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

A discrete two time scales model of a size-structured population of parasitized trees

The work presented a general discrete-time model of a population of trees affected by a parasite. The tree population was considered size-structured, and the parasite was represented by a single scalar variable. Parasite dynamics were assumed to act on a faster timescale than tree dynamics. The model was studied based on an associated nonlinear matrix model, in which the presence of the parasites was only reflected in the value of its parameters. For the model in all its generality, an explicit condition of viability/extinction of the parasite/tree community was found. In a simplified model with two size-classes of trees and particular forms of the vital rates, it was shown that the model undergoes a transcritical bifurcation and, likewise, a period-doubling bifurcation. It was found that, for any tree fertility rate that makes them viable without a parasite, if the parasite sufficiently reduces the survival of young trees, it can lead to the extinction of the entire community. The same cannot be assured if the parasite acts on adult trees. In situations where a high fertility rate coupled with a low survival rate of adult trees causes a non-parasitized population of trees to fluctuate, a parasite sufficiently damaging only young trees can stabilize the population. If, instead, the parasite acts on adult trees, we can find a destabilization condition on the tree population that brings them from a stable to an oscillating regime.

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.

Climate change impacts on plant pathogens, food security and paths forward

Plant disease outbreaks pose significant risks to global food security and environmental sustainability worldwide, and result in the loss of primary productivity and biodiversity that negatively impact the environmental and socio-economic conditions of affected regions. Climate change further increases outbreak risks by altering pathogen evolution and host-pathogen interactions and facilitating the emergence of new pathogenic strains. Pathogen range can shift, increasing the spread of plant diseases in new areas. In this Review, we examine how plant disease pressures are likely to change under future climate scenarios and how these changes will relate to plant productivity in natural and agricultural ecosystems. We explore current and future impacts of climate change on pathogen biogeography, disease incidence and severity, and their effects on natural ecosystems, agriculture and food production. We propose that amendment of the current conceptual framework and incorporation of eco-evolutionary theories into research could improve our mechanistic understanding and prediction of pathogen spread in future climates, to mitigate the future risk of disease outbreaks. We highlight the need for a science-policy interface that works closely with relevant intergovernmental organizations to provide effective monitoring and management of plant disease under future climate scenarios, to ensure long-term food and nutrient security and sustainability of natural ecosystems.

What Can Be Learned by a Synoptic Review of Plant Disease Epidemics and Outbreaks Published in 2021?

A synoptic review of plant disease epidemics and outbreaks was made using two complementary approaches. The first approach involved reviewing scientific literature published in 2021, in which quantitative data related to new plant disease epidemics or outbreaks were obtained via surveys or similar methodologies. The second approach involved retrieving new records added in 2021 to the CABI Distribution Database, which contains over a million global geographic records of organisms from over 50,000 species. The literature review retrieved 186 articles, describing studies in 62 categories (pathogen species/species complexes) across more than 40 host species on six continents. Pathogen species with more than five articles were Bursaphelenchus xylophilus, 'Candidatus Liberibacter asiaticus', cassava mosaic viruses, citrus tristeza virus, Erwinia amylovora, Fusarium spp. complexes, F. oxysporum f. sp. cubense, Magnaporthe oryzae, maize lethal necrosis co-infecting viruses, Meloidogyne spp. complexes, Pseudomonas syringae pvs., Puccinia striiformis f. sp. tritici, Xylella fastidiosa, and Zymoseptoria tritici. Automated searches of the CABI Distribution Database identified 617 distribution records new in 2021 of 283 plant pathogens. A further manual review of these records confirmed 15 pathogens reported in new locations: apple hammerhead viroid, apple rubbery wood viruses, Aphelenchoides besseyi, Biscogniauxia mediterranea, 'Ca. Liberibacter asiaticus', citrus tristeza virus, Colletotrichum siamense, cucurbit chlorotic yellows virus, Erwinia rhapontici, Erysiphe corylacearum, F. oxysporum f. sp. cubense Tropical race 4, Globodera rostochiensis, Nothophoma quercina, potato spindle tuber viroid, and tomato brown rugose fruit virus. Of these, four pathogens had at least 25% of all records reported in 2021. We assessed two of these pathogens-tomato brown rugose fruit virus and cucurbit chlorotic yellows virus-to be actively emerging in/spreading to new locations. Although three important pathogens-'Ca. Liberibacter asiaticus', citrus tristeza virus, and F. oxysporum f. sp. cubense-were represented in the results of both our literature review and our interrogation of the CABI Distribution Database, in general, our dual approaches revealed distinct sets of plant disease outbreaks and new records, with little overlap. [Formula: see text] Copyright © 2023 The Author(s). This is an open access article distributed under the CC BY 4.0 International license.

Optimal Epidemic Control under Uncertainty: Tradeoffs between Information Collection and Other Actions

BACKGROUND

Recent epidemics and measures taken to control them-through vaccination or other actions-have highlighted the role and importance of uncertainty in public health. There is generally a tradeoff between information collection and other uses of resources. Whether this tradeoff is solved explicitly or implicitly, the concept of value of information is central to inform policy makers in an uncertain environment.

METHOD

We use a deterministic SIR (susceptible, infectious, recovered) disease emergence and transmission model with vaccination that can be administered as 1 or 2 doses. The disease parameters and vaccine characteristics are uncertain. We study the tradeoffs between information acquisition and 2 other measures: bringing vaccination forward and acquiring more vaccine doses. To do this, we quantify the expected value of perfect information (EVPI) under different constraints faced by public health authorities (i.e., the time of the vaccination campaign implementation and the number of vaccine doses available).

RESULTS

We discuss the appropriateness of different responses under uncertainty. We show that, in some cases, vaccinating later or with less vaccine doses but more information about the epidemic, and the efficacy of control strategies may bring better results than vaccinating earlier or with more doses and less information, respectively.

CONCLUSION

In the present methodological article, we show in an abstract setting how clearly defining and treating the tradeoff between information acquisition and the relaxation of constraints can improve public health decision making.

HIGHLIGHTS

Uncertainties can seriously hinder epidemic control, but resolving them is costly. Thus, there are tradeoffs between information collection and alternative uses of resources.We use a generic SIR model with vaccination and a value-of-information framework to explore these tradeoffs.We show in which cases vaccinating later with more information about the epidemic and the efficacy of control measures may be better-or not-than vaccinating earlier with less information.We show in which cases vaccinating with fewer vaccine doses and more information about the epidemic and the efficacy of control measures may be better-or not-than vaccinating with more doses and less information.

Non-pharmaceutical interventions and the emergence of pathogen variants

Non-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, are important public health measures that can reduce pathogen transmission. In addition to playing a crucial role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply, restricting the availability of susceptible hosts, and altering the strength of selection for novel variants. Yet it is unclear how NPIs might affect the emergence of novel variants that are able to escape pre-existing immunity (partially or fully), are more transmissible or cause greater mortality. We analyse a stochastic two-strain epidemiological model to determine how the strength and timing of NPIs affect the emergence of variants with similar or contrasting life-history characteristics to the wild type. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross-immunity to have a greater probability of emerging at intermediate levels of NPIs. This is because intermediate levels of NPIs allow an epidemic of the wild type that is neither too small (facilitating high mutation supply), nor too large (leaving a large pool of susceptible hosts), to prevent a novel variant from becoming established in the host population. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be an implementation of strong, timely NPIs.

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.

Dynamic resource allocation for controlling pathogen spread on a large metapopulation network

To control the spread of an infectious disease over a large network, the optimal allocation by a social planner of a limited resource is a fundamental and difficult problem. We address this problem for a livestock disease that propagates on an animal trade network according to an epidemiological-demographic model based on animal demographics and trade data. We assume that the resource is dynamically allocated following a certain score, up to the limit of resource availability. We adapt a greedy approach to the metapopulation framework, obtaining new scores that minimize approximations of two different objective functions, for two control measures: vaccination and treatment. Through intensive simulations, we compare the greedy scores with several heuristics. Although topology-based scores can limit the spread of the disease, information on herd health status seems crucial to eradicating the disease. In particular, greedy scores are among the most effective in reducing disease prevalence, even though they do not always perform the best. However, some scores may be preferred in real life because they are easier to calculate or because they use a smaller amount of resources. The developed approach could be adapted to other epidemiological models or to other control measures in the metapopulation setting.

Optimal strategies to protect a sub-population at risk due to an established epidemic

Epidemics can particularly threaten certain sub-populations. For example, for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the elderly are often preferentially protected. For diseases of plants and animals, certain sub-populations can drive mitigation because they are intrinsically more valuable for ecological, economic, socio-cultural or political reasons. Here, we use optimal control theory to identify strategies to optimally protect a ‘high-value’ sub-population when there is a limited budget and epidemiological uncertainty. We use protection of the Redwood National Park in California in the face of the large ongoing state-wide epidemic of sudden oak death (caused by Phytophthora ramorum) as a case study. We concentrate on whether control should be focused entirely within the National Park itself, or whether treatment of the growing epidemic in the surrounding ‘buffer region’ can instead be more profitable. We find that, depending on rates of infection and the size of the ongoing epidemic, focusing control on the high-value region is often optimal. However, priority should sometimes switch from the buffer region to the high-value region only as the local outbreak grows. We characterize how the timing of any switch depends on epidemiological and logistic parameters, and test robustness to systematic misspecification of these factors due to imperfect prior knowledge.

The impact of spatial and social structure on an SIR epidemic on a weighted multilayer network

A key factor in the transmission of infectious diseases is the structure of disease transmitting contacts. In the context of the current COVID-19 pandemic and with some data based on the Hungarian population we develop a theoretical epidemic model (susceptible-infected-removed, SIR) on a multilayer network. The layers include the Hungarian household structure, with population divided into children, adults and elderly, as well as schools and workplaces, some spatial embedding and community transmission due to sharing communal spaces, service and public spaces. We investigate the sensitivity of the model (via the time evolution and final size of the epidemic) to the different contact layers and we map out the relation between peak prevalence and final epidemic size. When compared to the classic compartmental model and for the same final epidemic size, we find that epidemics on multilayer network lead to higher peak prevalence meaning that the risk of overwhelming the health care system is higher. Based on our model we found that keeping cliques/bubbles in school as isolated as possible has a major effect while closing workplaces had a mild effect as long as workplaces are of relatively small size.

Evaluating online and tangible interfaces for engaging stakeholders in forecasting and control of biological invasions

Ecological forecasts will be best suited to inform intervention strategies if they are accessible to a diversity of decision-makers. Researchers are developing intuitive forecasting interfaces to guide stakeholders through the development of intervention strategies and visualization of results. Yet, few studies to date have evaluated how user interface design facilitates the coordinated, cross-boundary management required for controlling biological invasions. We used a participatory approach to develop complementary tangible and online interfaces for collaboratively forecasting biological invasions and devising control strategies. A diverse group of stakeholders evaluated both systems in the real-world context of controlling sudden oak death, an emerging forest disease killing millions of trees in California and Oregon. Our findings suggest that while both interfaces encouraged adaptive experimentation, tangible interfaces are particularly well suited to support collaborative decision-making. Reflecting on the strengths of both systems, we suggest workbench-style interfaces that support simultaneous interactions and dynamic geospatial visualizations.

The persistent threat of emerging plant disease pandemics to global food security

Plant disease outbreaks are increasing and threaten food security for the vulnerable in many areas of the world. Now a global human pandemic is threatening the health of millions on our planet. A stable, nutritious food supply will be needed to lift people out of poverty and improve health outcomes. Plant diseases, both endemic and recently emerging, are spreading and exacerbated by climate change, transmission with global food trade networks, pathogen spillover, and evolution of new pathogen lineages. In order to tackle these grand challenges, a new set of tools that include disease surveillance and improved detection technologies including pathogen sensors and predictive modeling and data analytics are needed to prevent future outbreaks. Herein, we describe an integrated research agenda that could help mitigate future plant disease pandemics.

Optimal timing of one-shot interventions for epidemic control

The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a "one-shot intervention") on an epidemic and consider the impact of the intervention's timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately.

The effect of the definition of 'pandemic' on quantitative assessments of infectious disease outbreak risk

In the early stages of an outbreak, the term 'pandemic' can be used to communicate about infectious disease risk, particularly by those who wish to encourage a large-scale public health response. However, the term lacks a widely accepted quantitative definition. We show that, under alternate quantitative definitions of 'pandemic', an epidemiological metapopulation model produces different estimates of the probability of a pandemic. Critically, we show that using different definitions alters the projected effects of key parameters-such as inter-regional travel rates, degree of pre-existing immunity, and heterogeneity in transmission rates between regions-on the risk of a pandemic. Our analysis provides a foundation for understanding the scientific importance of precise language when discussing pandemic risk, illustrating how alternative definitions affect the conclusions of modelling studies. This serves to highlight that those working on pandemic preparedness must remain alert to the variability in the use of the term 'pandemic', and provide specific quantitative definitions when undertaking one of the types of analysis that we show to be sensitive to the pandemic definition.

Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic

Forecasting whether or not initial reports of disease will be followed by a severe epidemic is an important component of disease management. Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. However, an alternative assessment is to predict whether or not initial cases will lead to a severe epidemic in which available control resources are exceeded. We show how this risk can be estimated by considering three practically relevant potential definitions of a severe epidemic; namely, an outbreak in which: (i) a large number of hosts are infected simultaneously; (ii) a large total number of infections occur; and (iii) the pathogen remains in the population for a long period. We show that the probability of a severe epidemic under these definitions often coincides with the standard branching process estimate for the major epidemic probability. However, these practically relevant risk assessments can also be different from the major epidemic probability, as well as from each other. This holds in different epidemiological systems, highlighting that careful consideration of how to classify a severe epidemic is vital for accurate epidemic risk quantification.

Optimising risk-based surveillance for early detection of invasive plant pathogens

Emerging infectious diseases (EIDs) of plants continue to devastate ecosystems and livelihoods worldwide. Effective management requires surveillance to detect epidemics at an early stage. However, despite the increasing use of risk-based surveillance programs in plant health, it remains unclear how best to target surveillance resources to achieve this. We combine a spatially explicit model of pathogen entry and spread with a statistical model of detection and use a stochastic optimisation routine to identify which arrangement of surveillance sites maximises the probability of detecting an invading epidemic. Our approach reveals that it is not always optimal to target the highest-risk sites and that the optimal strategy differs depending on not only patterns of pathogen entry and spread but also the choice of detection method. That is, we find that spatial correlation in risk can make it suboptimal to focus solely on the highest-risk sites, meaning that it is best to avoid ‘putting all your eggs in one basket’. However, this depends on an interplay with other factors, such as the sensitivity of available detection methods. Using the economically important arboreal disease huanglongbing (HLB), we demonstrate how our approach leads to a significant performance gain and cost saving in comparison with conventional methods to targeted surveillance.

Emerging infectious diseases of plants continue to devastate ecosystems and livelihoods worldwide. By linking a mathematical model of pest spread with a computational optimisation routine, this study identifies where to look for invasive pests if we wish to detect them at an early stage; this method improves upon conventional methods of risk-based surveillance and is robust to model misspecification.

Key questions for modelling COVID-19 exit strategies

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

Preface to theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'

This preface forms 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'.

Translating surveillance data into incidence estimates

Monitoring a population for a disease requires the hosts to be sampled and tested for the pathogen. This results in sampling series from which we may estimate the disease incidence, i.e. the proportion of hosts infected. Existing estimation methods assume that disease incidence does not change between monitoring rounds, resulting in an underestimation of the disease incidence. In this paper, we develop an incidence estimation model accounting for epidemic growth with monitoring rounds that sample varying incidence. We also show how to accommodate the asymptomatic period that is the characteristic of most diseases. For practical use, we produce an approximation of the model, which is subsequently shown to be accurate for relevant epidemic and sampling parameters. Both the approximation and the full model are applied to stochastic spatial simulations of epidemics. The results prove their consistency for a very wide range of situations. The estimation model is made available as an online application. 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'.

How decision makers can use quantitative approaches to guide outbreak responses

Decision makers are responsible for directing staffing, logistics, selecting public health interventions, communicating to professionals and the public, planning future response needs, and establishing strategic and tactical priorities along with their funding requirements. Decision makers need to rapidly synthesize data from different experts across multiple disciplines, bridge data gaps and translate epidemiological analysis into an operational set of decisions for disease control. Analytic approaches can be defined for specific response phases: investigation, scale-up and control. These approaches include: improved applications of quantitative methods to generate insightful epidemiological descriptions of outbreaks; robust investigations of causal agents and risk factors; tools to assess response needs; identifying and monitoring optimal interventions or combinations of interventions; and forecasting for response planning. Data science and quantitative approaches can improve decision-making in outbreak response. To realize these benefits, we need to develop a structured approach that will improve the quality and timeliness of data collected during outbreaks, establish analytic teams within the response structure and define a research agenda for data analytics in outbreak response.

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’.

Applying optimal control theory to complex epidemiological models to inform real-world disease management

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. 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'.

Detection, forecasting and control of infectious disease epidemics: modelling outbreaks in humans, animals and plants

The 1918 influenza pandemic is one of the most devastating infectious disease epidemics on record, having caused approximately 50 million deaths worldwide. Control measures, including prohibiting non-essential gatherings as well as closing cinemas and music halls, were applied with varying success and limited knowledge of transmission dynamics. One hundred years later, following developments in the field of mathematical epidemiology, models are increasingly used to guide decision-making and devise appropriate interventions that mitigate the impacts of epidemics. Epidemiological models have been used as decision-making tools during outbreaks in human, animal and plant populations. However, as the subject has developed, human, animal and plant disease modelling have diverged. Approaches have been developed independently for pathogens of each host type, often despite similarities between the models used in these complementary fields. With the increased importance of a One Health approach that unifies human, animal and plant health, we argue that more inter-disciplinary collaboration would enhance each of the related disciplines. This pair of theme issues presents research articles written by human, animal and plant disease modellers. In this introductory article, we compare the questions pertinent to, and approaches used by, epidemiological modellers of human, animal and plant pathogens, and summarize the articles in these theme issues. We encourage future collaboration that transcends disciplinary boundaries and links the closely related areas of human, animal and plant disease epidemic modelling. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

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.

Modelling and control of a banana soilborne pest in a multi-seasonal framework

We study the infestation dynamics of banana or plantain plants by Radopholus similis, a plant-parasitic nematode that causes severe damages. Two control strategies are implemented in our model: pesticides, which are widely used, and fallows, which are more environmentally friendly. To represent the host-parasite dynamics, two semi-discrete models are proposed. During each cropping season, free nematodes enter the plant roots, on which they feed and reproduce. At the end of the cropping season, fruits are harvested. In the first model, the parent plant is cut down to be replaced by one of its suckers and pesticides are applied. In the second model, the parent plant is uprooted and a fallow period is introduced, inducing the decay of the free pest populations; at the beginning of the next cropping season, a pest-free vitroplant is planted. For both models, the effective reproduction number of pests is computed, assuming that the infestation dynamics are fast compared to the other processes, which leads to the model order reduction. Conditions on the pesticide load or the fallow duration are then derived to ensure the stability of the periodic pest free solution. Finally, numerical simulations illustrate these theoretical results.

Small world in the real world: Long distance dispersal governs epidemic dynamics in agricultural landscapes

Outbreaks of a plant disease in a landscape can be meaningfully modelled using networks with nodes representing individual crop-fields, and edges representing potential infection pathways between them. Their spatial structure, which resembles that of a regular lattice, makes such networks fairly robust against epidemics. Yet, it is well-known how the addition of a few shortcuts can turn robust regular lattices into vulnerable 'small world' networks. Although the relevance of this phenomenon has been shown theoretically for networks with nodes corresponding to individual host plants, its real-world implications at a larger scale (i.e. in networks with nodes representing crop fields or other plantations) remain elusive. Focusing on realistic spatial networks connecting olive orchards in Andalusia (Southern Spain), the world's leading olive producer, we show how even very small probabilities of long distance dispersal of infectious vectors result in a small-world effect that dramatically exacerbates a hypothetical outbreak of a disease targeting olive trees (loosely modelled on known epidemiological information on the bacterium Xylella fastidiosa, an important emerging threat for European agriculture). More specifically, we found that the probability of long distance vector dispersal has a disproportionately larger effect on epidemic dynamics compared to pathogen's intrinsic infectivity, increasing total infected area by up to one order of magnitude (in the absence of quarantine). Furthermore, even a very small probability of long distance dispersal increased the effort needed to halt a hypothetical outbreak through quarantine by about 50% in respect to scenarios modelling local/short distance pathogen's dispersal only. This highlights how identifying (and disrupting) long distance dispersal processes may be more efficacious to contain a plant disease epidemic than surveillance and intervention concentrated on local scale transmission processes.

Improved inference of time-varying reproduction numbers during infectious disease outbreaks

Accurate estimation of the parameters characterising infectious disease transmission is vital for optimising control interventions during epidemics. A valuable metric for assessing the current threat posed by an outbreak is the time-dependent reproduction number, i.e. the expected number of secondary cases caused by each infected individual. This quantity can be estimated using data on the numbers of observed new cases at successive times during an epidemic and the distribution of the serial interval (the time between symptomatic cases in a transmission chain). Some methods for estimating the reproduction number rely on pre-existing estimates of the serial interval distribution and assume that the entire outbreak is driven by local transmission. Here we show that accurate inference of current transmissibility, and the uncertainty associated with this estimate, requires: (i) up-to-date observations of the serial interval to be included, and; (ii) cases arising from local transmission to be distinguished from those imported from elsewhere. We demonstrate how pathogen transmissibility can be inferred appropriately using datasets from outbreaks of H1N1 influenza, Ebola virus disease and Middle-East Respiratory Syndrome. We present a tool for estimating the reproduction number in real-time during infectious disease outbreaks accurately, which is available as an R software package (EpiEstim 2.2). It is also accessible as an interactive, user-friendly online interface (EpiEstim App), permitting its use by non-specialists. Our tool is easy to apply for assessing the transmission potential, and hence informing control, during future outbreaks of a wide range of invading pathogens.

Improved inference of time-varying reproduction numbers during infectious disease outbreaks

Accurate estimation of the parameters characterising infectious disease transmission is vital for optimising control interventions during epidemics. A valuable metric for assessing the current threat posed by an outbreak is the time-dependent reproduction number, i.e. the expected number of secondary cases caused by each infected individual. This quantity can be estimated using data on the numbers of observed new cases at successive times during an epidemic and the distribution of the serial interval (the time between symptomatic cases in a transmission chain). Some methods for estimating the reproduction number rely on pre-existing estimates of the serial interval distribution and assume that the entire outbreak is driven by local transmission. Here we show that accurate inference of current transmissibility, and the uncertainty associated with this estimate, requires: (i) up-to-date observations of the serial interval to be included, and; (ii) cases arising from local transmission to be distinguished from those imported from elsewhere. We demonstrate how pathogen transmissibility can be inferred appropriately using datasets from outbreaks of H1N1 influenza, Ebola virus disease and Middle-East Respiratory Syndrome. We present a tool for estimating the reproduction number in real-time during infectious disease outbreaks accurately, which is available as an R software package (EpiEstim 2.2). It is also accessible as an interactive, user-friendly online interface (EpiEstim App), permitting its use by non-specialists. Our tool is easy to apply for assessing the transmission potential, and hence informing control, during future outbreaks of a wide range of invading pathogens.

Applying optimal control theory to complex epidemiological models to inform real-world disease management

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. 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'.

Improving Management Strategies of Plant Diseases Using Sequential Sensitivity Analyses

Improvement of management strategies of epidemics is often hampered by constraints on experiments at large spatiotemporal scales. A promising approach consists of modeling the biological epidemic process and human interventions, which both impact disease spread. However, few methods enable the simultaneous optimization of the numerous parameters of sophisticated control strategies. To do so, we propose a heuristic approach (i.e., a practical improvement method approximating an optimal solution) based on sequential sensitivity analyses. In addition, we use an economic improvement criterion based on the net present value, accounting for both the cost of the different control measures and the benefit generated by disease suppression. This work is motivated by sharka (caused by Plum pox virus), a vector-borne disease of prunus trees (especially apricot, peach, and plum), the management of which in orchards is mainly based on surveillance and tree removal. We identified the key parameters of a spatiotemporal model simulating sharka spread and control and approximated optimal values for these parameters. The results indicate that the current French management of sharka efficiently controls the disease, but it can be economically improved using alternative strategies that are identified and discussed. The general approach should help policy makers to design sustainable and cost-effective strategies for disease management.

BOARD INVITED REVIEW: Prospects for improving management of animal disease introductions using disease-dynamic models

Management and policy decisions are continually made to mitigate disease introductions in animal populations despite often limited surveillance data or knowledge of disease transmission processes. Science-based management is broadly recognized as leading to more effective decisions yet application of models to actively guide disease surveillance and mitigate risks remains limited. Disease-dynamic models are an efficient method of providing information for management decisions because of their ability to integrate and evaluate multiple, complex processes simultaneously while accounting for uncertainty common in animal diseases. Here we review disease introduction pathways and transmission processes crucial for informing disease management and models at the interface of domestic animals and wildlife. We describe how disease transmission models can improve disease management and present a conceptual framework for integrating disease models into the decision process using adaptive management principles. We apply our framework to a case study of African swine fever virus in wild and domestic swine to demonstrate how disease-dynamic models can improve mitigation of introduction risk. We also identify opportunities to improve the application of disease models to support decision-making to manage disease at the interface of domestic and wild animals. First, scientists must focus on objective-driven models providing practical predictions that are useful to those managing disease. In order for practical model predictions to be incorporated into disease management a recognition that modeling is a means to improve management and outcomes is important. This will be most successful when done in a cross-disciplinary environment that includes scientists and decision-makers representing wildlife and domestic animal health. Lastly, including economic principles of value-of-information and cost-benefit analysis in disease-dynamic models can facilitate more efficient management decisions and improve communication of model forecasts. Integration of disease-dynamic models into management and decision-making processes is expected to improve surveillance systems, risk mitigations, outbreak preparedness, and outbreak response activities.