Bayesian inference for an emerging arboreal epidemic in the presence of control

Bayesian inference for spatio-temporal stochastic transmission of plant disease in the presence of roguing: A case study to characterise the dispersal of Flavescence dorée

Estimating the distance at which pathogens disperse from one season to the next is crucial for designing efficient control strategies for invasive plant pathogens and a major milestone in the reduction of pesticide use in agriculture. However, we still lack such estimates for many diseases, especially for insect-vectored pathogens, such as Flavescence dorée (FD). FD is a quarantine disease threatening European vineyards. Its management is based on mandatory insecticide treatments and the removal of infected plants identified during annual surveys. This paper introduces a general statistical framework to model the epidemiological dynamics of FD in a mechanistic manner that can take into account missing hosts in surveyed fields (resulting from infected plant removals). We parameterized the model using Markov chain Monte Carlo (MCMC) and data augmentation from surveillance data gathered in Bordeaux vineyards. The data mainly consist of two snapshot maps of the infectious status of all the plants in three adjacent fields during two consecutive years. We demonstrate that heavy-tailed dispersal kernels best fit the spread of FD and that on average, 50% (resp. 80%) of new infection occurs within 10.5 m (resp. 22.2 m) of the source plant. These values are in agreement with estimates of the flying capacity of Scaphoideus titanus, the leafhopper vector of FD, reported in the literature using mark-capture techniques. Simulations of simple removal scenarios using the fitted model suggest that cryptic infection hampered FD management. Future efforts should explore whether strategies relying on reactive host removal can improve FD management.

Emerging Themes and Approaches in Plant Virus Epidemiology

Plant diseases caused by viruses share many common features with those caused by other pathogen taxa in terms of the host-pathogen interaction, but there are also distinctive features in epidemiology, most apparent where transmission is by vectors. Consequently, the host-virus-vector-environment interaction presents a continuing challenge in attempts to understand and predict the course of plant virus epidemics. Theoretical concepts, based on the underlying biology, can be expressed in mathematical models and tested through quantitative assessments of epidemics in the field; this remains a goal in understanding why plant virus epidemics occur and how they can be controlled. To this end, this review identifies recent emerging themes and approaches to fill in knowledge gaps in plant virus epidemiology. We review quantitative work on the impact of climatic fluctuations and change on plants, viruses, and vectors under different scenarios where impacts on the individual components of the plant-virus-vector interaction may vary disproportionately; there is a continuing, sometimes discordant, debate on host resistance and tolerance as plant defense mechanisms, including aspects of farmer behavior and attitudes toward disease management that may affect deployment in crops; disentangling host-virus-vector-environment interactions, as these contribute to temporal and spatial disease progress in field populations; computational techniques for estimating epidemiological parameters from field observations; and the use of optimal control analysis to assess disease control options. We end by proposing new challenges and questions in plant virus epidemiology.

Modelling the spread and mitigation of an emerging vector-borne pathogen: Citrus greening in the U.S

Predictive models, based upon epidemiological principles and fitted to surveillance data, play an increasingly important role in shaping regulatory and operational policies for emerging outbreaks. Data for parameterising these strategically important models are often scarce when rapid actions are required to change the course of an epidemic invading a new region. We introduce and test a flexible epidemiological framework for landscape-scale disease management of an emerging vector-borne pathogen for use with endemic and invading vector populations. We use the framework to analyse and predict the spread of Huanglongbing disease or citrus greening in the U.S. We estimate epidemiological parameters using survey data from one region (Texas) and show how to transfer and test parameters to construct predictive spatio-temporal models for another region (California). The models are used to screen effective coordinated and reactive management strategies for different regions.

Inference for epidemic models with time-varying infection rates: Tracking the dynamics of oak processionary moth in the UK

Invasive pests pose a great threat to forest, woodland, and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South‐East England, OPM continues to spread.

Here, we analyze data consisting of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state‐of‐the‐art Bayesian inference scheme, we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, and removed) model with a time‐varying infestation rate to describe the spread of OPM.

We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with R0 between one and two). This shows further controls must be taken to reduce R0 below one and stop the advance of OPM into other areas of England.

Synthesis. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time‐varying infestation rate, applicable to other partially observed time series epidemic data.

Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between 'spatial' and 'non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

Phylogenetic inference enables reconstruction of a long-overlooked outbreak of almond leaf scorch disease (Xylella fastidiosa) in Europe

The recent introductions of the bacterium Xylella fastidiosa (Xf) into Europe are linked to the international plant trade. However, both how and when these entries occurred remains poorly understood. Here, we show how almond scorch leaf disease, which affects ~79% of almond trees in Majorca (Spain) and was previously attributed to fungal pathogens, was in fact triggered by the introduction of Xf around 1993 and subsequently spread to grapevines (Pierceʼs disease). We reconstructed the progression of almond leaf scorch disease by using broad phylogenetic evidence supported by epidemiological data. Bayesian phylogenetic inference predicted that both Xf subspecies found in Majorca, fastidiosa ST1 (95% highest posterior density, HPD: 1990–1997) and multiplex ST81 (95% HPD: 1991–1998), shared their most recent common ancestors with Californian Xf populations associated with almonds and grapevines. Consistent with this chronology, Xf-DNA infections were identified in tree rings dating to 1998. Our findings uncover a previously unknown scenario in Europe and reveal how Pierce’s disease reached the continent.

Eduardo Moralejo et al. report a phylogenetic reconstruction tracing the origin and progression of a European outbreak of the almond scorch disease pathogen Xylella fastidiosa (Xf). Their data suggest Xf was introduced into Europe via grafting from infected Californian buds and was subsequently spread by the meadow spittlebug to multiple plant hosts.

Latent likelihood ratio tests for assessing spatial kernels in epidemic models

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

Trade-off between local transmission and long-range dispersal drives infectious disease outbreak size in spatially structured populations

Transmission of infectious diseases between immobile hosts (e.g., plants, farms) is strongly dependent on the spatial distribution of hosts and the distance-dependent probability of transmission. As the interplay between these factors is poorly understood, we use spatial process and transmission modelling to investigate how epidemic size is shaped by host clustering and spatial range of transmission. We find that for a given degree of clustering and individual-level infectivity, the probability that an epidemic occurs after an introduction is generally higher if transmission is predominantly local. However, local transmission also impedes transfer of the infection to new clusters. A consequence is that the total number of infections is maximal if the range of transmission is intermediate. In highly clustered populations, the infection dynamics is strongly determined by the probability of transmission between clusters of hosts, whereby local clusters act as multiplier of infection. We show that in such populations, a metapopulation model sometimes provides a good approximation of the total epidemic size, using probabilities of local extinction, the final size of infections in local clusters, and probabilities of cluster-to-cluster transmission. As a real-world example we analyse the case of avian influenza transmission between poultry farms in the Netherlands.

Transmission of infectious diseases between immobile hosts depends on the transmission characteristics of the infection and on the spatial distribution of hosts. Examples include infectious diseases of plants that are spread by wind or via vectors (e.g., Asiatic citrus canker spread between citrus trees), diseases that are transmitted between local host populations (e.g., sylvatic plague transmitted between rodents living in burrows), diseases of production animals that are spread between farms (e.g., avian influenza in poultry transmitted from farm to farm). We use spatial transmission modelling to investigate how the total number of infections over the course of an epidemic is determined by host clustering and spatial range of transmission. We find that for a given degree of clustering and infectivity of hosts, the number of infections is maximal if the spatial range of transmission is intermediate. In highly clustered populations we show that epidemic size can be approximated by a metapopulation model, illustrating that in such populations the transmission dynamics is dominated by transmission between clusters of hosts.

Using models to provide rapid programme support for California's efforts to suppress Huanglongbing disease of citrus

We describe a series of operational questions posed during the state-wide response in California to the arrival of the invasive citrus disease Huanglongbing. The response is coordinated by an elected committee from the citrus industry and operates in collaboration with the California Department of Food and Agriculture, which gives it regulatory authority to enforce the removal of infected trees. The paper reviews how surveillance for disease and resource allocation between detection and delimitation have been addressed, based on epidemiological principles. In addition, we describe how epidemiological analyses have been used to support rule-making to enact costly but beneficial regulations and we highlight two recurring themes in the programme support work: (i) data are often insufficient for quantitative analyses of questions and (ii) modellers and decision-makers alike may be forced to accept the need to make decisions on the basis of simple or incomplete analyses that are subject to considerable uncertainty. 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 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.

What makes or breaks a campaign to stop an invading plant pathogen?

Diseases in humans, animals and plants remain an important challenge in our society. Effective control of invasive pathogens often requires coordinated concerted action of a large group of stakeholders. Both epidemiological and human behavioural factors influence the outcome of a disease control campaign. In mathematical models that are frequently used to guide such campaigns, human behaviour is often ill-represented, if at all. Existing models of human, animal and plant disease that do incorporate participation or compliance are often driven by pay-offs or direct observations of the disease state. It is however very well known that opinion is an important driving factor of human decision making. Here we consider the case study of Citrus Huanglongbing disease (HLB), which is an acute bacterial disease that threatens the sustainability of citrus production across the world. We show how by coupling an epidemiological model of this invasive disease with an opinion dynamics model we are able to answer the question: What makes or breaks the effectiveness of a disease control campaign? Frequent contact between stakeholders and advisors is shown to increase the probability of successful control. More surprisingly, we show that informing stakeholders about the effectiveness of control methods is of much greater importance than prematurely increasing their perceptions of the risk of infection. We discuss the overarching consequences of this finding and the effect on human as well as plant disease epidemics.

The successful regional control of emerging and invasive diseases often requires that a sufficiently large proportion of the population comply with the control strategy. This is notably the case in diseases such as measles but also applies to epidemics in animals and plants. If insufficient numbers of stakeholders comply with disease control, or if control becomes uncoordinated for some reason, then control fails. Therefore, both epidemiological and human behavioural factors influence the outcome of emerging, endemic, and invasive disease control campaigns. Mathematical models are often used to determine factors that are important for disease control to be successful, but these models tend to focus on the epidemiology and efficacy of control, frequently neglecting human behaviour. A number of mathematical models of human disease, and to some extent animal disease do incorporate participation or compliance behaviours; however, studies looking at human actions and attitudes towards plant disease control are quite rare and almost exclusively driven by pay-offs or direct observations of the disease state. It is however very well known that opinion, for example about how effective control is perceived to be, is also a key driving factor of human decision making. Here we consider the case study of Citrus Huanglongbing disease (HLB), a devastating invasive disease in citrus which threatens production worldwide. We show how by coupling an epidemiological model with an opinion dynamics model it is possible to answer the question: What makes or breaks the effectiveness of a disease control campaign?

Canine olfactory detection of a vectored phytobacterial pathogen, Liberibacter asiaticus, and integration with disease control

Exotic infectious pathogens, like citrus huanglongbing (HLB), are increasingly introduced into agrosystems. Early detection is the key to mitigating their destructive effects. Human visual assessment is insufficiently sensitive to detect new plant infections in a responsive timeframe, and molecular assays are expensive and not easily deployable over large crop landscapes. We turned to detector dogs, an ancient technology, which can rapidly survey large plantings without laborious sample collection or laboratory processing. Dogs detected infections (>99% accuracy) weeks to years prior to visual survey and molecular methods and were highly specific, accurately discriminating target pathogens from other pathogens. Epidemiological models indicated that dogs were more effective and economical than current early detection methods for sustainable disease control.

Early detection and rapid response are crucial to avoid severe epidemics of exotic pathogens. However, most detection methods (molecular, serological, chemical) are logistically limited for large-scale survey of outbreaks due to intrinsic sampling issues and laboratory throughput. Evaluation of 10 canines trained for detection of a severe exotic phytobacterial arboreal pathogen, Candidatus Liberibacter asiaticus (CLas), demonstrated 0.9905 accuracy, 0.8579 sensitivity, and 0.9961 specificity. In a longitudinal study, cryptic CLas infections that remained subclinical visually were detected within 2 wk postinfection compared with 1 to 32 mo for qPCR. When allowed to interrogate a diverse range of in vivo pathogens infecting an international citrus pathogen collection, canines only reacted to Liberibacter pathogens of citrus and not to other bacterial, viral, or spiroplasma pathogens. Canines trained to detect CLas-infected citrus also alerted on CLas-infected tobacco and periwinkle, CLas-bearing psyllid insect vectors, and CLas cocultured with other bacteria but at CLas titers below the level of molecular detection. All of these observations suggest that canines can detect CLas directly rather than only host volatiles produced by the infection. Detection in orchards and residential properties was real time, ∼2 s per tree. Spatiotemporal epidemic simulations demonstrated that control of pathogen prevalence was possible and economically sustainable when canine detection was followed by intervention (i.e., culling infected individuals), whereas current methods of molecular (qPCR) and visual detection failed to contribute to the suppression of an exponential trajectory of infection.

Analyzing the Influence of Landscape Aggregation on Disease Spread to Improve Management Strategies

Epidemiological models are increasingly used to predict epidemics and improve management strategies. However, they rarely consider landscape characteristics although such characteristics can influence the epidemic dynamics and, thus, the effectiveness of disease management strategies. Here, we present a generic in silico approach which assesses the influence of landscape aggregation on the costs associated with an epidemic and on improved management strategies. We apply this approach to sharka, one of the most damaging diseases of Prunus trees, for which a management strategy is already applied in France. Epidemic simulations were carried out with a spatiotemporal stochastic model under various management strategies in landscapes differing in patch aggregation. Using sensitivity analyses, we highlight the impact of management parameters on the economic output of the model. We also show that the sensitivity analysis can be exploited to identify several strategies that are, according to the model, more profitable than the current French strategy. Some of these strategies are specific to a given aggregation level, which shows that management strategies should generally be tailored to each specific landscape. However, we also identified a strategy that is efficient for all levels of landscape aggregation. This one-size-fits-all strategy has important practical implications because of its simple applicability at a large scale.

Model diagnostics and refinement for phylodynamic models

Phylodynamic modelling, which studies the joint dynamics of epidemiological and evolutionary processes, has made significant progress in recent years due to increasingly available genomic data and advances in statistical modelling. These advances have greatly improved our understanding of transmission dynamics of many important pathogens. Nevertheless, there remains a lack of effective, targetted diagnostic tools for systematically detecting model mis-specification. Development of such tools is essential for model criticism, refinement, and calibration. The idea of utilising latent residuals for model assessment has already been exploited in general spatio-temporal epidemiological settings. Specifically, by proposing appropriately designed non-centered, re-parameterizations of a given epidemiological process, one can construct latent residuals with known sampling distributions which can be used to quantify evidence of model mis-specification. In this paper, we extend this idea to formulate a novel model-diagnostic framework for phylodynamic models. Using simulated examples, we show that our framework may effectively detect a particular form of mis-specification in a phylodynamic model, particularly in the event of superspreading. We also exemplify our approach by applying the framework to a dataset describing a local foot-and-mouth (FMD) outbreak in the UK, eliciting strong evidence against the assumption of no within-host-diversity in the outbreak. We further demonstrate that our framework can facilitate model calibration in real-life scenarios, by proposing a within-host-diversity model which appears to offer a better fit to data than one that assumes no within-host-diversity of FMD virus.

Integrated modelling of conventional epidemiological data and modern genomic data (i.e. phylodynamics) has made significant progress in recent years, due to the ever-increasing availability of genomic data and development of statistical methods. However, there is a lack of tools for carrying out effective diagnostics for phylodynamic models. We propose a novel model diagnostic framework that involves a latent residual process which is a priori independent of model assumptions and which can be used to quantify, and reveal the nature of, model inadequacy. Our results suggest that our framework may systematically detect deviation from a particular model assumption and greatly facilitate subsequent model calibration.

Regional Spatial-Temporal Spread of Citrus Huanglongbing Is Affected by Rain in Florida

Citrus huanglongbing (HLB), associated with 'Candidatus Liberibacter asiaticus' (Las), disseminated by Asian citrus psyllid (ACP), has devastated citrus in Florida since 2005. Data on HLB occurrence were stored in databases (2005 to 2012). Cumulative HLB-positive citrus blocks were subjected to kernel density analysis and kriging. Relative disease incidence per county was calculated by dividing HLB numbers by relative tree numbers and maximum incidence. Spatiotemporal HLB distributions were correlated with weather. Relative HLB incidence correlated positively with rainfall. The focus expansion rate was 1626 m month^-1, similar to that in Brazil. Relative HLB incidence in counties with primarily large groves increased at a lower rate (0.24 year^-1) than in counties with smaller groves in hotspot areas (0.67 year^-1), confirming reports that large-scale HLB management may slow epidemic progress.

Xylella fastidiosa: Insights into an Emerging Plant Pathogen

The bacterium Xylella fastidiosa re-emerged as a plant pathogen of global importance in 2013 when it was first associated with an olive tree disease epidemic in Italy. The current threat to Europe and the Mediterranean basin, as well as other world regions, has increased as multiple X. fastidiosa genotypes have now been detected in Italy, France, and Spain. Although X. fastidiosa has been studied in the Americas for more than a century, there are no therapeutic solutions to suppress disease development in infected plants. Furthermore, because X. fastidiosa is an obligatory plant and insect vector colonizer, the epidemiology and dynamics of each pathosystem are distinct. They depend on the ecological interplay of plant, pathogen, and vector and on how interactions are affected by biotic and abiotic factors, including anthropogenic activities and policy decisions. Our goal with this review is to stimulate discussion and novel research by contextualizing available knowledge on X. fastidiosa and how it may be applicable to emerging diseases.

Assessing the durability and efficiency of landscape-based strategies to deploy plant resistance to pathogens

Genetically-controlled plant resistance can reduce the damage caused by pathogens. However, pathogens have the ability to evolve and overcome such resistance. This often occurs quickly after resistance is deployed, resulting in significant crop losses and a continuing need to develop new resistant cultivars. To tackle this issue, several strategies have been proposed to constrain the evolution of pathogen populations and thus increase genetic resistance durability. These strategies mainly rely on varying different combinations of resistance sources across time (crop rotations) and space. The spatial scale of deployment can vary from multiple resistance sources occurring in a single cultivar (pyramiding), in different cultivars within the same field (cultivar mixtures) or in different fields (mosaics). However, experimental comparison of the efficiency (i.e. ability to reduce disease impact) and durability (i.e. ability to limit pathogen evolution and delay resistance breakdown) of landscape-scale deployment strategies presents major logistical challenges. Therefore, we developed a spatially explicit stochastic model able to assess the epidemiological and evolutionary outcomes of the four major deployment options described above, including both qualitative resistance (i.e. major genes) and quantitative resistance traits against several components of pathogen aggressiveness: infection rate, latent period duration, propagule production rate, and infectious period duration. This model, implemented in the R package landsepi, provides a new and useful tool to assess the performance of a wide range of deployment options, and helps investigate the effect of landscape, epidemiological and evolutionary parameters. This article describes the model and its parameterisation for rust diseases of cereal crops, caused by fungi of the genus Puccinia. To illustrate the model, we use it to assess the epidemiological and evolutionary potential of the combination of a major gene and different traits of quantitative resistance. The comparison of the four major deployment strategies described above will be the objective of future studies.

There are many recent examples which demonstrate the evolutionary potential of plant pathogens to overcome the resistances deployed in agricultural landscapes to protect our crops. Increasingly, it is recognised that how resistance is deployed spatially and temporally can impact on rates of pathogen evolution and resistance breakdown. Such deployment strategies are mainly based on the combination of several sources of resistance at different spatiotemporal scales. However, comparison of these strategies in a predictive sense is not an easy task, owing to the logistical difficulties associated with experiments involving the spread of a pathogen at large spatio-temporal scales. Moreover, both the durability of a strategy and the epidemiological protection it provides to crops must be assessed since these evaluation criteria are not necessarily correlated. Surprisingly, no current simulation model allows a thorough comparison of the different options. Here we describe a spatio-temporal model able to simulate a wide range of deployment strategies and resistance sources. This model, implemented in the R package landsepi, facilitates assessment of both epidemiological and evolutionary outcomes across simulated scenarios. In this work, the model is used to investigate the combination of different sources of resistance against fungal diseases such as rusts of cereal crops.

Estimation of the dispersal distances of an aphid-borne virus in a patchy landscape

Characterising the spatio-temporal dynamics of pathogens in natura is key to ensuring their efficient prevention and control. However, it is notoriously difficult to estimate dispersal parameters at scales that are relevant to real epidemics. Epidemiological surveys can provide informative data, but parameter estimation can be hampered when the timing of the epidemiological events is uncertain, and in the presence of interactions between disease spread, surveillance, and control. Further complications arise from imperfect detection of disease and from the huge number of data on individual hosts arising from landscape-level surveys. Here, we present a Bayesian framework that overcomes these barriers by integrating over associated uncertainties in a model explicitly combining the processes of disease dispersal, surveillance and control. Using a novel computationally efficient approach to account for patch geometry, we demonstrate that disease dispersal distances can be estimated accurately in a patchy (i.e. fragmented) landscape when disease control is ongoing. Applying this model to data for an aphid-borne virus (Plum pox virus) surveyed for 15 years in 605 orchards, we obtain the first estimate of the distribution of flight distances of infectious aphids at the landscape scale. About 50% of aphid flights terminate beyond 90 m, which implies that most infectious aphids leaving a tree land outside the bounds of a 1-ha orchard. Moreover, long-distance flights are not rare-10% of flights exceed 1 km. By their impact on our quantitative understanding of winged aphid dispersal, these results can inform the design of management strategies for plant viruses, which are mainly aphid-borne.

Evidence-based controls for epidemics using spatio-temporal stochastic models in a Bayesian framework

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models considered here, are playing an increasing role in the design of control as agencies seek to strengthen the evidence on which selected strategies are based. Here, we investigate a general approach to informing the choice of control strategies using spatio-temporal models within the Bayesian framework. We illustrate the approach for the case of strategies based on pre-emptive removal of individual hosts. For an exemplar model, using simulated data and historic data on an epidemic of Asiatic citrus canker in Florida, we assess a range of measures for prioritizing individuals for removal that take account of observations of an emerging epidemic. These measures are based on the potential infection hazard a host poses to susceptible individuals (hazard), the likelihood of infection of a host (risk) and a measure that combines both the hazard and risk (threat). We find that the threat measure typically leads to the most effective control strategies particularly for clustered epidemics when resources are scarce. The extension of the methods to a range of other settings is discussed. A key feature of the approach is the use of functional-model representations of the epidemic model to couple epidemic trajectories under different control strategies. This induces strong positive correlations between the epidemic outcomes under the respective controls, serving to reduce both the variance of the difference in outcomes and, consequently, the need for extensive simulation.

A mechanistic spatio-temporal framework for modelling individual-to-individual transmission-With an application to the 2014-2015 West Africa Ebola outbreak

In recent years there has been growing availability of individual-level spatio-temporal disease data, particularly due to the use of modern communicating devices with GPS tracking functionality. These detailed data have been proven useful for inferring disease transmission to a more refined level than previously. However, there remains a lack of statistically sound frameworks to model the underlying transmission dynamic in a mechanistic manner. Such a development is particularly crucial for enabling a general epidemic predictive framework at the individual level. In this paper we propose a new statistical framework for mechanistically modelling individual-to-individual disease transmission in a landscape with heterogeneous population density. Our methodology is first tested using simulated datasets, validating our inferential machinery. The methodology is subsequently applied to data that describes a regional Ebola outbreak in Western Africa (2014-2015). Our results show that the methods are able to obtain estimates of key epidemiological parameters that are broadly consistent with the literature, while revealing a significantly shorter distance of transmission. More importantly, in contrast to existing approaches, we are able to perform a more general model prediction that takes into account the susceptible population. Finally, our results show that, given reasonable scenarios, the framework can be an effective surrogate for susceptible-explicit individual models which are often computationally challenging.

Availability of individual-level, spatio-temporal disease data (e.g. GPS locations of infected individuals) has been increasing in recent years, primarily due to the increased use of modern communication devices such as mobile phones. Such data create invaluable opportunities for researchers to study disease transmission on a more refined individual-to-individual level, facilitating the designs of potentially more effective control measures. However, the growing availability of such precise data has not been accompanied by development of statistically sound mechanistic frameworks. Developing such frameworks is an essential step for systematically extracting maximal information from data, in particular, evaluating the efficacy of individually-targeted control strategies and enabling forward epidemic prediction at the individual level. In this paper we develop a novel statistical framework that overcomes a few key limitations of existing approaches, enabling a machinery that can be used to infer the history of partially observed outbreaks and, more importantly, to produce a more comprehensive epidemic prediction. Our framework may also be a good surrogate for more computationally challenging individual-based models.

Foundational and Translational Research Opportunities to Improve Plant Health

Reader Comments | Submit a Comment The white paper reports the deliberations of a workshop focused on biotic challenges to plant health held in Washington, D.C. in September 2016. Ensuring health of food plants is critical to maintaining the quality and productivity of crops and for sustenance of the rapidly growing human population. There is a close linkage between food security and societal stability; however, global food security is threatened by the vulnerability of our agricultural systems to numerous pests, pathogens, weeds, and environmental stresses. These threats are aggravated by climate change, the globalization of agriculture, and an over-reliance on nonsustainable inputs. New analytical and computational technologies are providing unprecedented resolution at a variety of molecular, cellular, organismal, and population scales for crop plants as well as pathogens, pests, beneficial microbes, and weeds. It is now possible to both characterize useful or deleterious variation as well as precisely manipulate it. Data-driven, informed decisions based on knowledge of the variation of biotic challenges and of natural and synthetic variation in crop plants will enable deployment of durable interventions throughout the world. These should be integral, dynamic components of agricultural strategies for sustainable agriculture.

Risk-based management of invading plant disease

Effective control of plant disease remains a key challenge. Eradication attempts often involve removal of host plants within a certain radius of detection, targeting asymptomatic infection. Here we develop and test potentially more effective, epidemiologically motivated, control strategies, using a mathematical model previously fitted to the spread of citrus canker in Florida. We test risk-based control, which preferentially removes hosts expected to cause a high number of infections in the remaining host population. Removals then depend on past patterns of pathogen spread and host removal, which might be nontransparent to affected stakeholders. This motivates a variable radius strategy, which approximates risk-based control via removal radii that vary by location, but which are fixed in advance of any epidemic. Risk-based control outperforms variable radius control, which in turn outperforms constant radius removal. This result is robust to changes in disease spread parameters and initial patterns of susceptible host plants. However, efficiency degrades if epidemiological parameters are incorrectly characterised. Risk-based control including additional epidemiology can be used to improve disease management, but it requires good prior knowledge for optimal performance. This focuses attention on gaining maximal information from past epidemics, on understanding model transferability between locations and on adaptive management strategies that change over time.

Data-Driven Risk Assessment from Small Scale Epidemics: Estimation and Model Choice for Spatio-Temporal Data with Application to a Classical Swine Fever Outbreak

Livestock epidemics have the potential to give rise to significant economic, welfare, and social costs. Incursions of emerging and re-emerging pathogens may lead to small and repeated outbreaks. Analysis of the resulting data is statistically challenging but can inform disease preparedness reducing potential future losses. We present a framework for spatial risk assessment of disease incursions based on data from small localized historic outbreaks. We focus on between-farm spread of livestock pathogens and illustrate our methods by application to data on the small outbreak of Classical Swine Fever (CSF) that occurred in 2000 in East Anglia, UK. We apply models based on continuous time semi-Markov processes, using data-augmentation Markov Chain Monte Carlo techniques within a Bayesian framework to infer disease dynamics and detection from incompletely observed outbreaks. The spatial transmission kernel describing pathogen spread between farms, and the distribution of times between infection and detection, is estimated alongside unobserved exposure times. Our results demonstrate inference is reliable even for relatively small outbreaks when the data-generating model is known. However, associated risk assessments depend strongly on the form of the fitted transmission kernel. Therefore, for real applications, methods are needed to select the most appropriate model in light of the data. We assess standard Deviance Information Criteria (DIC) model selection tools and recently introduced latent residual methods of model assessment, in selecting the functional form of the spatial transmission kernel. These methods are applied to the CSF data, and tested in simulated scenarios which represent field data, but assume the data generation mechanism is known. Analysis of simulated scenarios shows that latent residual methods enable reliable selection of the transmission kernel even for small outbreaks whereas the DIC is less reliable. Moreover, compared with DIC, model choice based on latent residual assessment correlated better with predicted risk.

Mathematical models are a powerful method to understand and control the spread of Huanglongbing

Huanglongbing (HLB), or citrus greening, is a global citrus disease occurring in almost all citrus growing regions. It causes substantial economic burdens to individual growers, citrus industries and governments. Successful management strategies to reduce disease burden are desperately needed but with so many possible interventions and combinations thereof it is difficult to know which are worthwhile or cost-effective. We review how mathematical models have yielded useful insights into controlling disease spread for other vector-borne plant diseases, and the small number of mathematical models of HLB. We adapt a malaria model to HLB, by including temperature-dependent psyllid traits, "flushing" of trees, and economic costs, to show how models can be used to highlight the parameters that require more data collection or that should be targeted for intervention. We analyze the most common intervention strategy, insecticide spraying, to determine the most cost-effective spraying strategy. We find that fecundity and feeding rate of the vector require more experimental data collection, for wider temperatures ranges. Also, the best strategy for insecticide intervention is to spray for more days rather than pay extra for a more efficient spray. We conclude that mathematical models are able to provide useful recommendations for managing HLB spread.

Monitoring invasive pathogens in plant nurseries for early-detection and to minimise the probability of escape

The global increase in the movement of plant products in recent years has triggered an increase in the number of introduced plant pathogens. Plant nurseries importing material from abroad may play an important role in the introduction and spread of diseases such as ash dieback and sudden oak death which are thought to have been introduced through trade. The economic, environmental and social costs associated with the spread of invasive pathogens become considerably larger as the incidence of the pathogen increases. To control the movement of pathogens across the plant trade network it is crucial to develop monitoring programmes at key points of the network such as plant nurseries. By detecting the introduction of invasive pathogens at low incidence, the control and eradication of an epidemic is more likely to be successful. Equally, knowing the likelihood of having sold infected plants once a disease has been detected in a nursery can help designing tracing plans to control the onward spread of the disease. Here, we develop an epidemiological model to detect and track the movement of an invasive plant pathogen into and from a plant nursery. Using statistical methods, we predict the epidemic incidence given that a detection of the pathogen has occurred for the first time, considering that the epidemic has an asymptomatic period between infection and symptom development. Equally, we calculate the probability of having sold at least one infected plant during the period previous to the first disease detection. This analysis can aid stakeholder decisions to determine, when the pathogen is first discovered in a nursery, the need of tracking the disease to other points in the plant trade network in order to control the epidemic. We apply our method to high profile recent introductions including ash dieback and sudden oak death in the UK and citrus canker and Huanglongbing disease in Florida. These results provide new insight for the design of monitoring strategies at key points of the trade network.

Detecting Presymptomatic Infection Is Necessary to Forecast Major Epidemics in the Earliest Stages of Infectious Disease Outbreaks

We assess how presymptomatic infection affects predictability of infectious disease epidemics. We focus on whether or not a major outbreak (i.e. an epidemic that will go on to infect a large number of individuals) can be predicted reliably soon after initial cases of disease have appeared within a population. For emerging epidemics, significant time and effort is spent recording symptomatic cases. Scientific attention has often focused on improving statistical methodologies to estimate disease transmission parameters from these data. Here we show that, even if symptomatic cases are recorded perfectly, and disease spread parameters are estimated exactly, it is impossible to estimate the probability of a major outbreak without ambiguity. Our results therefore provide an upper bound on the accuracy of forecasts of major outbreaks that are constructed using data on symptomatic cases alone. Accurate prediction of whether or not an epidemic will occur requires records of symptomatic individuals to be supplemented with data concerning the true infection status of apparently uninfected individuals. To forecast likely future behavior in the earliest stages of an emerging outbreak, it is therefore vital to develop and deploy accurate diagnostic tests that can determine whether asymptomatic individuals are actually uninfected, or instead are infected but just do not yet show detectable symptoms.

Emerging epidemics pose a significant challenge to human health worldwide. Accurate real-time forecasts of whether or not initial reports will be followed by a major outbreak are necessary for efficient deployment of control. For all infectious diseases, there is a delay between infection and the appearance of symptoms, i.e. an initial period following first infection during which infected individuals remain presymptomatic. We use mathematical modeling to evaluate the effect of presymptomatic infection on predictions of major epidemics. Our results show rigorously, for the first time, that precise estimates of the current number of infected individuals—and consequently the chance of a major outbreak in future—cannot be inferred from data on symptomatic cases alone. This is the case even if the values of epidemiological parameters, such as the average infection and death or recovery rates of individuals in the population, can be estimated accurately. Accurate prediction is in fact impossible without additional data from which the number of currently infected but as yet presymptomatic individuals can be deduced.

A Systematic Bayesian Integration of Epidemiological and Genetic Data

Genetic sequence data on pathogens have great potential to inform inference of their transmission dynamics ultimately leading to better disease control. Where genetic change and disease transmission occur on comparable timescales additional information can be inferred via the joint analysis of such genetic sequence data and epidemiological observations based on clinical symptoms and diagnostic tests. Although recently introduced approaches represent substantial progress, for computational reasons they approximate genuine joint inference of disease dynamics and genetic change in the pathogen population, capturing partially the joint epidemiological-evolutionary dynamics. Improved methods are needed to fully integrate such genetic data with epidemiological observations, for achieving a more robust inference of the transmission tree and other key epidemiological parameters such as latent periods. Here, building on current literature, a novel Bayesian framework is proposed that infers simultaneously and explicitly the transmission tree and unobserved transmitted pathogen sequences. Our framework facilitates the use of realistic likelihood functions and enables systematic and genuine joint inference of the epidemiological-evolutionary process from partially observed outbreaks. Using simulated data it is shown that this approach is able to infer accurately joint epidemiological-evolutionary dynamics, even when pathogen sequences and epidemiological data are incomplete, and when sequences are available for only a fraction of exposures. These results also characterise and quantify the value of incomplete and partial sequence data, which has important implications for sampling design, and demonstrate the abilities of the introduced method to identify multiple clusters within an outbreak. The framework is used to analyse an outbreak of foot-and-mouth disease in the UK, enhancing current understanding of its transmission dynamics and evolutionary process.

In the midst of increasingly available sequence data of pathogens, a key challenge is to better integrate these data with traditional epidemiological data, with the proximate goal of reliable prediction and the ultimate aim of effective management of disease outbreaks. Although substantial advances have been made for such an integration, and they have improved our understandings of many disease dynamics which are not available otherwise, current methods have relied on fast algorithms, rather than achieving a systematic integration and accurate inference of the joint epidemiological-evolutionary process. Building on methods in current literature, this paper describes a novel Bayesian approach for systematically integrating these two streams of data. We propose a computationally tractable Bayesian inferential algorithm which takes the full joint epidemiological-evolutionary process into account. Using this algorithm, we study systematically the value of genetic data, providing valuable insights into future sampling designs. The algorithm is subsequently applied to real-world dataset describing the spread of animal foot-and-mouth disease in the UK, demonstrating the importance of such a systematic integration achieved with our methodology.

Bayesian data assimilation provides rapid decision support for vector-borne diseases

Predicting the spread of vector-borne diseases in response to incursions requires knowledge of both host and vector demographics in advance of an outbreak. Although host population data are typically available, for novel disease introductions there is a high chance of the pathogen using a vector for which data are unavailable. This presents a barrier to estimating the parameters of dynamical models representing host-vector-pathogen interaction, and hence limits their ability to provide quantitative risk forecasts. The Theileria orientalis (Ikeda) outbreak in New Zealand cattle demonstrates this problem: even though the vector has received extensive laboratory study, a high degree of uncertainty persists over its national demographic distribution. Addressing this, we develop a Bayesian data assimilation approach whereby indirect observations of vector activity inform a seasonal spatio-temporal risk surface within a stochastic epidemic model. We provide quantitative predictions for the future spread of the epidemic, quantifying uncertainty in the model parameters, case infection times and the disease status of undetected infections. Importantly, we demonstrate how our model learns sequentially as the epidemic unfolds and provide evidence for changing epidemic dynamics through time. Our approach therefore provides a significant advance in rapid decision support for novel vector-borne disease outbreaks.

Asymptomatic spread of huanglongbing and implications for disease control

Huanglongbing (HLB) is a bacterial infection of citrus trees transmitted by the Asian citrus psyllid Diaphorina citri. Mitigation of HLB has focused on spraying of insecticides to reduce the psyllid population and removal of trees when they first show symptoms of the disease. These interventions have been only marginally effective, because symptoms of HLB do not appear on leaves for months to years after initial infection. Limited knowledge about disease spread during the asymptomatic phase is exemplified by the heretofore unknown length of time from initial infection of newly developing cluster of young leaves, called flush, by adult psyllids until the flush become infectious. We present experimental evidence showing that young flush become infectious within 15 d after receiving an inoculum of Candidatus Liberibacter asiaticus (bacteria). Using this critical fact, we specify a microsimulation model of asymptomatic disease spread and intensity in a grove of citrus trees. We apply a range of psyllid introduction scenarios to show that entire groves can become infected with up to 12,000 psyllids per tree in less than 1 y, before most of the trees show any symptoms. We also show that intervention strategies that reduce the psyllid population by 75% during the flushing periods can delay infection of a full grove, and thereby reduce the amount of insecticide used throughout a year. This result implies that psyllid surveillance and control, using a variety of recently available technologies, should be used from the initial detection of invasion and throughout the asymptomatic period.

Optimising and communicating options for the control of invasive plant disease when there is epidemiological uncertainty

Although local eradication is routinely attempted following introduction of disease into a new region, failure is commonplace. Epidemiological principles governing the design of successful control are not well-understood. We analyse factors underlying the effectiveness of reactive eradication of localised outbreaks of invading plant disease, using citrus canker in Florida as a case study, although our results are largely generic, and apply to other plant pathogens (as we show via our second case study, citrus greening). We demonstrate how to optimise control via removal of hosts surrounding detected infection (i.e. localised culling) using a spatially-explicit, stochastic epidemiological model. We show how to define optimal culling strategies that take account of stochasticity in disease spread, and how the effectiveness of disease control depends on epidemiological parameters determining pathogen infectivity, symptom emergence and spread, the initial level of infection, and the logistics and implementation of detection and control. We also consider how optimal culling strategies are conditioned on the levels of risk acceptance/aversion of decision makers, and show how to extend the analyses to account for potential larger-scale impacts of a small-scale outbreak. Control of local outbreaks by culling can be very effective, particularly when started quickly, but the optimum strategy and its performance are strongly dependent on epidemiological parameters (particularly those controlling dispersal and the extent of any cryptic infection, i.e. infectious hosts prior to symptoms), the logistics of detection and control, and the level of local and global risk that is deemed to be acceptable. A version of the model we developed to illustrate our methodology and results to an audience of stakeholders, including policy makers, regulators and growers, is available online as an interactive, user-friendly interface at http://www.webidemics.com/. This version of our model allows the complex epidemiological principles that underlie our results to be communicated to a non-specialist audience.

Sharka epidemiology and worldwide management strategies: learning lessons to optimize disease control in perennial plants

Many plant epidemics that cause major economic losses cannot be controlled with pesticides. Among them, sharka epidemics severely affect prunus trees worldwide. Its causal agent, Plum pox virus (PPV; genus Potyvirus), has been classified as a quarantine pathogen in numerous countries. As a result, various management strategies have been implemented in different regions of the world, depending on the epidemiological context and on the objective (i.e., eradication, suppression, containment, or resilience). These strategies have exploited virus-free planting material, varietal improvement, surveillance and removal of trees in orchards, and statistical models. Variations on these management options lead to contrasted outcomes, from successful eradication to widespread presence of PPV in orchards. Here, we present management strategies in the light of sharka epidemiology to gain insights from this worldwide experience. Although focused on sharka, this review highlights more general levers and promising approaches to optimize disease control in perennial plants.