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

When should lockdown be implemented? Devising cost-effective strategies for managing epidemics amid vaccine uncertainty

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.

Misapplied management makes matters worse: Spatially explicit control leverages biotic interactions to slow invasion

A wide range of approaches has been used to manage the spread of invasive species, yet invaders continue to be a challenge to control. In some cases, management actions have no effect or may even inadvertently benefit the targeted invader. Here, we use the mid-20th century management of the Red Imported Fire Ant, Solenopsis invicta, in the US as a motivating case study to explore the conditions under which such wasted management effort may occur. Introduced in approximately 1940, the fire ant spread widely through the southeast US and became a problematic pest. Historically, fire ants were managed with broad-spectrum pesticides; unfortunately, these efforts were largely unsuccessful. One hypothesis suggests that, by also killing native ants, mass pesticide application reduced competitive burdens thereby enabling fire ants to invade more quickly than they would in the absence of management. We use a mechanistic competition model to demonstrate the landscape-level effects of such management. We explicitly model the extent and location of pesticide applications, showing that the same pesticide application can have a positive, neutral, or negative effect on the progress of an invasion, depending on where it is applied on the landscape with respect to the invasion front. When designing management, the target species is often considered alone; however, this work suggests that leveraging existing biotic interactions, specifically competition with native species, can increase the efficacy of management. Our model not only highlights the potential unintended consequences of ignoring biotic interactions, but also provides a framework for developing spatially explicit management strategies that take advantage of these biotic interactions to work smarter, not harder.

Scenario design for infectious disease projections: Integrating concepts from decision analysis and experimental design

Across many fields, scenario modeling has become an important tool for exploring long-term projections and how they might depend on potential interventions and critical uncertainties, with relevance to both decision makers and scientists. In the past decade, and especially during the COVID-19 pandemic, the field of epidemiology has seen substantial growth in the use of scenario projections. Multiple scenarios are often projected at the same time, allowing important comparisons that can guide the choice of intervention, the prioritization of research topics, or public communication. The design of the scenarios is central to their ability to inform important questions. In this paper, we draw on the fields of decision analysis and statistical design of experiments to propose a framework for scenario design in epidemiology, with relevance also to other fields. We identify six different fundamental purposes for scenario designs (decision making, sensitivity analysis, situational awareness, horizon scanning, forecasting, and value of information) and discuss how those purposes guide the structure of scenarios. We discuss other aspects of the content and process of scenario design, broadly for all settings and specifically for multi-model ensemble projections. As an illustrative case study, we examine the first 17 rounds of scenarios from the U.S. COVID-19 Scenario Modeling Hub, then reflect on future advancements that could improve the design of scenarios in epidemiological settings.

When do we need multiple infectious disease models? Agreement between projection rank and magnitude in a multi-model setting

Mathematical models are useful for public health planning and response to infectious disease threats. However, different models can provide differing results, which can hamper decision making if not synthesized appropriately. To address this challenge, multi-model hubs convene independent modeling groups to generate ensembles, known to provide more accurate predictions of future outcomes. Yet, these hubs are resource intensive, and how many models are sufficient in a hub is not known. Here, we compare the benefit of predictions from multiple models in different contexts: (1) decision settings that depend on predictions of quantitative outcomes (e.g., hospital capacity planning), where assessments of the benefits of multi-model ensembles have largely focused; and (2) decisions settings that require the ranking of alternative epidemic scenarios (e.g., comparing outcomes under multiple possible interventions and biological uncertainties). We develop a mathematical framework to mimic a multi-model prediction setting, and use this framework to quantify how frequently predictions from different models agree. We further explore multi-model agreement using real-world, empirical data from 14 rounds of U.S. COVID-19 Scenario Modeling Hub projections. Our results suggest that the value of multiple models could be different in different decision contexts, and if only a few models are available, focusing on the rank of alternative epidemic scenarios could be more robust than focusing on quantitative outcomes. Although additional exploration of the sufficient number of models for different contexts is still needed, our results indicate that it may be possible to identify decision contexts where it is robust to rely on fewer models, a finding that can inform the use of modeling resources during future public health crises.

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.

Scenario Design for Infectious Disease Projections: Integrating Concepts from Decision Analysis and Experimental Design

Across many fields, scenario modeling has become an important tool for exploring long-term projections and how they might depend on potential interventions and critical uncertainties, with relevance to both decision makers and scientists. In the past decade, and especially during the COVID-19 pandemic, the field of epidemiology has seen substantial growth in the use of scenario projections. Multiple scenarios are often projected at the same time, allowing important comparisons that can guide the choice of intervention, the prioritization of research topics, or public communication. The design of the scenarios is central to their ability to inform important questions. In this paper, we draw on the fields of decision analysis and statistical design of experiments to propose a framework for scenario design in epidemiology, with relevance also to other fields. We identify six different fundamental purposes for scenario designs (decision making, sensitivity analysis, value of information, situational awareness, horizon scanning, and forecasting) and discuss how those purposes guide the structure of scenarios. We discuss other aspects of the content and process of scenario design, broadly for all settings and specifically for multi-model ensemble projections. As an illustrative case study, we examine the first 17 rounds of scenarios from the U.S. COVID-19 Scenario Modeling Hub, then reflect on future advancements that could improve the design of scenarios in epidemiological settings.

Understanding the impact of disease and vaccine mechanisms on the importance of optimal vaccine allocation

Vaccination is an important epidemic intervention strategy. However, it is generally unclear how the outcomes of different vaccine strategies change depending on population characteristics, vaccine mechanisms and allocation objective. In this paper we develop a conceptual mathematical model to simulate strategies for pre-epidemic vaccination. We extend the SEIR model to incorporate a range of vaccine mechanisms and disease characteristics. We then compare the outcomes of optimal and suboptimal vaccination strategies for three public health objectives (total infections, total symptomatic infections and total deaths) using numerical optimisation. Our comparison shows that the difference in outcomes between vaccinating optimally and suboptimally depends on vaccine mechanisms, disease characteristics, and objective considered. Our modelling finds vaccines that impact transmission produce better outcomes as transmission is reduced for all strategies. For vaccines that impact the likelihood of symptomatic disease or dying due to infection, the improvement in outcome as we decrease these variables is dependent on the strategy implemented. Through a principled model-based process, this work highlights the importance of designing effective vaccine allocation strategies. We conclude that efficient allocation of resources can be just as crucial to the success of a vaccination strategy as the vaccine effectiveness and/or amount of vaccines available.

An exploration of within-herd dynamics of a transboundary livestock disease: A foot and mouth disease case study

Transboundary livestock diseases are a high priority for policy makers because of the serious economic burdens associated with infection. In order to make well informed preparedness and response plans, policy makers often utilize mathematical models to understand possible outcomes of different control strategies and outbreak scenarios. Many of these models focus on the transmission between herds and the overall trajectory of the outbreak. While the course of infection within herds has not been the focus of the majority of models, a thorough understanding of within-herd dynamics can provide valuable insight into a disease system by providing information on herd-level biological properties of the infection, which can be used to inform decision making in both endemic and outbreak settings and to inform larger between-herd models. In this study, we develop three stochastic simulation models to study within-herd foot and mouth disease dynamics and the implications of different empirical data-based assumptions about the timing of the onset of infectiousness and clinical signs. We also study the influence of herd size and the proportion of the herd that is initially infected on the outcome of the infection. We find that increasing herd size increases the duration of infectiousness and that the size of the herd plays a more significant role in determining this duration than the number of initially infected cattle in that herd. We also find that the assumptions made regarding the onset of infectiousness and clinical signs, which are based on contradictory empirical findings, can result in the predictions about when infection would be detectable differing by several days. Therefore, the disease progression used to characterize the course of infection in a single bovine host could have significant implications for determining when herds can be detected and subsequently controlled; the timing of which could influence the overall predicted trajectory of outbreaks.

Optimal reduced-mixing for an SIS infectious-disease model

Which reduced-mixing strategy maximizes economic output during a disease outbreak? To answer this question, we formulate an optimal-control problem that maximizes the difference between revenue, due to healthy individuals, and medical costs, associated with infective individuals, for SIS disease dynamics. The control variable is the level of mixing in the population, which influences both revenue and the spread of the disease. Using Pontryagin's maximum principle, we find a closed-form solution for our problem. We explore an example of our problem with parameters for the transmission of Staphylococcus aureus in dairy cows, and we perform sensitivity analyses to determine how model parameters affect optimal strategies. We find that less mixing is preferable when the transmission rate is high, the per-capita recovery rate is low, or when the revenue parameter is much smaller than the cost parameter.

Mechanistic models of Rift Valley fever virus transmission: A systematic review

Rift Valley fever (RVF) is a zoonotic arbovirosis which has been reported across Africa including the northernmost edge, South West Indian Ocean islands, and the Arabian Peninsula. The virus is responsible for high abortion rates and mortality in young ruminants, with economic impacts in affected countries. To date, RVF epidemiological mechanisms are not fully understood, due to the multiplicity of implicated vertebrate hosts, vectors, and ecosystems. In this context, mathematical models are useful tools to develop our understanding of complex systems, and mechanistic models are particularly suited to data-scarce settings. Here, we performed a systematic review of mechanistic models studying RVF, to explore their diversity and their contribution to the understanding of this disease epidemiology. Researching Pubmed and Scopus databases (October 2021), we eventually selected 48 papers, presenting overall 49 different models with numerical application to RVF. We categorized models as theoretical, applied, or grey, depending on whether they represented a specific geographical context or not, and whether they relied on an extensive use of data. We discussed their contributions to the understanding of RVF epidemiology, and highlighted that theoretical and applied models are used differently yet meet common objectives. Through the examination of model features, we identified research questions left unexplored across scales, such as the role of animal mobility, as well as the relative contributions of host and vector species to transmission. Importantly, we noted a substantial lack of justification when choosing a functional form for the force of infection. Overall, we showed a great diversity in RVF models, leading to important progress in our comprehension of epidemiological mechanisms. To go further, data gaps must be filled, and modelers need to improve their code accessibility.

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.

Vote-processing rules for combining control recommendations from multiple models

Mathematical modelling is used during disease outbreaks to compare control interventions. Using multiple models, the best method to combine model recommendations is unclear. Existing methods weight model projections, then rank control interventions using the combined projections, presuming model outputs are directly comparable. However, the way each model represents the epidemiological system will vary. We apply electoral vote-processing rules to combine model-generated rankings of interventions. Combining rankings of interventions, instead of combining model projections, avoids assuming that projections are comparable as all comparisons of projections are made within each model. We investigate four rules: First-past-the-post, Alternative Vote (AV), Coombs Method and Borda Count. We investigate rule sensitivity by including models that favour only one action or including those that rank interventions randomly. We investigate two case studies: the 2014 Ebola outbreak in West Africa (37 compartmental models) and a hypothetical foot-and-mouth disease outbreak in UK (four individual-based models). The Coombs Method was least susceptible to adding models that favoured a single action, Borda Count and AV were most susceptible to adding models that ranked interventions randomly. Each rule chose the same intervention as when ranking interventions by mean projections, suggesting that combining rankings provides similar recommendations with fewer assumptions about model comparability. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Optimizing management of invasions in an uncertain world using dynamic spatial models

Dispersal drives invasion dynamics of nonnative species and pathogens. Applying knowledge of dispersal to optimize the management of invasions can mean the difference between a failed and a successful control program and dramatically improve the return on investment of control efforts. A common approach to identifying optimal management solutions for invasions is to optimize dynamic spatial models that incorporate dispersal. Optimizing these spatial models can be very challenging because the interaction of time, space, and uncertainty rapidly amplifies the number of dimensions being considered. Addressing such problems requires advances in and the integration of techniques from multiple fields, including ecology, decision analysis, bioeconomics, natural resource management, and optimization. By synthesizing recent advances from these diverse fields, we provide a workflow for applying ecological theory to advance optimal management science and highlight priorities for optimizing the control of invasions. One of the striking gaps we identify is the extremely limited consideration of dispersal uncertainty in optimal management frameworks, even though dispersal estimates are highly uncertain and greatly influence invasion outcomes. In addition, optimization frameworks rarely consider multiple types of uncertainty (we describe five major types) and their interrelationships. Thus, feedbacks from management or other sources that could magnify uncertainty in dispersal are rarely considered. Incorporating uncertainty is crucial for improving transparency in decision risks and identifying optimal management strategies. We discuss gaps and solutions to the challenges of optimization using dynamic spatial models to increase the practical application of these important tools and improve the consistency and robustness of management recommendations for invasions.

The African swine fever modelling challenge: Model comparison and lessons learnt

Robust epidemiological knowledge and predictive modelling tools are needed to address challenging objectives, such as: understanding epidemic drivers; forecasting epidemics; and prioritising control measures. Often, multiple modelling approaches can be used during an epidemic to support effective decision making in a timely manner. Modelling challenges contribute to understanding the pros and cons of different approaches and to fostering technical dialogue between modellers. In this paper, we present the results of the first modelling challenge in animal health - the ASF Challenge - which focused on a synthetic epidemic of African swine fever (ASF) on an island. The modelling approaches proposed by five independent international teams were compared. We assessed their ability to predict temporal and spatial epidemic expansion at the interface between domestic pigs and wild boar, and to prioritise a limited number of alternative interventions. We also compared their qualitative and quantitative spatio-temporal predictions over the first two one-month projection phases of the challenge. Top-performing models in predicting the ASF epidemic differed according to the challenge phase, host species, and in predicting spatial or temporal dynamics. Ensemble models built using all team-predictions outperformed any individual model in at least one phase. The ASF Challenge demonstrated that accounting for the interface between livestock and wildlife is key to increasing our effectiveness in controlling emerging animal diseases, and contributed to improving the readiness of the scientific community to face future ASF epidemics. Finally, we discuss the lessons learnt from model comparison to guide decision making.

Optimal health and economic impact of non-pharmaceutical intervention measures prior and post vaccination in England: a mathematical modelling study

Background. Even with good progress on vaccination, SARS-CoV-2 infections in the UK may continue to impose a high burden of disease and therefore pose substantial challenges for health policy decision makers. Stringent government-mandated physical distancing measures (lockdown) have been demonstrated to be epidemiologically effective, but can have both positive and negative economic consequences. The duration and frequency of any intervention policy could, in theory, be optimized to maximize economic benefits while achieving substantial reductions in disease. Methods. Here, we use a pre-existing SARS-CoV-2 transmission model to assess the health and economic implications of different strengths of control through time in order to identify optimal approaches to non-pharmaceutical intervention stringency in the UK, considering the role of vaccination in reducing the need for future physical distancing measures. The model is calibrated to the COVID-19 epidemic in England and we carry out retrospective analysis of the optimal timing of precautionary breaks in 2020 and the optimal relaxation policy from the January 2021 lockdown, considering the willingness to pay (WTP) for health improvement. Results. We find that the precise timing and intensity of interventions is highly dependent upon the objective of control. As intervention measures are relaxed, we predict a resurgence in cases, but the optimal intervention policy can be established dependent upon the WTP per quality adjusted life year loss avoided. Our results show that establishing an optimal level of control can result in a reduction in net monetary loss of billions of pounds, dependent upon the precise WTP value. Conclusion. It is vital, as the UK emerges from lockdown, but continues to face an on-going pandemic, to accurately establish the overall health and economic costs when making policy decisions. We demonstrate how some of these can be quantified, employing mechanistic infectious disease transmission models to establish optimal levels of control for the ongoing COVID-19 pandemic.

The African swine fever modelling challenge: Objectives, model description and synthetic data generation

African swine fever (ASF) is an emerging disease currently spreading at the interface between wild boar and pig farms in Europe and Asia. Current disease control regulations, which involve massive culling with significant economic and animal welfare costs, need to be improved. Modelling enables relevant control measures to be explored, but conducting the exercise during an epidemic is extremely difficult. Modelling challenges enhance modellers' ability to timely advice policy makers, improve their readiness when facing emerging threats, and promote international collaborations. The ASF-Challenge, which ran between August 2020 and January 2021, was the first modelling challenge in animal health. In this paper, we describe the objectives and rules of the challenge. We then demonstrate the mechanistic multi-host model that was used to mimic as accurately as possible an ASF-like epidemic, provide a detailed explanation of the surveillance and intervention strategies that generated the synthetic data, and describe the different management strategies that were assessed by the competing modelling teams. We then outline the different technical steps of the challenge as well as its environment. Finally, we synthesize the lessons we learnt along the way to guide future modelling challenges in animal health.

Modelling livestock infectious disease control policy under differing social perspectives on vaccination behaviour

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.

The COVID-19 pandemic has shown how crucial human behaviour is in controlling the spread of an infectious disease. The same is true of livestock, where farmer behaviour is critical to reduce the spread of an infection to enhance animal welfare and reduce economic losses. An ongoing concern for livestock owners is therefore ensuring they have adequate disease management procedures. However, what an individual farmer considers an appropriate way to control an infection in their own livestock may not be the best way to prevent an infection for every farmer’s livestock in the population. We describe a mathematical model combining epidemiological and behavioural elements to study the tension between individual and population-level control of livestock diseases. Applied to representative livestock systems in two counties in England (Cumbria and Devon), and splitting farmers into three types of vaccine behaviour groups (precautionary, reactionary, non-vaccination), we show what individual farmers see as an effective way to reduce infection is not the same as would benefit every farmer. The preferred response to protect every farmer’s livestock is to encourage wider uptake of reactive vaccination, whereas optimising the spatial extent of reactive vaccination for the average individual increases the chance of larger disease outbreaks.

Economic evaluation of disease elimination: An extension to the net-benefit framework and application to human African trypanosomiasis

The global health community has earmarked a number of diseases for elimination or eradication, and these goals have often been praised on the premise of long-run cost savings. However, decision makers must contend with a multitude of demands on health budgets in the short or medium term, and costs per case often rise as the burden of a disease falls, rendering such efforts beyond the cost-effective use of scarce resources. In addition, these decisions must be made in the presence of substantial uncertainty regarding the feasibility and costs of elimination or eradication efforts. Therefore, analytical frameworks are necessary to consider the additional effort for reaching global goals, like elimination or eradication, that are beyond the cost-effective use of country resources. We propose a modification to the net-benefit framework to consider the implications of switching from an optimal strategy, in terms of cost-per-burden averted, to a strategy with a higher likelihood of meeting the global target of elimination or eradication. We illustrate the properties of our framework by considering the economic case of efforts to eliminate the transmission of gambiense human African trypanosomiasis (gHAT), a vector-borne, parasitic disease in West and Central Africa, by 2030.

Governance structure affects transboundary disease management under alternative objectives

Background

The development of public health policy is inextricably linked with governance structure. In our increasingly globalized world, human migration and infectious diseases often span multiple administrative jurisdictions that might have different systems of government and divergent management objectives. However, few studies have considered how the allocation of regulatory authority among jurisdictions can affect disease management outcomes.

Methods

Here we evaluate the relative merits of decentralized and centralized management by developing and numerically analyzing a two-jurisdiction SIRS model that explicitly incorporates migration. In our model, managers choose between vaccination, isolation, medication, border closure, and a travel ban on infected individuals while aiming to minimize either the number of cases or the number of deaths.

Results

We consider a variety of scenarios and show how optimal strategies differ for decentralized and centralized management levels. We demonstrate that policies formed in the best interest of individual jurisdictions may not achieve global objectives, and identify situations where locally applied interventions can lead to an overall increase in the numbers of cases and deaths.

Conclusions

Our approach underscores the importance of tailoring disease management plans to existing regulatory structures as part of an evidence-based decision framework. Most importantly, we demonstrate that there needs to be a greater consideration of the degree to which governance structure impacts disease outcomes.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12889-021-11797-3).

Synergistic interventions to control COVID-19: Mass testing and isolation mitigates reliance on distancing

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.

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions.

A Simulation Study of the Use of Vaccination to Control Foot-and-Mouth Disease Outbreaks Across Australia

This study examines the potential for foot-and-mouth disease (FMD) control strategies that incorporate vaccination to manage FMD spread for a range of incursion scenarios across Australia. Stakeholder consultation was used to formulate control strategies and incursion scenarios to ensure relevance to the diverse range of Australian livestock production regions and management systems. The Australian Animal Disease Spread model (AADIS) was used to compare nine control strategies for 13 incursion scenarios, including seven control strategies incorporating vaccination. The control strategies with vaccination differed in terms of their approaches for targeting areas and species. These strategies are compared with two benchmark strategies based on stamping out only. Outbreak size and duration were compared in terms of the total number of infected premises, the duration of the control stage of an FMD outbreak, and the number of vaccinated animals. The three key findings from this analysis are as follows: (1) smaller outbreaks can be effectively managed by stamping out without vaccination, (2) the size and duration of larger outbreaks can be significantly reduced when vaccination is used, and (3) different vaccination strategies produced similar reductions in the size and duration of an outbreak, but the number of animals vaccinated varied. Under current international standards for regaining FMD-free status, vaccinated animals need to be removed from the population at the end of the outbreak to minimize trade impacts. We have shown that selective, targeted vaccination strategies could achieve effective FMD control while significantly reducing the number of animals vaccinated.

Weighing the unknowns: Value of Information for biological and operational uncertainty in invasion management

The management of biological invasions is a worldwide conservation priority. Unfortunately, decision-making on optimal invasion management can be impeded by lack of information about the biological processes that determine invader success (i.e. biological uncertainty) or by uncertainty about the effectiveness of candidate interventions (i.e. operational uncertainty). Concurrent assessment of both sources of uncertainty within the same framework can help to optimize control decisions.Here, we present a Value of Information (VoI) framework to simultaneously analyse the effects of biological and operational uncertainties on management outcomes. We demonstrate this approach with a case study: minimizing the long-term population growth of musk thistle Carduus nutans, a widespread invasive plant, using several insects as biological control agents, including Trichosirocalus horridus, Rhinocyllus conicus and Urophora solstitialis.The ranking of biocontrol agents was sensitive to differences in the target weed's demography and also to differences in the effectiveness of the different biocontrol agents. This finding suggests that accounting for both biological and operational uncertainties is valuable when making management recommendations for invasion control. Furthermore, our VoI analyses show that reduction of all uncertainties across all combinations of demographic model and biocontrol effectiveness explored in the current study would lead, on average, to a 15.6% reduction in musk thistle population growth rate. The specific growth reduction that would be observed in any instance would depend on how the uncertainties actually resolve. Resolving biological uncertainty (across demographic model combinations) or operational uncertainty (across biocontrol effectiveness combinations) alone would reduce expected population growth rate by 8.5% and 10.5% respectively.Synthesis and applications. Our study demonstrates that intervention rank is determined both by biological processes in the targeted invasive populations and by intervention effectiveness. Ignoring either biological uncertainty or operational uncertainty may result in a suboptimal recommendation. Therefore, it is important to simultaneously acknowledge both sources of uncertainty during the decision-making process in invasion management. The framework presented here can accommodate diverse data sources and modelling approaches, and has wide applicability to guide invasive species management and conservation efforts.

Strategic testing approaches for targeted disease monitoring can be used to inform pandemic decision-making

More than 1.6 million Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) tests were administered daily in the United States at the peak of the epidemic, with a significant focus on individual treatment. Here, we show that objective-driven, strategic sampling designs and analyses can maximize information gain at the population level, which is necessary to increase situational awareness and predict, prepare for, and respond to a pandemic, while also continuing to inform individual treatment. By focusing on specific objectives such as individual treatment or disease prediction and control (e.g., via the collection of population-level statistics to inform lockdown measures or vaccine rollout) and drawing from the literature on capture-recapture methods to deal with nonrandom sampling and testing errors, we illustrate how public health objectives can be achieved even with limited test availability when testing programs are designed a priori to meet those objectives.

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.

Active responses to outbreaks of infectious wildlife diseases: objectives, strategies and constraints determine feasibility and success

Emerging wildlife diseases are taking a heavy toll on animal and plant species worldwide. Mitigation, particularly in the initial epidemic phase, is hindered by uncertainty about the epidemiology and management of emerging diseases, but also by vague or poorly defined objectives. Here, we use a quantitative analysis to assess how the decision context of mitigation objectives, available strategies and practical constraints influences the decision of whether and how to respond to epidemics in wildlife. To illustrate our approach, we parametrized the model for European fire salamanders affected by Batrachochytrium salamandrivorans, and explored different combinations of conservation, containment and budgetary objectives. We found that in approximately half of those scenarios, host removal strategies perform equal to or worse than no management at all during a local outbreak, particularly where removal cannot exclusively target infected individuals. Moreover, the window for intervention shrinks rapidly if an outbreak is detected late or if a response is delayed. Clearly defining the decision context is, therefore, vital to plan meaningful responses to novel outbreaks. Explicitly stating objectives, strategies and constraints, if possible before an outbreak occurs, avoids wasting precious resources and creating false expectations about what can and cannot be achieved during the epidemic phase.

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.

COVID-19 reopening strategies at the county level in the face of uncertainty: Multiple Models for Outbreak Decision Support

Policymakers make decisions about COVID-19 management in the face of considerable uncertainty. We convened multiple modeling teams to evaluate reopening strategies for a mid-sized county in the United States, in a novel process designed to fully express scientific uncertainty while reducing linguistic uncertainty and cognitive biases. For the scenarios considered, the consensus from 17 distinct models was that a second outbreak will occur within 6 months of reopening, unless schools and non-essential workplaces remain closed. Up to half the population could be infected with full workplace reopening; non-essential business closures reduced median cumulative infections by 82%. Intermediate reopening interventions identified no win-win situations; there was a trade-off between public health outcomes and duration of workplace closures. Aggregate results captured twice the uncertainty of individual models, providing a more complete expression of risk for decision-making purposes.

Influencing public health policy with data-informed mathematical models of infectious diseases: Recent developments and new challenges

Modern data and computational resources, coupled with algorithmic and theoretical advances to exploit these, allow disease dynamic models to be parameterised with increasing detail and accuracy. While this enhances models' usefulness in prediction and policy, major challenges remain. In particular, lack of identifiability of a model's parameters may limit the usefulness of the model. While lack of parameter identifiability may be resolved through incorporation into an inference procedure of prior knowledge, formulating such knowledge is often difficult. Furthermore, there are practical challenges associated with acquiring data of sufficient quantity and quality. Here, we discuss recent progress on these issues.

Applying optimal control theory to a spatial simulation model of sudden oak death: ongoing surveillance protects tanoak while conserving biodiversity

Sudden oak death has devastated tree populations across California. However, management might still slow disease spread at local scales. We demonstrate how to unambiguously characterize effective, local management strategies using a detailed, spatially explicit simulation model of spread in a single forest stand. This pre-existing, parameterized simulation is approximated here by a carefully calibrated, non-spatial model, explicitly constructed to be sufficiently simple to allow optimal control theory (OCT) to be applied. By lifting management strategies from the approximate model to the detailed simulation, effective time-dependent controls can be identified. These protect tanoak-a culturally and ecologically important species-while conserving forest biodiversity within a limited budget. We also consider model predictive control, in which both the approximating model and optimal control are repeatedly updated as the epidemic progresses. This allows management which is robust to both parameter uncertainty and systematic differences between simulation and approximate models. Including the costs of disease surveillance then introduces an optimal intensity of surveillance. Our study demonstrates that successful control of sudden oak death is likely to rely on adaptive strategies updated via ongoing surveillance. More broadly, it illustrates how OCT can inform effective real-world management, even when underpinning disease spread models are highly complex.

Identification and characterization of linear B cell epitopes on the nucleocapsid protein of porcine epidemic diarrhea virus using monoclonal antibodies

The nucleocapsid (N) protein of porcine epidemic diarrhea virus (PEDV), the most important pathogen causing severe diarrhea in piglets, is a highly conserved structural protein. In this study, 5 monoclonal antibodies (McAbs) against the PEDV N-protein were prepared and identified. Three new epitopes, ⁵⁶QIRWRMRRGERI⁶⁷, ³¹⁸GYAQIASLAPNVAALLFGGNVA VRE³⁴² and ³⁹⁸HEEAIYDDV⁴⁰⁶, were firstly identified in the viral N-protein, by using McAbs 3F10, 6A11, and 1C9. The epitope ³⁹⁸HEEAIYDDV⁴⁰⁶ was deleted in SH strain (isolated by our lab) and different between CV777 and YZ strain (isolated by our lab). To study the characters of this epitope, four peptides were synthesized according to the sequence of SH and CV777 and used in the study. The result showed that the 398^th amino acid maybe an important amino acid of the epitope. Biological information analysis showed that the three B cell linear epitopes are highly conserved among different PEDV isolates. In addition, McAb 1C9, which attached to the epitope ³⁹⁸HEEAIYDDV⁴⁰⁶, showed variant reactivity with PEDV CV777, SH, YZ and MS strains. McAb 1C9 reacted with PEDV strains CV777 and YZ, but not with SH which had a deletion from 399 to 410 amino acids in N-protein (No. MK841494). Among the three McAbs, 6A11, 3F10 and 1C9, only 6A11 reacted with porcine transmissible gastroenteritis virus (TGEV) in immunofluorescence assay, therefore the other two could be used to distinguish TGEV and PEDV. These mAbs and their defined epitopes may provide useful tool for the study of the PEDV N-protein structure and function, and facilitate the development of diagnostic methods for PEDV.

Cross-Validation of Generic Risk Assessment Tools for Animal Disease Incursion Based on a Case Study for African Swine Fever

In recent years, several generic risk assessment (RA) tools have been developed that can be applied to assess the incursion risk of multiple infectious animal diseases allowing for a rapid response to a variety of newly emerging or re-emerging diseases. Although these tools were originally developed for different purposes, they can be used to answer similar or even identical risk questions. To explore the opportunities for cross-validation, seven generic RA tools were used to assess the incursion risk of African swine fever (ASF) to the Netherlands and Finland for the 2017 situation and for two hypothetical scenarios in which ASF cases were reported in wild boar and/or domestic pigs in Germany. The generic tools ranged from qualitative risk assessment tools to stochastic spatial risk models but were all parameterized using the same global databases for disease occurrence and trade in live animals and animal products. A comparison of absolute results was not possible, because output parameters represented different endpoints, varied from qualitative probability levels to quantitative numbers, and were expressed in different units. Therefore, relative risks across countries and scenarios were calculated for each tool, for the three pathways most in common (trade in live animals, trade in animal products, and wild boar movements) and compared. For the 2017 situation, all tools evaluated the risk to the Netherlands to be higher than Finland for the live animal trade pathway, the risk to Finland the same or higher as the Netherlands for the wild boar pathway, while the tools were inconclusive on the animal products pathway. All tools agreed that the hypothetical presence of ASF in Germany increased the risk to the Netherlands, but not to Finland. The ultimate aim of generic RA tools is to provide risk-based evidence to support risk managers in making informed decisions to mitigate the incursion risk of infectious animal diseases. The case study illustrated that conclusions on the ASF risk were similar across the generic RA tools, despite differences observed in calculated risks. Hence, it was concluded that the cross-validation contributed to the credibility of their results.

Systematic selection between age and household structure for models aimed at emerging epidemic predictions

Numerous epidemic models have been developed to capture aspects of human contact patterns, making model selection challenging when they fit (often-scarce) early epidemic data equally well but differ in predictions. Here we consider the invasion of a novel directly transmissible infection and perform an extensive, systematic and transparent comparison of models with explicit age and/or household structure, to determine the accuracy loss in predictions in the absence of interventions when ignoring either or both social components. We conclude that, with heterogeneous and assortative contact patterns relevant to respiratory infections, the model’s age stratification is crucial for accurate predictions. Conversely, the household structure is only needed if transmission is highly concentrated in households, as suggested by an empirical but robust rule of thumb based on household secondary attack rate. This work serves as a template to guide the simplicity/accuracy trade-off in designing models aimed at initial, rapid assessment of potential epidemic severity.

Models of emerging epidemics can be exceedingly helpful in planning the response, but early on model selection is a difficult task. Here, the authors explore the joint contribution of age stratification and household structure on epidemic spread, and provides a rule of thumb to guide model choice.

Infectious disease pandemic planning and response: Incorporating decision analysis

Freya Shearer and co-authors discuss the use of decision analysis in planning for infectious disease pandemics.

Effects of regional differences and demography in modelling foot-and-mouth disease in cattle at the national scale

Foot-and-mouth disease (FMD) is a fast-spreading viral infection that can produce large and costly outbreaks in livestock populations. Transmission occurs at multiple spatial scales, as can the actions used to control outbreaks. The US cattle industry is spatially expansive, with heterogeneous distributions of animals and infrastructure. We have developed a model that incorporates the effects of scale for both disease transmission and control actions, applied here in simulating FMD outbreaks in US cattle. We simulated infection initiating in each of the 3049 counties in the contiguous US, 100 times per county. When initial infection was located in specific regions, large outbreaks were more likely to occur, driven by infrastructure and other demographic attributes such as premises clustering and number of cattle on premises. Sensitivity analyses suggest these attributes had more impact on outbreak metrics than the ranges of estimated disease parameter values. Additionally, although shipping accounted for a small percentage of overall transmission, areas receiving the most animal shipments tended to have other attributes that increase the probability of large outbreaks. The importance of including spatial and demographic heterogeneity in modelling outbreak trajectories and control actions is illustrated by specific regions consistently producing larger outbreaks than others.

Epidemic growth rates and host movement patterns shape management performance for pathogen spillover at the wildlife-livestock interface

Managing pathogen spillover at the wildlife-livestock interface is a key step towards improving global animal health, food security and wildlife conservation. However, predicting the effectiveness of management actions across host-pathogen systems with different life histories is an on-going challenge since data on intervention effectiveness are expensive to collect and results are system-specific. We developed a simulation model to explore how the efficacies of different management strategies vary according to host movement patterns and epidemic growth rates. The model suggested that fast-growing, fast-moving epidemics like avian influenza were best-managed with actions like biosecurity or containment, which limited and localized overall spillover risk. For fast-growing, slower-moving diseases like foot-and-mouth disease, depopulation or prophylactic vaccination were competitive management options. Many actions performed competitively when epidemics grew slowly and host movements were limited, and how management efficacy related to epidemic growth rate or host movement propensity depended on what objective was used to evaluate management performance. This framework offers one means of classifying and prioritizing responses to novel pathogen spillover threats, and evaluating current management actions for pathogens emerging at the wildlife-livestock interface. This article is part of the theme issue 'Dynamic and integrative approaches to understanding pathogen spillover'.

Optimal control of epidemic size and duration with limited resources

The total number of infections (epidemic size) and the time needed for the infection to go extinct (epidemic duration) represent two of the main indicators for the severity of infectious disease epidemics in human and livestock. However, few attempts have been made to address the problem of minimizing at the same time the epidemic size and duration from a theoretical point of view by using optimal control theory. Here, we investigate the multi-objective optimal control problem aiming to minimize, through either vaccination or isolation, a suitable combination of epidemic size and duration when both maximum control effort and total amount of resources available during the entire epidemic period are limited. Application of Pontryagin's Maximum Principle to a Susceptible-Infected-Removed epidemic model, shows that, when the resources are not sufficient to maintain the maximum control effort for the entire duration of the epidemic, the optimal vaccination control admits only bang-bang solutions with one or two switches, while the optimal isolation control admits only bang-bang solutions with one switch. We also find that, especially when the maximum control effort is low, there may exist a trade-off between the minimization of the two objectives. Consideration of this conflict among objectives can be crucial in successfully tackling real-world problems, where different stakeholders with potentially different objectives are involved. Finally, the particular case of the minimum time optimal control problem with limited resources is discussed.

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'.

Concurrent assessment of epidemiological and operational uncertainties for optimal outbreak control: Ebola as a case study

Determining how best to manage an infectious disease outbreak may be hindered by both epidemiological uncertainty (i.e. about epidemiological processes) and operational uncertainty (i.e. about the effectiveness of candidate interventions). However, these two uncertainties are rarely addressed concurrently in epidemic studies. We present an approach to simultaneously address both sources of uncertainty, to elucidate which source most impedes decision-making. In the case of the 2014 West African Ebola outbreak, epidemiological uncertainty is represented by a large ensemble of published models. Operational uncertainty about three classes of interventions is assessed for a wide range of potential intervention effectiveness. We ranked each intervention by caseload reduction in each model, initially assuming an unlimited budget as a counterfactual. We then assessed the influence of three candidate cost functions relating intervention effectiveness and cost for different budget levels. The improvement in management outcomes to be gained by resolving uncertainty is generally high in this study; appropriate information gain could reduce expected caseload by more than 50%. The ranking of interventions is jointly determined by the underlying epidemiological process, the effectiveness of the interventions and the size of the budget. An epidemiologically effective intervention might not be optimal if its costs outweigh its epidemiological benefit. Under higher-budget conditions, resolution of epidemiological uncertainty is most valuable. When budgets are tight, however, operational and epidemiological uncertainty are equally important. Overall, our study demonstrates that significant reductions in caseload could result from a careful examination of both epidemiological and operational uncertainties within the same modelling structure. This approach can be applied to decision-making for the management of other diseases for which multiple models and multiple interventions are available.

Quantitative impacts of incubation phase transmission of foot-and-mouth disease virus

The current investigation applied a Bayesian modeling approach to a unique experimental transmission study to estimate the occurrence of transmission of foot-and-mouth disease (FMD) during the incubation phase amongst group-housed pigs. The primary outcome was that transmission occurred approximately one day prior to development of visible signs of disease (posterior median 21 hours, 95% CI: 1.1-45.0). Updated disease state durations were incorporated into a simulation model to examine the importance of addressing preclinical transmission in the face of robust response measures. Simulation of FMD outbreaks in the US pig production sector demonstrated that including a preclinical infectious period of one day would result in a 40% increase in the median number of farms affected (166 additional farms and 664,912 pigs euthanized) compared to the scenario of no preclinical transmission, assuming suboptimal outbreak response. These findings emphasize the importance of considering transmission of FMD during the incubation phase in modeling and response planning.

Dynamics of the 2004 avian influenza H5N1 outbreak in Thailand: The role of duck farming, sequential model fitting and control

The Highly Pathogenic Avian Influenza (HPAI) subtype H5N1 virus persists in many countries and has been circulating in poultry, wild birds. In addition, the virus has emerged in other species and frequent zoonotic spillover events indicate that there remains a significant risk to human health. It is crucial to understand the dynamics of the disease in the poultry industry to develop a more comprehensive knowledge of the risks of transmission and to establish a better distribution of resources when implementing control. In this paper, we develop a set of mathematical models that simulate the spread of HPAI H5N1 in the poultry industry in Thailand, utilising data from the 2004 epidemic. The model that incorporates the intensity of duck farming when assessing transmision risk provides the best fit to the spatiotemporal characteristics of the observed outbreak, implying that intensive duck farming drives transmission of HPAI in Thailand. We also extend our models using a sequential model fitting approach to explore the ability of the models to be used in “real time” during novel disease outbreaks. We conclude that, whilst predictions of epidemic size are estimated poorly in the early stages of disease outbreaks, the model can infer the preferred control policy that should be deployed to minimise the impact of the disease.

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.

Modeling Dynamic Human Behavioral Changes in Animal Disease Models: Challenges and Opportunities for Addressing Bias

Over the past several decades, infectious disease modeling has become an essential tool for creating counterfactual scenarios that allow the effectiveness of different disease control policies to be evaluated prior to implementation in the real world. For livestock diseases, these models have become increasingly sophisticated as researchers have gained access to rich national livestock traceability databases, which enables inclusion of explicit spatial and temporal patterns in animal movements through network-based approaches. However, there are still many limitations in how we currently model animal disease dynamics. Critical among these is that many models make the assumption that human behaviors remain constant over time. As many studies have shown, livestock owners change their behaviors around trading, on-farm biosecurity, and disease management in response to complex factors such as increased awareness of disease risks, pressure to conform with social expectations, and the direct imposition of new national animal health regulations; all of which may significantly influence how a disease spreads within and between farms. Failing to account for these dynamics may produce a substantial layer of bias in infectious disease models, yet surprisingly little is currently known about the effects on model inferences. Here, we review the growing evidence on why these assumptions matter. We summarize the current knowledge about farmers' behavioral change in on-farm biosecurity and livestock trading practices and highlight the knowledge gaps that prohibit these behavioral changes from being incorporated into disease modeling frameworks. We suggest this knowledge gap can be filled only by more empirical longitudinal studies on farmers' behavioral change as well as theoretical modeling studies that can help to identify human behavioral changes that are important in disease transmission dynamics. Moreover, we contend it is time to shift our research approach: from modeling a single disease to modeling interactions between multiple diseases and from modeling a single farmer behavior to modeling interdependencies between multiple behaviors. In order to solve these challenges, there is a strong need for interdisciplinary collaboration across a wide range of fields including animal health, epidemiology, sociology, and animal welfare.

Logistical constraints lead to an intermediate optimum in outbreak response vaccination

Dynamic models in disease ecology have historically evaluated vaccination strategies under the assumption that they are implemented homogeneously in space and time. However, this approach fails to formally account for operational and logistical constraints inherent in the distribution of vaccination to the population at risk. Thus, feedback between the dynamic processes of vaccine distribution and transmission might be overlooked. Here, we present a spatially explicit, stochastic Susceptible-Infected-Recovered-Vaccinated model that highlights the density-dependence and spatial constraints of various diffusive strategies of vaccination during an outbreak. The model integrates an agent-based process of disease spread with a partial differential process of vaccination deployment. We characterize the vaccination response in terms of a diffusion rate that describes the distribution of vaccination to the population at risk from a central location. This generates an explicit trade-off between slow diffusion, which concentrates effort near the central location, and fast diffusion, which spreads a fixed vaccination effort thinly over a large area. We use stochastic simulation to identify the optimum vaccination diffusion rate as a function of population density, interaction scale, transmissibility, and vaccine intensity. Our results show that, conditional on a timely response, the optimal strategy for minimizing outbreak size is to distribute vaccination resource at an intermediate rate: fast enough to outpace the epidemic, but slow enough to achieve local herd immunity. If the response is delayed, however, the optimal strategy for minimizing outbreak size changes to a rapidly diffusive distribution of vaccination effort. The latter may also result in significantly larger outbreaks, thus suggesting a benefit of allocating resources to timely outbreak detection and response.

It has long been recognized that an epidemic of infectious disease can be prevented if a sufficient proportion of the susceptible population is vaccinated in advance. This logic also holds for vaccine-based outbreak response to stop an outbreak of a novel, or re-emerging pathogen, but with an important caveat. If vaccination is used in response to an outbreak, then it will necessarily take time to achieve the required level of vaccination coverage, during which time the outbreak may continue to spread. Thus, one must consider the logistical and operational constraints of vaccine distribution to assess the ability of outbreak response vaccination to slow or stop an advancing epidemic. We develop a simple mathematical framework for representing vaccine distribution in response to an epidemic and solve for the optimal distribution strategy under realistic constraints of total vaccination effort. Focused deployment near the outbreak epicenter concentrates resources in the area most in need, but may allow the outbreak to spread outside of the response zone. Broad deployment over the whole population may spread vaccination resources too thin, creating shortages and delays at the local scale that fail to prevent the advancing epidemic. Thus we found that, in general, the best strategy is an intermediate optimum that deploys vaccine neither too slow to prevent escape from the outbreak epicenter, nor too fast to spread resources too thin. The specific optimum rate for any given outbreak depends on the infectiousness of the pathogen, the population density, the range of contacts amongst individuals, the timeliness of the response, and the vaccine intensity. This insight only emerges from linking an epidemic model with a realistic model of outbreak response and highlights the need for further work to merge operations research with epidemic models to develop operationally relevant response strategies.

Evaluating vaccination strategies to control foot-and-mouth disease: a country comparison study

Vaccination is increasingly being recognised as a potential tool to supplement ‘stamping out’ for controlling foot-and-mouth disease (FMD) outbreaks in non-endemic countries. Infectious disease simulation models provide the opportunity to determine how vaccination might be used in the face of an FMD outbreak. Previously, consistent relative benefits of specific vaccination strategies across different FMD simulation modelling platforms have been demonstrated, using a UK FMD outbreak scenario. We extended this work to assess the relative effectiveness of selected vaccination strategies in five countries: Australia, New Zealand, the USA, the UK and Canada. A comparable, but not identical, FMD outbreak scenario was developed for each country with initial seeding of Pan Asia type O FMD virus into an area with a relatively high density of livestock farms. A series of vaccination strategies (in addition to stamping out (SO)) were selected to evaluate key areas of interest from a disease response perspective, including timing of vaccination, species considerations (e.g. vaccination of only those farms with cattle), risk area vaccination and resources available for vaccination. The study found that vaccination used with SO was effective in reducing epidemic size and duration in a severe outbreak situation. Early vaccination and unconstrained resources for vaccination consistently outperformed other strategies. Vaccination of only those farms with cattle produced comparable results, with some countries demonstrating that this could be as effective as all species vaccination. Restriction of vaccination to higher risk areas was less effective than other strategies. This study demonstrates consistency in the relative effectiveness of selected vaccination strategies under different outbreak start up conditions conditional on the assumption that each of the simulation models provide a realistic estimation of FMD virus spread. Preferred outbreak management approaches must however balance the principles identified in this study, working to clearly defined outbreak management objectives, while having a good understanding of logistic requirements and the socio-economic implications of different control measures.

Does Size Matter to Models? Exploring the Effect of Herd Size on Outputs of a Herd-Level Disease Spread Simulator

Disease spread modeling is widely used by veterinary authorities to predict the impact of emergency animal disease outbreaks in livestock and to evaluate the cost-effectiveness of different management interventions. Such models require knowledge of basic disease epidemiology as well as information about the population of animals at risk. Essential demographic information includes the production system, animal numbers, and their spatial locations yet many countries with significant livestock industries do not have publically available and accurate animal population information at the farm level that can be used in these models. The impact of inaccuracies in data on model outputs and the decisions based on these outputs is seldom discussed. In this analysis, we used the Australian Animal Disease model to simulate the spread of foot-and-mouth disease seeded into high-risk herds in six different farming regions in New Zealand. We used three different susceptible animal population datasets: (1) a gold standard dataset comprising known herd sizes, (2) a dataset where herd size was simulated from a beta-pert distribution for each herd production type, and (3) a dataset where herd size was simplified to the median herd size for each herd production type. We analyzed the model outputs to compare (i) the extent of disease spread, (ii) the length of the outbreaks, and (iii) the possible impacts on decisions made for simulated outbreaks in different regions. Model outputs using the different datasets showed statistically significant differences, which could have serious implications for decision making by a competent authority. Outbreak duration, number of infected properties, and vaccine doses used during the outbreak were all significantly smaller for the gold standard dataset when compared with the median herd size dataset. Initial outbreak location and disease control strategy also significantly influenced the duration of the outbreak and number of infected premises. The study findings demonstrate the importance of having accurate national-level population datasets to ensure effective decisions are made before and during disease outbreaks, reducing the damage and cost.

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.

Control fast or control smart: When should invading pathogens be controlled?

The intuitive response to an invading pathogen is to start disease management as rapidly as possible, since this would be expected to minimise the future impacts of disease. However, since more spread data become available as an outbreak unfolds, processes underpinning pathogen transmission can almost always be characterised more precisely later in epidemics. This allows the future progression of any outbreak to be forecast more accurately, and so enables control interventions to be targeted more precisely. There is also the chance that the outbreak might die out without any intervention whatsoever, making prophylactic control unnecessary. Optimal decision-making involves continuously balancing these potential benefits of waiting against the possible costs of further spread. We introduce a generic, extensible data-driven algorithm based on parameter estimation and outbreak simulation for making decisions in real-time concerning when and how to control an invading pathogen. The Control Smart Algorithm (CSA) resolves the trade-off between the competing advantages of controlling as soon as possible and controlling later when more information has become available. We show-using a generic mathematical model representing the transmission of a pathogen of agricultural animals or plants through a population of farms or fields-how the CSA allows the timing and level of deployment of vaccination or chemical control to be optimised. In particular, the algorithm outperforms simpler strategies such as intervening when the outbreak size reaches a pre-specified threshold, or controlling when the outbreak has persisted for a threshold length of time. This remains the case even if the simpler methods are fully optimised in advance. Our work highlights the potential benefits of giving careful consideration to the question of when to start disease management during emerging outbreaks, and provides a concrete framework to allow policy-makers to make this decision.

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.