COVID-19 are reminiscent of the 2001 FMD epidemic in the UK, as are the use of movement restrictions, not normally a feature of human disease control. The UK experience is internationally relevant as few countries have experienced national epidemic crises for both diseases. In this review, we reflect on the experiences and lessons learnt from UK and international responses to FMD and COVID-19 with respect to their management, including the challenge of preclinical viral transmission, threat awareness, early detection, different interpretations of scientific information, lockdown, biosecurity behaviour change, shortage of testing capacity and the choices for eradication versus living with infection. A major lesson is that the similarity of issues and critical resources needed to manage large-scale outbreaks demonstrates that there is benefit to a ‘One Health’ approach to preparedness, with potential for greater cooperation in planning and the consideration of shared critical resources.

Latent likelihood ratio tests for assessing spatial kernels in epidemic models

One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial separation of infected and susceptible hosts. As the design of control strategies is often based on an assessment of the distance over which transmission can realistically occur and estimation of this distance is very sensitive to the choice of kernel function, it is important that models used to inform control strategies can be scrutinised in the light of observation in order to elicit possible evidence against the selected kernel function. While a range of approaches to model criticism is in existence, the field remains one in which the need for further research is recognised. In this paper, building on earlier contributions by the authors, we introduce a new approach to assessing the validity of spatial kernels—the latent likelihood ratio tests—which use likelihood-based discrepancy variables that can be used to compare the fit of competing models, and compare the capacity of this approach to detect model mis-specification with that of tests based on the use of infection-link residuals. We demonstrate that the new approach can be used to formulate tests with greater power than infection-link residuals to detect kernel mis-specification particularly when the degree of mis-specification is modest. This new tests avoid the use of a fully Bayesian approach which may introduce undesirable complications related to computational complexity and prior sensitivity.

Transmission network reconstruction for foot-and-mouth disease outbreaks incorporating farm-level covariates

Transmission network modelling to infer ‘who infected whom’ in infectious disease outbreaks is a highly active area of research. Outbreaks of foot-and-mouth disease have been a key focus of transmission network models that integrate genomic and epidemiological data. The aim of this study was to extend Lau’s systematic Bayesian inference framework to incorporate additional parameters representing predominant species and numbers of animals held on a farm. Lau’s Bayesian Markov chain Monte Carlo algorithm was reformulated, verified and pseudo-validated on 100 simulated outbreaks populated with demographic data Japan and Australia. The modified model was then implemented on genomic and epidemiological data from the 2010 outbreak of foot-and-mouth disease in Japan, and outputs compared to those from the SCOTTI model implemented in BEAST2. The modified model achieved improvements in overall accuracy when tested on the simulated outbreaks. When implemented on the actual outbreak data from Japan, infected farms that held predominantly pigs were estimated to have five times the transmissibility of infected cattle farms and be 49% less susceptible. The farm-level incubation period was 1 day shorter than the latent period, the timing of the seeding of the outbreak in Japan was inferred, as were key linkages between clusters and features of farms involved in widespread dissemination of this outbreak. To improve accessibility the modified model has been implemented as the R package ‘BORIS’ for use in future outbreaks.

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.

Context matters: using reinforcement learning to develop human-readable, state-dependent outbreak response policies

The number of all possible epidemics of a given infectious disease that could occur on a given landscape is large for systems of real-world complexity. Furthermore, there is no guarantee that the control actions that are optimal, on average, over all possible epidemics are also best for each possible epidemic. Reinforcement learning (RL) and Monte Carlo control have been used to develop machine-readable context-dependent solutions for complex problems with many possible realizations ranging from video-games to the game of Go. RL could be a valuable tool to generate context-dependent policies for outbreak response, though translating the resulting policies into simple rules that can be read and interpreted by human decision-makers remains a challenge. Here we illustrate the application of RL to the development of context-dependent outbreak response policies to minimize outbreaks of foot-and-mouth disease. We show that control based on the resulting context-dependent policies, which adapt interventions to the specific outbreak, result in smaller outbreaks than static policies. We further illustrate two approaches for translating the complex machine-readable policies into simple heuristics that can be evaluated by human decision-makers. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Unraveling R0: Considerations for Public Health Applications

We assessed public health use of R 0, the basic reproduction number, which estimates the speed at which a disease is capable of spreading in a population. These estimates are of great public health interest, as evidenced during the 2009 influenza A (H1N1) virus pandemic.

We reviewed methods commonly used to estimate R 0, examined their practical utility, and assessed how estimates of this epidemiological parameter can inform mitigation strategy decisions.

In isolation, R 0 is a suboptimal gauge of infectious disease dynamics across populations; other disease parameters may provide more useful information. Nonetheless, estimation of R 0 for a particular population is useful for understanding transmission in the study population. Considered in the context of other epidemiologically important parameters, the value of R 0 may lie in better understanding an outbreak and in preparing a public health response.

The implementation of cattle market closure strategies to mitigate the foot-and-mouth disease epidemics: A contact modeling approach

Foot-and-mouth disease (FMD) is one of the most endemic diseases in livestock worldwide. The disease occurrence generally results in a huge economic impact. The virus may distribute across countries or even continents along the contact network of animal movements. The present study, therefore, aimed to explore a cattle movement network originated in Tak, a Thailand-Myanmar bordered province and to demonstrate how FMDV spread among the nodes of market, source and destination. Subsequently, we examined the effectiveness of market closure intervention. The market-market (M-M) network was constructed to highlight the inter-market connections and the FMDV was modeled to spread along the trade chain. Four market closure scenarios based on rapidness and duration of implementation were examined. Our results indicate that two of the three major markets located in the province were highly connected and a strongly connected component was identified. The intra-provincial animal movements, which were currently overlooked, should be moved into sights as most of the high-risk sources for FMD epidemics were recognized in a close proximity to the cattle markets. Simultaneously, remote destinations across the country were identified. The inter-provincial animal movement control must be strengthened once FMD outbreak is notified. Based on our simulations, closing markets with low inter-market connectivity may not prevent the spread of FMDV. A selective market closure strategy targeting highly connected markets together with cattle trader tracking system was an alternative approach. However, socio-economic consequences regarding this intervention must be considered.

The impact of surveillance and control on highly pathogenic avian influenza outbreaks in poultry in Dhaka division, Bangladesh

In Bangladesh, the poultry industry is an economically and socially important sector, but it is persistently threatened by the effects of H5N1 highly pathogenic avian influenza. Thus, identifying the optimal control policy in response to an emerging disease outbreak is a key challenge for policy-makers. To inform this aim, a common approach is to carry out simulation studies comparing plausible strategies, while accounting for known capacity restrictions. In this study we perform simulations of a previously developed H5N1 influenza transmission model framework, fitted to two separate historical outbreaks, to assess specific control objectives related to the burden or duration of H5N1 outbreaks among poultry farms in the Dhaka division of Bangladesh. In particular, we explore the optimal implementation of ring culling, ring vaccination and active surveillance measures when presuming disease transmission predominately occurs from premises-to-premises, versus a setting requiring the inclusion of external factors. Additionally, we determine the sensitivity of the management actions under consideration to differing levels of capacity constraints and outbreaks with disparate transmission dynamics. While we find that reactive culling and vaccination policies should pay close attention to these factors to ensure intervention targeting is optimised, across multiple settings the top performing control action amongst those under consideration were targeted proactive surveillance schemes. Our findings may advise the type of control measure, plus its intensity, that could potentially be applied in the event of a developing outbreak of H5N1 amongst originally H5N1 virus-free commercially-reared poultry in the Dhaka division of Bangladesh.

Ongoing circulation of avian influenza H5N1 viruses in poultry pose a global public health risk and cause extensive damage to the livestock industry. One of several countries in South Asia gravely affected is Bangladesh, where the poultry industry is an economically and socially important sector. Identifying the optimal control response in anticipation of further outbreaks is therefore a key challenge for policy-makers. This study tested a series of culling, vaccination and active surveillance intervention actions, assessing specific control objectives related to the burden or duration of H5N1 outbreaks among commercial poultry farms in the Dhaka division. This assessment was achieved through performing computational simulations of a previously developed H5N1 influenza transmission mathematical model. The findings of this assessment indicate that the impact of reactive culling and vaccination control policies are dependent upon transmission characteristics, control objectives and availability of resources to enact the control action, whereas proactive surveillance schemes significantly outperform reactive surveillance procedures irrespective of these conditions.

Real-time decision-making during emergency disease outbreaks

In the event of a new infectious disease outbreak, mathematical and simulation models are commonly used to inform policy by evaluating which control strategies will minimize the impact of the epidemic. In the early stages of such outbreaks, substantial parameter uncertainty may limit the ability of models to provide accurate predictions, and policymakers do not have the luxury of waiting for data to alleviate this state of uncertainty. For policymakers, however, it is the selection of the optimal control intervention in the face of uncertainty, rather than accuracy of model predictions, that is the measure of success that counts. We simulate the process of real-time decision-making by fitting an epidemic model to observed, spatially-explicit, infection data at weekly intervals throughout two historical outbreaks of foot-and-mouth disease, UK in 2001 and Miyazaki, Japan in 2010, and compare forward simulations of the impact of switching to an alternative control intervention at the time point in question. These are compared to policy recommendations generated in hindsight using data from the entire outbreak, thereby comparing the best we could have done at the time with the best we could have done in retrospect. Our results show that the control policy that would have been chosen using all the data is also identified from an early stage in an outbreak using only the available data, despite high variability in projections of epidemic size. Critically, we find that it is an improved understanding of the locations of infected farms, rather than improved estimates of transmission parameters, that drives improved prediction of the relative performance of control interventions. However, the ability to estimate undetected infectious premises is a function of uncertainty in the transmission parameters. Here, we demonstrate the need for both real-time model fitting and generating projections to evaluate alternative control interventions throughout an outbreak. Our results highlight the use of using models at outbreak onset to inform policy and the importance of state-dependent interventions that adapt in response to additional information throughout an outbreak.

Need for speed: An optimized gridding approach for spatially explicit disease simulations

Numerical models for simulating outbreaks of infectious diseases are powerful tools for informing surveillance and control strategy decisions. However, large-scale spatially explicit models can be limited by the amount of computational resources they require, which poses a problem when multiple scenarios need to be explored to provide policy recommendations. We introduce an easily implemented method that can reduce computation time in a standard Susceptible-Exposed-Infectious-Removed (SEIR) model without introducing any further approximations or truncations. It is based on a hierarchical infection process that operates on entire groups of spatially related nodes (cells in a grid) in order to efficiently filter out large volumes of susceptible nodes that would otherwise have required expensive calculations. After the filtering of the cells, only a subset of the nodes that were originally at risk are then evaluated for actual infection. The increase in efficiency is sensitive to the exact configuration of the grid, and we describe a simple method to find an estimate of the optimal configuration of a given landscape as well as a method to partition the landscape into a grid configuration. To investigate its efficiency, we compare the introduced methods to other algorithms and evaluate computation time, focusing on simulated outbreaks of foot-and-mouth disease (FMD) on the farm population of the USA, the UK and Sweden, as well as on three randomly generated populations with varying degree of clustering. The introduced method provided up to 500 times faster calculations than pairwise computation, and consistently performed as well or better than other available methods. This enables large scale, spatially explicit simulations such as for the entire continental USA without sacrificing realism or predictive power.

Numerical models for simulating the outbreak of infectious disease are powerful tools that can be used to inform policy decisions by simulating outbreaks and control actions. However, they rely on considerable computational power to explore all outcomes and scenarios of interest. Focusing on model types commonly used for livestock diseases, we here introduce novel algorithms for efficient computation, alongside techniques to optimize them based on simplifying assumptions. Through simulations of FMD outbreak in the US, the UK and Sweden, as well as in computer generated landscapes, we test how these methods perform under realistic conditions. We find that our optimization techniques works well, and when the introduced algorithms are implemented with these optimizations, computation time can be reduced by more than two orders of magnitude compared to pairwise calculations. We propose that the considered algorithms—which are straight forward to implement—will be useful for simulation of a wide range of diseases, and will promote the use of simulation models for policy recommendation.

Assessing the Economic Impact of Vaccine Availability When Controlling Foot and Mouth Disease Outbreaks

Predictive models have been used extensively to assess the likely effectiveness of vaccination policies as part of control measures in the event of a foot and mouth disease (FMD) outbreak. However, the availability of vaccine stocks and the impact of vaccine availability on disease control strategies represent a key uncertainty when assessing potential control strategies. Using an epidemiological, spatially explicit, simulation model in combination with a direct cost calculator, we assessed how vaccine availability constraints may affect the economic benefit of a “vaccination-to-live” strategy during a FMD outbreak in Scotland, when implemented alongside culling of infected premises and dangerous contacts. We investigated the impact of vaccine stock size and restocking delays on epidemiological and economic outcomes. We also assessed delays in the initial decision to vaccinate, maximum daily vaccination capacity, and vaccine efficacy. For scenarios with conditions conducive to large outbreaks, all vaccination strategies perform better than the strategy where only culling is implemented. A stock of 200,000 doses, enough to vaccinate 12% of the Scottish cattle population, would be sufficient to maximize the relative benefits of vaccination, both epidemiologically and economically. However, this generates a wider variation in economic cost than if vaccination is not implemented, making outcomes harder to predict. The probability of direct costs exceeding £500 million is reduced when vaccination is used and is steadily reduced further as the size of initial vaccine stock increases. If only a suboptimal quantity of vaccine doses is initially available (100,000 doses), restocking delays of more than 2 weeks rapidly increase the cost of controlling outbreaks. Impacts of low vaccine availability or restocking delays are particularly aggravated by delays in the initial decision to vaccinate, or low vaccine efficacy. Our findings confirm that implementing an emergency vaccination-to-live strategy in addition to the conventional stamping out strategy is economically beneficial in scenarios with conditions conducive to large FMD outbreaks in Scotland. However, the size of the initial vaccine stock available at the start of the outbreak and the interplay with other factors, such as vaccine efficacy and delays in restocking or implementing vaccination, should be considered in making decisions about optimal control strategies for FMD outbreaks.

Efficient use of sentinel sites: detection of invasive honeybee pests and diseases in the UK

Sentinel sites, where problems can be identified early or investigated in detail, form an important part of planning for exotic disease outbreaks in humans, livestock and plants. Key questions are: how many sentinels are required, where should they be positioned and how effective are they at rapidly identifying new invasions? The sentinel apiary system for invasive honeybee pests and diseases illustrates the costs and benefits of such approaches. Here, we address these issues with two mathematical modelling approaches. The first approach is generic and uses probabilistic arguments to calculate the average number of affected sites when an outbreak is first detected, providing rapid and general insights that we have applied to a range of infectious diseases. The second approach uses a computationally intensive, stochastic, spatial model to simulate multiple outbreaks and to determine appropriate sentinel locations for UK apiaries. Both models quantify the anticipated increase in success of sentinel sites as their number increases and as non-sentinel sites become worse at detection; however, unexpectedly sentinels perform relatively better for faster growing outbreaks. Additionally, the spatial model allows us to quantify the substantial role that carefully positioned sentinels can play in the rapid detection of exotic invasions.

Evaluation of Strategies to Control a Potential Outbreak of Foot-and-Mouth Disease in Sweden

To minimize the potential consequences of an introduction of foot-and-mouth disease (FMD) in Europe, European Union (EU) member states are required to present a contingency plan. This study used a simulation model to study potential outbreak scenarios in Sweden and evaluate the best control strategies. The model was informed by the Swedish livestock structure using herd information from cattle, pig, and small ruminant holdings in the country. The contact structure was based on animal movement data and studies investigating the movements between farms of veterinarians, service trucks, and other farm visitors. All scenarios of outbreak control included depopulation of detected herds, 3 km protection and 10 km surveillance zones, movement tracing, and 3 days national standstill. The effect of availability of surveillance resources, i.e., number of field veterinarians per day, and timeliness of enforcement of interventions, was assessed. With the estimated currently available resources, an FMD outbreak in Sweden is expected to be controlled (i.e., last infected herd detected) within 3 weeks of detection in any evaluated scenario. The density of farms in the area where the epidemic started would have little impact on the time to control the outbreak, but spread in high density areas would require more surveillance resources, compared to areas of lower farm density. The use of vaccination did not result in a reduction in the expected number of infected herds. Preemptive depopulation was able to reduce the number of infected herds in extreme scenarios designed to test a combination of worst-case conditions of virus introduction and spread, but at the cost of doubling the number of herds culled. This likely resulted from a combination of the small outbreaks predicted by the spread model, and the high efficacy of the basic control measures evaluated, under the conditions of the Swedish livestock industry, and considering the assumed control resources available. The results indicate that the duration and extent of FMD outbreaks could be kept limited in Sweden using the EU standard control strategy and a 3 days national standstill.

Modelling H5N1 in Bangladesh across spatial scales: Model complexity and zoonotic transmission risk

Highly pathogenic avian influenza H5N1 remains a persistent public health threat, capable of causing infection in humans with a high mortality rate while simultaneously negatively impacting the livestock industry. A central question is to determine regions that are likely sources of newly emerging influenza strains with pandemic causing potential. A suitable candidate is Bangladesh, being one of the most densely populated countries in the world and having an intensifying farming system. It is therefore vital to establish the key factors, specific to Bangladesh, that enable both continued transmission within poultry and spillover across the human-animal interface. We apply a modelling framework to H5N1 epidemics in the Dhaka region of Bangladesh, occurring from 2007 onwards, that resulted in large outbreaks in the poultry sector and a limited number of confirmed human cases. This model consisted of separate poultry transmission and zoonotic transmission components. Utilising poultry farm spatial and population information a set of competing nested models of varying complexity were fitted to the observed case data, with parameter inference carried out using Bayesian methodology and goodness-of-fit verified by stochastic simulations. For the poultry transmission component, successfully identifying a model of minimal complexity, which enabled the accurate prediction of the size and spatial distribution of cases in H5N1 outbreaks, was found to be dependent on the administration level being analysed. A consistent outcome of non-optimal reporting of infected premises materialised in each poultry epidemic of interest, though across the outbreaks analysed there were substantial differences in the estimated transmission parameters. The zoonotic transmission component found the main contributor to spillover transmission of H5N1 in Bangladesh was found to differ from one poultry epidemic to another. We conclude by discussing possible explanations for these discrepancies in transmission behaviour between epidemics, such as changes in surveillance sensitivity and biosecurity practices.

Quantifying the Value of Perfect Information in Emergency Vaccination Campaigns

Foot-and-mouth disease outbreaks in non-endemic countries can lead to large economic costs and livestock losses but the use of vaccination has been contentious, partly due to uncertainty about emergency FMD vaccination. Value of information methods can be applied to disease outbreak problems such as FMD in order to investigate the performance improvement from resolving uncertainties. Here we calculate the expected value of resolving uncertainty about vaccine efficacy, time delay to immunity after vaccination and daily vaccination capacity for a hypothetical FMD outbreak in the UK. If it were possible to resolve all uncertainty prior to the introduction of control, we could expect savings of £55 million in outbreak cost, 221,900 livestock culled and 4.3 days of outbreak duration. All vaccination strategies were found to be preferable to a culling only strategy. However, the optimal vaccination radius was found to be highly dependent upon vaccination capacity for all management objectives. We calculate that by resolving the uncertainty surrounding vaccination capacity we would expect to return over 85% of the above savings, regardless of management objective. It may be possible to resolve uncertainty about daily vaccination capacity before an outbreak, and this would enable decision makers to select the optimal control action via careful contingency planning.

In the UK during 2001 there was an outbreak of foot-and-mouth disease (FMD) which cost the economy an estimated £8 billion and led to the culling of approximately 7 million livestock. The main methods used to control the epidemic were movement bans and culling of infected and high-risk livestock. FMD vaccines were available but not used because of concerns about their effectiveness and how their use would affect the UK’s disease-free status. Using the Warwick FMD model, we ran simulations of FMD outbreaks in the UK including ring vaccination as a method of outbreak control with varying levels of vaccine efficacy, time delay between vaccination and conferral of immunity, and vaccination capacity. We applied value of information analysis to these results and found that the most important factor in determining the optimal vaccination strategy was knowledge of the vaccination capacity. In contrast, vaccine efficacy and delay between vaccination and immunity were relatively unimportant from a decision making perspective. This work could inform contingency planning that would lead to cost savings in the event of a future FMD outbreak and could also be applied to other infectious diseases.

Controlling viral outbreaks: Quantitative strategies

Preparing for and responding to outbreaks of serious livestock infectious diseases are critical measures to safeguard animal health, public health, and food supply. Almost all of the current control strategies are empirical, and mass culling or “stamping out” is frequently the principal strategy for controlling epidemics. However, there are ethical, ecological, and economic reasons to consider less drastic control strategies. Here we use modeling to quantitatively study the efficacy of different control measures for viral outbreaks, where the infectiousness, transmissibility and death rate of animals commonly depends on their viral load. We develop a broad theoretical framework for exploring and understanding this heterogeneity. The model includes both direct transmission from infectious animals and indirect transmission from an environmental reservoir. We then incorporate a large variety of control measures, including vaccination, antivirals, isolation, environmental disinfection, and several forms of culling, which may result in fewer culled animals. We provide explicit formulae for the basic reproduction number, R₀, for each intervention and for combinations. We evaluate the control methods for a realistic simulated outbreak of low pathogenic avian influenza on a mid-sized turkey farm. In this simulated outbreak, culling results in more total dead birds and dramatically more when culling all of the infected birds.

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.

Spatiotemporal Variation in Distance Dependent Animal Movement Contacts: One Size Doesn't Fit All

The structure of contacts that mediate transmission has a pronounced effect on the outbreak dynamics of infectious disease and simulation models are powerful tools to inform policy decisions. Most simulation models of livestock disease spread rely to some degree on predictions of animal movement between holdings. Typically, movements are more common between nearby farms than between those located far away from each other. Here, we assessed spatiotemporal variation in such distance dependence of animal movement contacts from an epidemiological perspective. We evaluated and compared nine statistical models, applied to Swedish movement data from 2008. The models differed in at what level (if at all), they accounted for regional and/or seasonal heterogeneities in the distance dependence of the contacts. Using a kernel approach to describe how probability of contacts between farms changes with distance, we developed a hierarchical Bayesian framework and estimated parameters by using Markov Chain Monte Carlo techniques. We evaluated models by three different approaches of model selection. First, we used Deviance Information Criterion to evaluate their performance relative to each other. Secondly, we estimated the log predictive posterior distribution, this was also used to evaluate their relative performance. Thirdly, we performed posterior predictive checks by simulating movements with each of the parameterized models and evaluated their ability to recapture relevant summary statistics. Independent of selection criteria, we found that accounting for regional heterogeneity improved model accuracy. We also found that accounting for seasonal heterogeneity was beneficial, in terms of model accuracy, according to two of three methods used for model selection. Our results have important implications for livestock disease spread models where movement is an important risk factor for between farm transmission. We argue that modelers should refrain from using methods to simulate animal movements that assume the same pattern across all regions and seasons without explicitly testing for spatiotemporal variation.

Preserving privacy whilst maintaining robust epidemiological predictions

Mathematical models are invaluable tools for quantifying potential epidemics and devising optimal control strategies in case of an outbreak. State-of-the-art models increasingly require detailed individual farm-based and sensitive data, which may not be available due to either lack of capacity for data collection or privacy concerns. However, in many situations, aggregated data are available for use. In this study, we systematically investigate the accuracy of predictions made by mathematical models initialised with varying data aggregations, using the UK 2001 Foot-and-Mouth Disease Epidemic as a case study. We consider the scenario when the only data available are aggregated into spatial grid cells, and develop a metapopulation model where individual farms in a single subpopulation are assumed to behave uniformly and transmit randomly. We also adapt this standard metapopulation model to capture heterogeneity in farm size and composition, using farm census data. Our results show that homogeneous models based on aggregated data overestimate final epidemic size but can perform well for predicting spatial spread. Recognising heterogeneity in farm sizes improves predictions of the final epidemic size, identifying risk areas, determining the likelihood of epidemic take-off and identifying the optimal control strategy. In conclusion, in cases where individual farm-based data are not available, models can still generate meaningful predictions, although care must be taken in their interpretation and use.

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

‘Big-data’ epidemic models are being increasingly used to influence government policy to help with control and eradication of infectious diseases. In the case of livestock, detailed movement records have been used to parametrize realistic transmission models. While livestock movement data are readily available in the UK and other countries in the EU, in many countries around the world, such detailed data are not available. By using a comprehensive database of the UK cattle trade network, we implement various sampling strategies to determine the quantity of network data required to give accurate epidemiological predictions. It is found that by targeting nodes with the highest number of movements, accurate predictions on the size and spatial spread of epidemics can be made. This work has implications for countries such as the USA, where access to data is limited, and developing countries that may lack the resources to collect a full dataset on livestock movements.

Spread of Coxiella burnetii between dairy cattle herds in an enzootic region: modelling contributions of airborne transmission and trade

Q fever, a worldwide zoonotic disease caused by Coxiella burnetii, is a looming concern for livestock and public health. Epidemiological features of inter-herd transmission of C. burnetii in cattle herds by wind and trade of cows are poorly understood. We present a novel dynamic spatial model describing the inter-herd regional spread of C. burnetii in dairy cattle herds, quantifying the ability of airborne transmission and animal trade in C. burnetii propagation in an enzootic region. Among all the new herd infections, 92% were attributed to airborne transmission and the rest to cattle trade. Infections acquired following airborne transmission were shown to cause relatively small and ephemeral intra-herd outbreaks. On the contrary, disease-free herds purchasing an infectious cow experienced significantly higher intra-herd prevalence. The results also indicated that, for short duration, both transmission routes were independent from each other without any synergistic effect. The model outputs applied to the Finistère department in western France showed satisfactory sensitivity (0.71) and specificity (0.80) in predicting herd infection statuses at the end of one year in a neighbourhood of 3 km around expected incident herds, when compared with data. The model developed here thus provides important insights into the spread of C. burnetii between dairy cattle herds and paves the way for implementation and assessment of control strategies.

The Biosurveillance Analytics Resource Directory (BARD): Facilitating the Use of Epidemiological Models for Infectious Disease Surveillance

Epidemiological modeling for infectious disease is important for disease management and its routine implementation needs to be facilitated through better description of models in an operational context. A standardized model characterization process that allows selection or making manual comparisons of available models and their results is currently lacking. A key need is a universal framework to facilitate model description and understanding of its features. Los Alamos National Laboratory (LANL) has developed a comprehensive framework that can be used to characterize an infectious disease model in an operational context. The framework was developed through a consensus among a panel of subject matter experts. In this paper, we describe the framework, its application to model characterization, and the development of the Biosurveillance Analytics Resource Directory (BARD; http://brd.bsvgateway.org/brd/), to facilitate the rapid selection of operational models for specific infectious/communicable diseases. We offer this framework and associated database to stakeholders of the infectious disease modeling field as a tool for standardizing model description and facilitating the use of epidemiological models.

Evidence for Emergency Vaccination Having Played a Crucial Role to Control the 1965/66 Foot-and-Mouth Disease Outbreak in Switzerland

Foot-and-mouth disease (FMD) is a highly contagious disease that caused several large outbreaks in Europe in the last century. The last important outbreak in Switzerland took place in 1965/66 and affected more than 900 premises and more than 50,000 animals were slaughtered. Large-scale emergency vaccination of the cattle and pig population has been applied to control the epidemic. In recent years, many studies have used infectious disease models to assess the impact of different disease control measures, including models developed for diseases exotic for the specific region of interest. Often, the absence of real outbreak data makes a validation of such models impossible. This study aimed to evaluate whether a spatial, stochastic simulation model (the Davis Animal Disease Simulation model) can predict the course of a Swiss FMD epidemic based on the available historic input data on population structure, contact rates, epidemiology of the virus, and quality of the vaccine. In addition, the potential outcome of the 1965/66 FMD epidemic without application of vaccination was investigated. Comparing the model outcomes to reality, only the largest 10% of the simulated outbreaks approximated the number of animals being culled. However, the simulation model highly overestimated the number of culled premises. While the outbreak duration could not be well reproduced by the model compared to the 1965/66 epidemic, it was able to accurately estimate the size of the area infected. Without application of vaccination, the model predicted a much higher mean number of culled animals than with vaccination, demonstrating that vaccination was likely crucial in disease control for the Swiss FMD outbreak in 1965/66. The study demonstrated the feasibility to analyze historical outbreak data with modern analytical tools. However, it also confirmed that predicted epidemics from a most carefully parameterized model cannot integrate all eventualities of a real epidemic. Therefore, decision makers need to be aware that infectious disease models are useful tools to support the decision-making process but their results are not equal valuable as real observations and should always be interpreted with caution.

Decision-making for foot-and-mouth disease control: Objectives matter

Formal decision-analytic methods can be used to frame disease control problems, the first step of which is to define a clear and specific objective. We demonstrate the imperative of framing clearly-defined management objectives in finding optimal control actions for control of disease outbreaks. We illustrate an analysis that can be applied rapidly at the start of an outbreak when there are multiple stakeholders involved with potentially multiple objectives, and when there are also multiple disease models upon which to compare control actions. The output of our analysis frames subsequent discourse between policy-makers, modellers and other stakeholders, by highlighting areas of discord among different management objectives and also among different models used in the analysis. We illustrate this approach in the context of a hypothetical foot-and-mouth disease (FMD) outbreak in Cumbria, UK using outputs from five rigorously-studied simulation models of FMD spread. We present both relative rankings and relative performance of controls within each model and across a range of objectives. Results illustrate how control actions change across both the base metric used to measure management success and across the statistic used to rank control actions according to said metric. This work represents a first step towards reconciling the extensive modelling work on disease control problems with frameworks for structured decision making.

Data-Driven Models of Foot-and-Mouth Disease Dynamics: A Review

Foot-and-mouth disease virus (FMDV) threatens animal health and leads to considerable economic losses worldwide. Progress towards minimizing both veterinary and financial impact of the disease will be made with targeted disease control policies. To move towards targeted control, specific targets and detailed control strategies must be defined. One approach for identifying targets is to use mathematical and simulation models quantified with accurate and fine-scale data to design and evaluate alternative control policies. Nevertheless, published models of FMDV vary in modelling techniques and resolution of data incorporated. In order to determine which models and data sources contain enough detail to represent realistic control policy alternatives, we performed a systematic literature review of all FMDV dynamical models that use host data, disease data or both data types. For the purpose of evaluating modelling methodology, we classified models by control strategy represented, resolution of models and data, and location modelled. We found that modelling methodology has been well developed to the point where multiple methods are available to represent detailed and contact-specific transmission and targeted control. However, detailed host and disease data needed to quantify these models are only available from a few outbreaks. To address existing challenges in data collection, novel data sources should be considered and integrated into models of FMDV transmission and control. We suggest modelling multiple endemic areas to advance local control and global control and better understand FMDV transmission dynamics. With incorporation of additional data, models can assist with both the design of targeted control and identification of transmission drivers across geographic boundaries.

Serotype-Specific Transmission and Waning Immunity of Endemic Foot-and-Mouth Disease Virus in Cameroon

Foot-and-mouth disease virus (FMDV) causes morbidity and mortality in a range of animals and threatens local economies by acting as a barrier to international trade. The outbreak in the United Kingdom in 2001 that cost billions to control highlighted the risk that the pathogen poses to agriculture. In response, several mathematical models have been developed to parameterize and predict both transmission dynamics and optimal disease control. However, a lack of understanding of the multi-strain etiology prevents characterization of multi-strain dynamics. Here, we use data from FMDV serology in an endemic setting to probe strain-specific transmission and immunodynamics. Five serotypes of FMDV affect cattle in the Far North Region of Cameroon. We fit both catalytic and reverse catalytic models to serological data to estimate the force of infection and the rate of waning immunity, and to detect periods of sustained transmission. For serotypes SAT2, SAT3, and type A, a model assuming life-long immunity fit better. For serotypes SAT1 and type O, the better-fit model suggests that immunity may wane over time. Our analysis further indicates that type O has the greatest force of infection and the longest duration of immunity. Estimates for the force of infection were time-varying and indicated that serotypes SAT1 and O displayed endemic dynamics, serotype A displayed epidemic dynamics, and SAT2 and SAT3 did not sustain local chains of transmission. Since these results were obtained from the same population at the same time, they highlight important differences in transmission specific to each serotype. They also show that immunity wanes at rates specific to each serotype, which influences patterns of local persistence. Overall, this work shows that viral serotypes can differ significantly in their epidemiological and immunological characteristics. Patterns and processes that drive transmission in endemic settings must consider complex viral dynamics for accurate representation and interpretation.

A Bayesian ensemble approach for epidemiological projections

Mathematical models are powerful tools for epidemiology and can be used to compare control actions. However, different models and model parameterizations may provide different prediction of outcomes. In other fields of research, ensemble modeling has been used to combine multiple projections. We explore the possibility of applying such methods to epidemiology by adapting Bayesian techniques developed for climate forecasting. We exemplify the implementation with single model ensembles based on different parameterizations of the Warwick model run for the 2001 United Kingdom foot and mouth disease outbreak and compare the efficacy of different control actions. This allows us to investigate the effect that discrepancy among projections based on different modeling assumptions has on the ensemble prediction. A sensitivity analysis showed that the choice of prior can have a pronounced effect on the posterior estimates of quantities of interest, in particular for ensembles with large discrepancy among projections. However, by using a hierarchical extension of the method we show that prior sensitivity can be circumvented. We further extend the method to include a priori beliefs about different modeling assumptions and demonstrate that the effect of this can have different consequences depending on the discrepancy among projections. We propose that the method is a promising analytical tool for ensemble modeling of disease outbreaks.

Rapid simulation of spatial epidemics: a spectral method

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel.

The impact of movements and animal density on continental scale cattle disease outbreaks in the United States

Globalization has increased the potential for the introduction and spread of novel pathogens over large spatial scales necessitating continental-scale disease models to guide emergency preparedness. Livestock disease spread models, such as those for the 2001 foot-and-mouth disease (FMD) epidemic in the United Kingdom, represent some of the best case studies of large-scale disease spread. However, generalization of these models to explore disease outcomes in other systems, such as the United States's cattle industry, has been hampered by differences in system size and complexity and the absence of suitable livestock movement data. Here, a unique database of US cattle shipments allows estimation of synthetic movement networks that inform a near-continental scale disease model of a potential FMD-like (i.e., rapidly spreading) epidemic in US cattle. The largest epidemics may affect over one-third of the US and 120,000 cattle premises, but cattle movement restrictions from infected counties, as opposed to national movement moratoriums, are found to effectively contain outbreaks. Slow detection or weak compliance may necessitate more severe state-level bans for similar control. Such results highlight the role of large-scale disease models in emergency preparedness, particularly for systems lacking comprehensive movement and outbreak data, and the need to rapidly implement multi-scale contingency plans during a potential US outbreak.

Dynamics of infectious diseases

Modern infectious disease epidemiology has a strong history of using mathematics both for prediction and to gain a deeper understanding. However the study of infectious diseases is a highly interdisciplinary subject requiring insights from multiple disciplines, in particular a biological knowledge of the pathogen, a statistical description of the available data and a mathematical framework for prediction. Here we begin with the basic building blocks of infectious disease epidemiology--the SIS and SIR type models--before considering the progress that has been made over the recent decades and the challenges that lie ahead. Throughout we focus on the understanding that can be developed from relatively simple models, although accurate prediction will inevitably require far greater complexity beyond the scope of this review. In particular, we focus on three critical aspects of infectious disease models that we feel fundamentally shape their dynamics: heterogeneously structured populations, stochasticity and spatial structure. Throughout we relate the mathematical models and their results to a variety of real-world problems.

Unraveling R0: considerations for public health applications

We assessed public health use of R0, the basic reproduction number, which estimates the speed at which a disease is capable of spreading in a population. These estimates are of great public health interest, as evidenced during the 2009 influenza A (H1N1) virus pandemic. We reviewed methods commonly used to estimate R0, examined their practical utility, and assessed how estimates of this epidemiological parameter can inform mitigation strategy decisions. In isolation, R0 is a suboptimal gauge of infectious disease dynamics across populations; other disease parameters may provide more useful information. Nonetheless, estimation of R0 for a particular population is useful for understanding transmission in the study population. Considered in the context of other epidemiologically important parameters, the value of R0 may lie in better understanding an outbreak and in preparing a public health response.

Using quantitative disease dynamics as a tool for guiding response to avian influenza in poultry in the United States of America

Wild birds are the primary source of genetic diversity for influenza A viruses that eventually emerge in poultry and humans. Much progress has been made in the descriptive ecology of avian influenza viruses (AIVs), but contributions are less evident from quantitative studies (e.g., those including disease dynamic models). Transmission between host species, individuals and flocks has not been measured with sufficient accuracy to allow robust quantitative evaluation of alternate control protocols. We focused on the United States of America (USA) as a case study for determining the state of our quantitative knowledge of potential AIV emergence processes from wild hosts to poultry. We identified priorities for quantitative research that would build on existing tools for responding to AIV in poultry and concluded that the following knowledge gaps can be addressed with current empirical data: (1) quantification of the spatio-temporal relationships between AIV prevalence in wild hosts and poultry populations, (2) understanding how the structure of different poultry sectors impacts within-flock transmission, (3) determining mechanisms and rates of between-farm spread, and (4) validating current policy-decision tools with data. The modeling studies we recommend will improve our mechanistic understanding of potential AIV transmission patterns in USA poultry, leading to improved measures of accuracy and reduced uncertainty when evaluating alternative control strategies.

The performance of approximations of farm contiguity compared to contiguity defined using detailed geographical information in two sample areas in Scotland: implications for foot-and-mouth disease modelling

BACKGROUND

When modelling infectious diseases, accurately capturing the pattern of dissemination through space is key to providing optimal recommendations for control. Mathematical models of disease spread in livestock, such as for foot-and-mouth disease (FMD), have done this by incorporating a transmission kernel which describes the decay in transmission rate with increasing Euclidean distance from an infected premises (IP). However, this assumes a homogenous landscape, and is based on the distance between point locations of farms. Indeed, underlying the spatial pattern of spread are the contact networks involved in transmission. Accordingly, area-weighted tessellation around farm point locations has been used to approximate field-contiguity and simulate the effect of contiguous premises (CP) culling for FMD. Here, geographic data were used to determine contiguity based on distance between premises' fields and presence of landscape features for two sample areas in Scotland. Sensitivity, positive predictive value, and the True Skill Statistic (TSS) were calculated to determine how point distance measures and area-weighted tessellation compared to the 'gold standard' of the map-based measures in identifying CPs. In addition, the mean degree and density of the different contact networks were calculated.

RESULTS

Utilising point distances <1 km and <5 km as a measure for contiguity resulted in poor discrimination between map-based CPs/non-CPs (TSS 0.279-0.344 and 0.385-0.400, respectively). Point distance <1 km missed a high proportion of map-based CPs; <5 km point distance picked up a high proportion of map-based non-CPs as CPs. Area-weighted tessellation performed best, with reasonable discrimination between map-based CPs/non-CPs (TSS 0.617-0.737) and comparable mean degree and density. Landscape features altered network properties considerably when taken into account.

CONCLUSION

The farming landscape is not homogeneous. Basing contiguity on geographic locations of field boundaries and including landscape features known to affect transmission into FMD models are likely to improve individual farm-level accuracy of spatial predictions in the event of future outbreaks. If a substantial proportion of FMD transmission events are by contiguous spread, and CPs should be assigned an elevated relative transmission rate, the shape of the kernel could be significantly altered since ability to discriminate between map-based CPs and non-CPs is different over different Euclidean distances.

Vaccination against foot-and-mouth disease: do initial conditions affect its benefit?

When facing incursion of a major livestock infectious disease, the decision to implement a vaccination programme is made at the national level. To make this decision, governments must consider whether the benefits of vaccination are sufficient to outweigh potential additional costs, including further trade restrictions that may be imposed due to the implementation of vaccination. However, little consensus exists on the factors triggering its implementation on the field. This work explores the effect of several triggers in the implementation of a reactive vaccination-to-live policy when facing epidemics of foot-and-mouth disease. In particular, we tested whether changes in the location of the incursion and the delay of implementation would affect the epidemiological benefit of such a policy in the context of Scotland. To reach this goal, we used a spatial, premises-based model that has been extensively used to investigate the effectiveness of mitigation procedures in Great Britain. The results show that the decision to vaccinate, or not, is not straightforward and strongly depends on the underlying local structure of the population-at-risk. With regards to disease incursion preparedness, simply identifying areas of highest population density may not capture all complexities that may influence the spread of disease as well as the benefit of implementing vaccination. However, if a decision to vaccinate is made, we show that delaying its implementation in the field may markedly reduce its benefit. This work provides guidelines to support policy makers in their decision to implement, or not, a vaccination-to-live policy when facing epidemics of infectious livestock disease.

Modeling the spread and control of foot-and-mouth disease in Pennsylvania following its discovery and options for control

In this paper, we simulate outbreaks of foot-and-mouth disease in the Commonwealth of Pennsylvania, USA - after the introduction of a state-wide movement ban - as they might unfold in the presence of mitigation strategies. We have adapted a model previously used to investigate FMD control policies in the UK to examine the potential for disease spread given an infection seeded in each county in Pennsylvania. The results are highly dependent upon the county of introduction and the spatial scale of transmission. Should the transmission kernel be identical to that for the UK, the epidemic impact is limited to fewer than 20 premises, regardless of the county of introduction. However, for wider kernels where infection can spread further, outbreaks seeded in or near the county with highest density of premises and animals result in large epidemics (>150 premises). Ring culling and vaccination reduce epidemic size, with the optimal radius of the rings being dependent upon the county of introduction. Should the kernel width exceed a given county-dependent threshold, ring culling is unable to control the epidemic. We find that a vaccinate-to-live policy is generally preferred to ring culling (in terms of reducing the overall number of premises culled), indicating that well-targeted control can dramatically reduce the risk of large scale outbreaks of foot-and-mouth disease occurring in Pennsylvania.

How to make predictions about future infectious disease risks

Formal, quantitative approaches are now widely used to make predictions about the likelihood of an infectious disease outbreak, how the disease will spread, and how to control it. Several well-established methodologies are available, including risk factor analysis, risk modelling and dynamic modelling. Even so, predictive modelling is very much the ‘art of the possible’, which tends to drive research effort towards some areas and away from others which may be at least as important. Building on the undoubted success of quantitative modelling of the epidemiology and control of human and animal diseases such as AIDS, influenza, foot-and-mouth disease and BSE, attention needs to be paid to developing a more holistic framework that captures the role of the underlying drivers of disease risks, from demography and behaviour to land use and climate change. At the same time, there is still considerable room for improvement in how quantitative analyses and their outputs are communicated to policy makers and other stakeholders. A starting point would be generally accepted guidelines for ‘good practice’ for the development and the use of predictive models.

Spread of E. coli O157 infection among Scottish cattle farms: stochastic models and model selection

Identifying risk factors for the presence of Escherichia coli O157 infection on cattle farms is important for understanding the epidemiology of this zoonotic infection in its main reservoir and for informing the design of interventions to reduce the public health risk. Here, we use data from a large-scale field study carried out in Scotland to fit both "SIS"-type dynamical models and statistical risk factor models. By comparing the fit (assessed using maximum likelihood) of different dynamical models we are able to identify the most parsimonious model (using the AIC statistic) and compare it with the model suggested by risk factor analysis. Both approaches identify 2 key risk factors: the movement of cattle onto the farm and the number of cattle on the farm. There was no evidence for a role of other livestock species or seasonality, or of significant risk of local spread. However, the most parsimonious dynamical model does predict that farms can infect other farms through routes other than cattle movement, and that there is a nonlinear relationship between the force of infection and the number of infected farms. An important prediction from the most parsimonious model is that although only approximately 20% farms may harbour E. coli O157 infection at any given time approximately 80% may harbour infection at some point during the course of a year.