Since 2020, large-scale outbreaks of highly pathogenic avian influenza (HPAI) H5N1 in Great Britain have resulted in substantial poultry mortality and economic losses. Alongside the costs, the risk of circulation leading to a viral reassortment that causes zoonotic spillover raises additional concerns. However, the precise mechanisms driving transmission between poultry premises and the impact of potential control measures in Great Britain, such as vaccination, are not fully understood. We have developed a spatial transmission model for the spread of HPAI in poultry premises calibrated to infected premises data for the 2022-23 season using Markov chain Monte Carlo. Our results indicate that reducing the susceptibility of the premises surrounding an identified infected premises (for example, through enhanced biosecurity measures and/or vaccination) can substantially reduce the overall number of infected premises. Our findings highlight that enhanced control measures could limit the future impact of HPAI on the poultry industry and reduce the risk of broader health threats.

Previous research efforts on highly pathogenic H5N1 avian influenza (HPAI) suggest that different avian species exhibit a varied severity of clinical signs after infection. Waterfowl, such as ducks or geese, can be asymptomatic and act as silent carriers of H5N1, making detection harder and increasing the risk of further transmission, potentially leading to significant economic losses. For backyard hobby farmers, passive reporting is a common HPAI detection strategy. We aim to develop a computational, mechanistic model to quantify the effectiveness of this strategy by simulating the spread of H5N1 in a mixed-species, small-population backyard flock. Quantities such as detection time and undetected burden of infection in various scenarios are compared. Our results indicate that the presence of ducks can lead to a higher risk of an outbreak and a higher burden of infection. If most ducks within a flock are resistant to H5N1, detection can be significantly delayed. We find that within-flock infection dynamics can heavily depend on the species composition in backyard farms. Ducks, in particular, can pose a higher risk of transmission within a flock or between flocks. Our findings can help inform surveillance and intervention strategies at the flock and local levels.

Foot and Mouth Disease (FMD) affects cloven-hoofed animals globally and has become a major economic burden for many countries around the world. Countries that have had recent FMD outbreaks are prohibited from exporting most meat products; this has major economic consequences for farmers in those countries, particularly farmers that experience outbreaks or are near outbreaks. Reducing the number of FMD outbreaks in countries where the disease is endemic is an important challenge that could drastically improve the livelihoods of millions of people. As a result, significant effort is expended on surveillance; but there is a concern that uninformative surveillance strategies may waste resources that could be better used on control management. Rapid detection through sentinel surveillance may be a useful tool to reduce the scale and burden of outbreaks. In this study, we use an extensive outbreak and cattle shipment network dataset from the Republic of Türkiye to retrospectively test three possible strategies for sentinel surveillance allocation in countries with endemic FMD and minimal existing FMD surveillance infrastructure that differ in their data requirements: ranging from low to high data needs, we allocate limited surveillance to [1] farms that frequently send and receive shipments of animals (Network Connectivity), [2] farms near other farms with past outbreaks (Spatial Proximity) and [3] farms that receive many shipments from other farms with past outbreaks (Network Proximity). We determine that all of these surveillance methods find a similar number of outbreaks - 2-4.5 times more outbreaks than were detected by surveying farms at random. On average across surveillance efforts, the Network Proximity and Network Connectivity methods each find a similar number of outbreaks and the Spatial Proximity method always finds the fewest outbreaks. Since the Network Proximity method does not outperform the other methods, these results indicate that incorporating both cattle shipment data and outbreak data provides only marginal benefit over the less data-intensive surveillance allocation methods for this objective. We also find that these methods all find more outbreaks when outbreaks are rare. This is encouraging, as early detection is critical for outbreak management. Overall, since the Spatial Proximity and Network Connectivity methods find a similar proportion of outbreaks, and are less data-intensive than the Network Proximity method, countries with endemic FMD whose resources are constrained could prioritize allocating sentinels based on whichever of those two methods requires less additional data collection.

For many infectious diseases, the risk of outbreaks varies seasonally. If a pathogen is usually absent from a host population, a key public health policy question is whether the pathogen's arrival will initiate local transmission, which depends on the season in which arrival occurs. This question can be addressed by estimating the "probability of a major outbreak" (the probability that introduced cases will initiate sustained local transmission). A standard approach for inferring this probability exists for seasonal pathogens (involving calculating the Case Epidemic Risk; CER) based on the mathematical theory of branching processes. Under that theory, the probability of pathogen extinction is estimated, neglecting depletion of susceptible individuals. The CER is then one minus the extinction probability. However, as we show, if transmission cannot occur for long periods of the year (e.g., over winter or over summer), the pathogen will most likely go extinct, leading to a CER that is equal (or very close) to zero even if seasonal outbreaks can occur. This renders the CER uninformative in those scenarios. We therefore devise an alternative approach for inferring outbreak risks for seasonal pathogens (involving calculating the Threshold Epidemic Risk; TER). Estimation of the TER involves calculating the probability that introduced cases will initiate a local outbreak in which a threshold number of cumulative infections is exceeded before outbreak extinction. For simple seasonal epidemic models, such as the stochastic Susceptible-Infectious-Removed model, the TER can be calculated numerically (without model simulations). For more complex models, such as stochastic host-vector models, the TER can be estimated using model simulations. We demonstrate the application of our approach by considering chikungunya virus in northern Italy as a case study. In that context, transmission is most likely in summer, when environmental conditions promote vector abundance. We show that the TER provides more useful assessments of outbreak risks than the CER, enabling practically relevant risk quantification for seasonal pathogens.

[This corrects the article DOI: 10.1371/journal.pcbi.1011448.].

During an infectious disease outbreak, public health policy makers are tasked with strategically implementing interventions whilst balancing competing objectives. To provide a quantitative framework that can be used to guide these decisions, it is helpful to devise a clear and specific objective function that can be evaluated to determine the optimal outbreak response. In this study, we have developed a mathematical modelling framework representing outbreaks of a novel emerging pathogen for which non-pharmaceutical interventions (NPIs) are imposed or removed based on thresholds for hospital occupancy. These thresholds are set at different levels to define four unique strategies for disease control. We illustrate that the optimal intervention strategy is contingent on the choice of objective function. Specifically, the optimal strategy depends on the extent to which policy makers prioritise reducing health costs due to infection over the costs associated with maintaining interventions. Motivated by the scenario early in the COVID-19 pandemic, we incorporate the development of a vaccine into our modelling framework and demonstrate that a policy maker's belief about when a vaccine will become available in future, and its eventual coverage (and/or effectiveness), affects the optimal strategy to adopt early in the outbreak. Furthermore, we show how uncertainty in these quantities can be accounted for when deciding which interventions to introduce. This research highlights the benefits of policy makers being explicit about the precise objectives of introducing interventions.

African horse sickness is an equine orbivirus transmitted by Culicoides Latreille biting midges. In the last 80 years, it has caused several devastating outbreaks in the equine population in Europe, the Far and Middle East, North Africa, South-East Asia, and sub-Saharan Africa. The disease is endemic in South Africa; however, a unique control area has been set up in the Western Cape where increased surveillance and control measures have been put in place. A deterministic metapopulation model was developed to explore if an outbreak might occur, and how it might develop, if a latently infected horse was to be imported into the control area, by varying the geographical location and months of import. To do this, a previously published ordinary differential equation model was developed with a metapopulation approach and included a vaccinated horse population. Outbreak length, time to peak infection, number of infected horses at the peak, number of horses overall affected (recovered or dead), re-emergence, and Rv (the basic reproduction number in the presence of vaccination) were recorded and displayed using GIS mapping. The model predictions were compared to previous outbreak data to ensure validity. The warmer months (November to March) had longer outbreaks than the colder months (May to September), took more time to reach the peak, and had a greater total outbreak size with more horses infected at the peak. Rv appeared to be a poor predictor of outbreak dynamics for this simulation. A sensitivity analysis indicated that control measures such as vaccination and vector control are potentially effective to manage the spread of an outbreak, and shortening the vaccination window to July to September may reduce the risk of vaccine-associated outbreaks.

Quarantine has been long used as a public health response to emerging infectious diseases, particularly at the onset of an epidemic when the infected proportion of a population remains identifiable and logistically tractable. In theory, the same logic should apply to low-incidence infections; however, the application and impact of quarantine in low prevalence settings appears less common and lacks a formal analysis. Here, we present a quantitative framework using a series of progressively more biologically realistic models of canine rabies in domestic dogs and from dogs to humans, a suitable example system to characterize dynamical changes under varying levels of dog quarantine. We explicitly incorporate health-seeking behaviour data to inform the modelling of contact-tracing and exclusion of rabies suspect and probable dogs that can be identified through bite-histories of patients presenting at anti-rabies clinics. We find that a temporary quarantine of rabies suspect and probable dogs provides a powerful tool to curtail rabies transmission, especially in settings where optimal vaccination coverage is yet to be achieved, providing a critical stopgap to reduce the number of human and animal deaths due to rabid bites. We conclude that whilst comprehensive measures including sensitive surveillance and large-scale vaccination of dogs will be required to achieve disease elimination and sustained freedom given the persistent risk of rabies re-introductions, quarantine offers a low-cost community driven solution to intersectoral health burden.

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

The spread of infection amongst livestock depends not only on the traits of the pathogen and the livestock themselves, but also on the veterinary health behaviours of farmers and how this impacts their implementation of disease control measures. Controls that are costly may make it beneficial for individuals to rely on the protection offered by others, though that may be sub-optimal for the population. Failing to account for socio-behavioural properties may produce a substantial layer of bias in infectious disease models. We investigated the role of heterogeneity in vaccine response across a population of farmers on epidemic outbreaks amongst livestock, caused by pathogens with differential speed of spread over spatial landscapes of farms for two counties in England (Cumbria and Devon). Under different compositions of three vaccine behaviour groups (precautionary, reactionary, non-vaccination), we evaluated from population- and individual-level perspectives the optimum threshold distance to premises with notified infection that would trigger responsive vaccination by the reactionary vaccination group. We demonstrate a divergence between population and individual perspectives in the optimal scale of reactive voluntary vaccination response. In general, minimising the population-level perspective cost requires a broader reactive uptake of the intervention, whilst optimising the outcome for the average individual increased the likelihood of larger scale disease outbreaks. When the relative cost of vaccination was low and the majority of premises had undergone precautionary vaccination, then adopting a perspective that optimised the outcome for an individual gave a broader spatial extent of reactive response compared to a perspective wanting to optimise outcomes for everyone in the population. Under our assumed epidemiological context, the findings identify livestock disease intervention receptiveness and cost combinations where one would expect strong disagreement between the intervention stringency that is best from the perspective of a stakeholder responsible for supporting the livestock industry compared to a sole livestock owner. Were such discord anticipated and achieving a consensus view across perspectives desired, the findings may also inform those managing veterinary health policy the requisite reduction in intervention cost and/or the required extent of nurturing beneficial community attitudes towards interventions.

Rapid testing strategies that replace the isolation of close contacts through the use of lateral flow device tests (LFTs) have been suggested as a way of controlling SARS-CoV-2 transmission within schools that maintain low levels of pupil absences. We developed an individual-based model of a secondary school formed of exclusive year group bubbles (five year groups, with 200 pupils per year) to assess the likely impact of strategies using LFTs in secondary schools over the course of a seven-week half-term on transmission, absences, and testing volume, compared to a policy of isolating year group bubbles upon a pupil returning a positive polymerase chain reaction (PCR) test. We also considered the sensitivity of results to levels of participation in rapid testing and underlying model assumptions. While repeated testing of year group bubbles following case detection is less effective at reducing infections than a policy of isolating year group bubbles, strategies involving twice weekly mass testing can reduce infections to lower levels than would occur under year group isolation. By combining regular testing with serial contact testing or isolation, infection levels can be reduced further still. At high levels of pupil participation in lateral flow testing, strategies replacing the isolation of year group bubbles with testing substantially reduce absences, but require a high volume of testing. Our results highlight the conflict between the goals of minimising within-school transmission, minimising absences and minimising testing burden. While rapid testing strategies can reduce school transmission and absences, they may lead to a large number of daily tests.

As part of a concerted pandemic response to protect public health, businesses can enact non-pharmaceutical controls to minimise exposure to pathogens in workplaces and premises open to the public. Amendments to working practices can lead to the amount, duration and/or proximity of interactions being changed, ultimately altering the dynamics of disease spread. These modifications could be specific to the type of business being operated. We use a data-driven approach to parameterise an individual-based network model for transmission of SARS-CoV-2 amongst the working population, stratified into work sectors. The network is comprised of layered contacts to consider the risk of spread in multiple encounter settings (workplaces, households, social and other). We analyse several interventions targeted towards working practices: mandating a fraction of the population to work from home; using temporally asynchronous work patterns; and introducing measures to create 'COVID-secure' workplaces. We also assess the general role of adherence to (or effectiveness of) isolation and test and trace measures and demonstrate the impact of all these interventions across a variety of relevant metrics. The progress of the epidemic can be significantly hindered by instructing a significant proportion of the workforce to work from home. Furthermore, if required to be present at the workplace, asynchronous work patterns can help to reduce infections when compared with scenarios where all workers work on the same days, particularly for longer working weeks. When assessing COVID-secure workplace measures, we found that smaller work teams and a greater reduction in transmission risk reduced the probability of large, prolonged outbreaks. Finally, following isolation guidance and engaging with contact tracing without other measures is an effective tool to curb transmission, but is highly sensitive to adherence levels. In the absence of sufficient adherence to non-pharmaceutical interventions, our results indicate a high likelihood of SARS-CoV-2 spreading widely throughout a worker population. Given the heterogeneity of demographic attributes across worker roles, in addition to the individual nature of controls such as contact tracing, we demonstrate the utility of a network model approach to investigate workplace-targeted intervention strategies and the role of test, trace and isolation in tackling disease spread.

Stay-at-home orders and shutdowns of non-essential businesses are powerful, but socially costly, tools to control the pandemic spread of SARS-CoV-2. Mass testing strategies, which rely on widely administered frequent and rapid diagnostics to identify and isolate infected individuals, could be a potentially less disruptive management strategy, particularly where vaccine access is limited. In this paper, we assess the extent to which mass testing and isolation strategies can reduce reliance on socially costly non-pharmaceutical interventions, such as distancing and shutdowns. We develop a multi-compartmental model of SARS-CoV-2 transmission incorporating both preventative non-pharmaceutical interventions (NPIs) and testing and isolation to evaluate their combined effect on public health outcomes. Our model is designed to be a policy-guiding tool that captures important realities of the testing system, including constraints on test administration and non-random testing allocation. We show how strategic changes in the characteristics of the testing system, including test administration, test delays, and test sensitivity, can reduce reliance on preventative NPIs without compromising public health outcomes in the future. The lowest NPI levels are possible only when many tests are administered and test delays are short, given limited immunity in the population. Reducing reliance on NPIs is highly dependent on the ability of a testing program to identify and isolate unreported, asymptomatic infections. Changes in NPIs, including the intensity of lockdowns and stay at home orders, should be coordinated with increases in testing to ensure epidemic control; otherwise small additional lifting of these NPIs can lead to dramatic increases in infections, hospitalizations and deaths. Importantly, our results can be used to guide ramp-up of testing capacity in outbreak settings, allow for the flexible design of combined interventions based on social context, and inform future cost-benefit analyses to identify efficient pandemic management strategies.

Efforts to suppress transmission of SARS-CoV-2 in the UK have seen non-pharmaceutical interventions being invoked. The most severe measures to date include all restaurants, pubs and cafes being ordered to close on 20th March, followed by a "stay at home" order on the 23rd March and the closure of all non-essential retail outlets for an indefinite period. Government agencies are presently analysing how best to develop an exit strategy from these measures and to determine how the epidemic may progress once measures are lifted. Mathematical models are currently providing short and long term forecasts regarding the future course of the COVID-19 outbreak in the UK to support evidence-based policymaking. We present a deterministic, age-structured transmission model that uses real-time data on confirmed cases requiring hospital care and mortality to provide up-to-date predictions on epidemic spread in ten regions of the UK. The model captures a range of age-dependent heterogeneities, reduced transmission from asymptomatic infections and produces a good fit to the key epidemic features over time. We simulated a suite of scenarios to assess the impact of differing approaches to relaxing social distancing measures from 7th May 2020 on the estimated number of patients requiring inpatient and critical care treatment, and deaths. With regard to future epidemic outcomes, we investigated the impact of reducing compliance, ongoing shielding of elder age groups, reapplying stringent social distancing measures using region based triggers and the role of asymptomatic transmission. We find that significant relaxation of social distancing measures from 7th May onwards can lead to a rapid resurgence of COVID-19 disease and the health system being quickly overwhelmed by a sizeable, second epidemic wave. In all considered age-shielding based strategies, we projected serious demand on critical care resources during the course of the pandemic. The reintroduction and release of strict measures on a regional basis, based on ICU bed occupancy, results in a long epidemic tail, until the second half of 2021, but ensures that the health service is protected by reintroducing social distancing measures for all individuals in a region when required. Our work confirms the effectiveness of stringent non-pharmaceutical measures in March 2020 to suppress the epidemic. It also provides strong evidence to support the need for a cautious, measured approach to relaxation of lockdown measures, to protect the most vulnerable members of society and support the health service through subduing demand on hospital beds, in particular bed occupancy in intensive care units.

The COVID-19 outbreak has highlighted our vulnerability to novel infections. Faced with this threat and no effective treatment, in line with many other countries, the UK adopted enforced social distancing (lockdown) to reduce transmission-successfully reducing the reproductive number R below one. However, given the large pool of susceptible individuals that remain, complete relaxation of controls is likely to generate a substantial further outbreak. Vaccination remains the only foreseeable means of both containing the infection and returning to normal interactions and behaviour. Here, we consider the optimal targeting of vaccination within the UK, with the aim of minimising future deaths or quality adjusted life year (QALY) losses. We show that, for a range of assumptions on the action and efficacy of the vaccine, targeting older age groups first is optimal and may be sufficient to stem the epidemic if the vaccine prevents transmission as well as disease.

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

Early warning signals (EWS) identify systems approaching a critical transition, where the system undergoes a sudden change in state. For example, monitoring changes in variance or autocorrelation offers a computationally inexpensive method which can be used in real-time to assess when an infectious disease transitions to elimination. EWS have a promising potential to not only be used to monitor infectious diseases, but also to inform control policies to aid disease elimination. Previously, potential EWS have been identified for prevalence data, however the prevalence of a disease is often not known directly. In this work we identify EWS for incidence data, the standard data type collected by the Centers for Disease Control and Prevention (CDC) or World Health Organization (WHO). We show, through several examples, that EWS calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data. In particular, the variance displays a decreasing trend on the approach to disease elimination, contrary to that expected from critical slowing down theory; this could lead to unreliable indicators of elimination when calculated on real-world data. We derive analytical predictions which can be generalised for many epidemiological systems, and we support our theory with simulated studies of disease incidence. Additionally, we explore EWS calculated on the rate of incidence over time, a property which can be extracted directly from incidence data. We find that although incidence might not exhibit typical critical slowing down properties before a critical transition, the rate of incidence does, presenting a promising new data type for the application of statistical indicators.

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.

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.

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.

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.

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.

The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital for modelers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, the necessary demographic data are only available at an aggregate scale. We investigated the ability of models of livestock infectious diseases to predict epidemic spread and obtain optimal control policies in the event of imperfect, aggregated data. Taking a geographic information approach, we used land cover data to predict UK farm locations and investigated the influence of using these synthetic location data sets upon epidemiological predictions in the event of an outbreak of foot-and-mouth disease. When broadly classified land cover data were used to create synthetic farm locations, model predictions deviated significantly from those simulated on true data. However, when more resolved subclass land use data were used, moderate to highly accurate predictions of epidemic size, duration and optimal vaccination and ring culling strategies were obtained. This suggests that a geographic information approach may be useful where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock.