Studying the spatial temporal spread of the citrus tristeza virus through ODEs and Bernoulli trials.

The Citrus tristeza virus (CTV) is one of the most economically devastating citrus diseases worldwide. The spread of CTV in eastern Spain was studied by Gottwald et al. with the goal of determining the spatio-temporal mechanisms of spread. Since the subjects in this study are individual trees, it is natural to think of infections as Bernoulli trials. This approach is difficult however, due to the spatial and temporal dependence of the observations. Consequently, a system of ordinary differential equations (ODE) was used to model the probabilities of infection as well as the spatial and temporal dependence. Given the parameters in the ODE, the probabilities of infection are treated as conditionally independent. Using the conditional independence we then specify the joint likelihood function as a Poisson binomial distribution. For the purpose of model selection and hypothesis testing we, employed accumulated prediction error (APE) which has connections to both Bayesian and frequentist frameworks. We demonstrated the robustness of our method in accounting for spatio-temporal dependencies in the data by accurately predicting the spatial distribution of the disease through Join Counts.

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.

A probabilistic census-travel model to predict introduction sites of exotic plant, animal and human pathogens.

International travel offers an extensive network for new and recurring human-mediated introductions of exotic infectious pathogens and biota, freeing geographical constraints. We present a predictive census-travel model that integrates international travel with endpoint census data and epidemiological characteristics to predict points of introduction. Population demographics, inbound and outbound travel patterns, and quantification of source strength by country are combined to estimate and rank risk of introduction at user-scalable land parcel areas (e.g. state, county, zip code, census tract, gridded landscapes (1 mi2, 5 km2, etc.)). This risk ranking by parcel can be used to develop pathogen surveillance programmes, and has been incorporated in multiple US state/federal surveillance protocols. The census-travel model is versatile and independent of pathosystems, and applies a risk algorithm to generate risk maps for plant, human and animal contagions at different spatial scales. An interactive, user-friendly interface is available online (https://epi-models.shinyapps.io/Census_Travel/) to provide ease-of-use for regulatory agencies for early detection of high-risk exotics. The interface allows users to parametrize and run the model without knowledge of background code and underpinning data. 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'.

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'.

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.

Solar thermotherapy reduces the titer of Candidatus Liberibacter asiaticus and enhances canopy growth by altering gene expression profiles in HLB-affected citrus plants.

Huanglongbing (HLB), a systemic and destructive disease of citrus, is associated with 'Candidatus Liberibacter asiaticus' (Las) in the United States. Our earlier work has shown that Las bacteria were significantly reduced or eliminated when potted HLB-affected citrus were continuously exposed to high temperatures of 40 to 42 °C for a minimum of 48 h. To determine the feasibility and effectiveness of solar thermotherapy in the field, portable plastic enclosures were placed over commercial and residential citrus, exposing trees to high temperatures through solarization. Within 3-6 weeks after treatment, most trees responded with vigorous new growth. Las titer in new growth was greatly reduced for 18-36 months after treatment. Unlike with potted trees, exposure to high heat did not eradicate the Las population under field conditions. This may be attributed to reduced temperatures at night in the field compared to continuous high temperature exposure that can be maintained in growth chambers, and the failure to achieve therapeutic temperatures in the root zone. Despite the presence of Las in heat-treated commercial citrus, many trees produced abundant flush and grew vigorously for 2 to 3 years after treatment. Transcriptome analysis comparing healthy trees to HLB-affected citrus both before and after heat treatment demonstrated that post-treatment transcriptional expression patterns more closely resembled the expression patterns of healthy controls for most differentially expressed genes and that genes involved with plant-bacterium interactions are upregulated after heat treatment. Overall, these results indicate that solar thermotherapy can be an effective component of an integrated control strategy for citrus HLB.

Surveillance to Inform Control of Emerging Plant Diseases: An Epidemiological Perspective.

The rise in emerging pathogens and strains has led to increased calls for more effective surveillance in plant health. We show how epidemiological insights about the dynamics of disease spread can improve the targeting of when and where to sample. We outline some relatively simple but powerful statistical approaches to inform surveillance and describe how they can be adapted to include epidemiological information. This enables us to address questions such as: Following the first report of an invading pathogen, what is the likely incidence of disease? If no cases of disease have been found, how certain can we be that the disease was not simply missed by chance? We illustrate the use of spatially explicit stochastic models to optimize targeting of surveillance and control resources. Finally, we discuss how modern detection and diagnostic technologies as well as information from passive surveillance networks (e.g., citizen science) can be integrated into surveillance strategies.

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.

Susceptibility of Sixteen Citrus Genotypes to 'Candidatus Liberibacter asiaticus'.

Huanglongbing (HLB) disease is the most serious threat to citrus production worldwide and, in the last decade, has devastated the Florida citrus industry. In the United States, HLB is associated with the phloem-limited α-proteobacterium 'Candidatus Liberibacter asiaticus' and its insect vector, the Asian citrus psyllid (ACP; Diaphorina citri). Significant effort is being put forth to develop novel citrus germplasm that has a lower propensity to succumb to HLB than do currently available varieties. Effective methods of screening citrus germplasm for susceptibility to HLB are essential. In this study, we exposed small, grafted trees of 16 citrus types to free-ranging ACP vectors and 'Ca. L. asiaticus' inoculum in the greenhouse. During 45 weeks of exposure to ACP, the cumulative incidence of 'Ca. L. asiaticus' infection was 70%. Trees of Citrus macrophylla and C. medica were most susceptible to 'Ca. L. asiaticus', with 100% infection by the end of the test period in three trials, while the complex genetic hybrids 'US 1-4-59' and 'Fallglo' consistently were least susceptible, with approximately 30% infection. Results obtained in this greenhouse experiment showed good agreement with trends observed in the orchard, supporting the validity of our approach for screening citrus germplasm for susceptibility to HLB.

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.

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.

Thirteen challenges in modelling plant diseases.

The underlying structure of epidemiological models, and the questions that models can be used to address, do not necessarily depend on the host organism in question. This means that certain preoccupations of plant disease modellers are similar to those of modellers of diseases in human, livestock and wild animal populations. However, a number of aspects of plant epidemiology are very distinctive, and this leads to specific challenges in modelling plant diseases, which in turn sets a certain agenda for modellers. Here we outline a selection of 13 challenges, specific to plant disease epidemiology, that we feel are important targets for future work.

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

The spread of Huanglongbing through citrus groves is used as a case study for modeling an emerging epidemic in the presence of a control. Specifically, the spread of the disease is modeled as a susceptible-exposed-infectious-detected-removed epidemic, where the exposure and infectious times are not observed, detection times are censored, removal times are known, and the disease is spreading through a heterogeneous host population with trees of different age and susceptibility. We show that it is possible to characterize the disease transmission process under these conditions. Two innovations in our work are (i) accounting for control measures via time dependence of the infectious process and (ii) including seasonal and host age effects in the model of the latent period. By estimating parameters in different subregions of a large commercially cultivated orchard, we establish a temporal pattern of invasion, host age dependence of the dispersal parameters, and a close to linear relationship between primary and secondary infectious rates. The model can be used to simulate Huanglongbing epidemics to assess economic costs and potential benefits of putative control scenarios.

Bayesian analysis for inference of an emerging epidemic: citrus canker in urban landscapes.

Outbreaks of infectious diseases require a rapid response from policy makers. The choice of an adequate level of response relies upon available knowledge of the spatial and temporal parameters governing pathogen spread, affecting, amongst others, the predicted severity of the epidemic. Yet, when a new pathogen is introduced into an alien environment, such information is often lacking or of no use, and epidemiological parameters must be estimated from the first observations of the epidemic. This poses a challenge to epidemiologists: how quickly can the parameters of an emerging disease be estimated? How soon can the future progress of the epidemic be reliably predicted? We investigate these issues using a unique, spatially and temporally resolved dataset for the invasion of a plant disease, Asiatic citrus canker in urban Miami. We use epidemiological models, Bayesian Markov-chain Monte Carlo, and advanced spatial statistical methods to analyse rates and extent of spread of the disease. A rich and complex epidemic behaviour is revealed. The spatial scale of spread is approximately constant over time and can be estimated rapidly with great precision (although the evidence for long-range transmission is inconclusive). In contrast, the rate of infection is characterised by strong monthly fluctuations that we associate with extreme weather events. Uninformed predictions from the early stages of the epidemic, assuming complete ignorance of the future environmental drivers, fail because of the unpredictable variability of the infection rate. Conversely, predictions improve dramatically if we assume prior knowledge of either the main environmental trend, or the main environmental events. A contrast emerges between the high detail attained by modelling in the spatiotemporal description of the epidemic and the bottleneck imposed on epidemic prediction by the limits of meteorological predictability. We argue that identifying such bottlenecks will be a fundamental step in future modelling of weather-driven epidemics.

What interval characteristics make a good categorical disease assessment scale?

Plant pathologists most often obtain quantitative information on disease severity using visual assessments. Category scales have been used for assessing plant disease severity in field experiments, epidemiological studies, and for screening germplasm. The most widely used category scale is the Horsfall-Barratt (H-B) scale, but reports show that estimates of disease severity using the H-B scale are less precise compared with nearest percent estimates (NPEs) using the 0 to 100% ratio scale. Few studies have compared different category scales. The objective of this study was to compare NPEs, the H-B midpoint converted data, and four different linear category scales (5 and 10% increments, with and without additional grades at low severity [0.1, 0.5, 1.0, 2.0, 5.0, 10.0, 15.0, 20.0…100%, and 0.1, 0.5, 1.0, 2.0, 5.0, 10.0, 20.0, 30.0…100%, respectively]). Results of simulations based on known distributions of disease estimation using the type II error rate (the risk of failing to reject H0 when H0 is false) showed that at disease severity ≤ 5%, a 10% category scale had a greater probability of failing to reject H0 when H0 is false compared with all other methods, while the H-B scale performed least well at 20 to 50% severity. The 5% category scale performed as well as NPEs except when disease severity was ≤ 1%. Both the 5 and 10% category scales with the additional grades included performed as well as NPEs. These results were confirmed with a mixed model analysis and bootstrap analysis of the original rater assessment data. A better knowledge of the advantages and disadvantages of category scale types will provide a basis for plant pathologists and plant breeders seeking to maximize accuracy and reliability of assessments to make an informed decision when choosing a disease assessment method.

Spatial and temporal assessment of pollen- and seed-mediated gene flow from genetically engineered plum Prunus domestica.

Pollen flow from a 0.46 ha plot of genetically engineered (GE) Prunus domestica located in West Virginia, USA was evaluated from 2000-2010. Sentinel plum trees were planted at distances ranging from 132 to 854 m from the center of the GE orchard. Plots of mixed plum varieties and seedlings were located at 384, 484 and 998 m from the GE plot. Bee hives (Apis mellifera) were dispersed between the GE plum plot and the pollen flow monitoring sites. Pollen-mediated gene flow from out of the GE plum plot to non-GE plums under the study conditions was low, only occurring at all in 4 of 11 years and then in only 0.31% of the 12,116 seeds analyzed. When it occurred, gene flow, calculated as the number of GUS positive embryos/total embryos sampled, ranged from 0.215% at 132 m from the center of the GE plum plot (28 m from the nearest GE plum tree) to 0.033-0.017% at longer distances (384-998 m). Based on the percentage of GUS positive seeds per individual sampled tree the range was 0.4% to 12%. Within the GE field plot, gene flow ranged from 4.9 to 39%. Gene flow was related to distance and environmental conditions. A single year sample from a sentinel plot 132 m from the center of the GE plot accounted for 65% of the total 11-year gene flow. Spatial modeling indicated that gene flow dramatically decreased at distances over 400 m from the GE plot. Air temperature and rainfall were, respectively, positively and negatively correlated with gene flow, reflecting the effects of weather conditions on insect pollinator activity. Seed-mediated gene flow was not detected. These results support the feasibility of coexistence of GE and non-GE plum orchards.

Pecan Scab Severity-Effects of Assessment Methods.

Pecan scab is caused by the fungus Fusicladium effusum, and is the most destructive disease of pecan in the United States. Accurate and reliable disease assessments are needed to ensure that data provide a measure of actual disease intensity. The Horsfall-Barratt (H-B) category scale and its derivatives are commonly used to assess disease. Estimates using the H-B scale were compared with nearest percent estimate (NPEs) for rating disease severity of pecan scab on valves of fruit. Both inexperienced and experienced raters were included in the experiment. Lin's concordance correlation showed that agreement using NPEs was variable (ρc = 0.57 to 0.96), whereas estimates of disease severity using the H-B scale had similar agreement among most raters (ρc = 0.59 to 0.98). Converted values of NPEs to the H-B midpoints (NPEH-B) also provided a similar range (ρc = 0.61 to 0.96). Neither experienced nor inexperienced raters were consistently better using any of the three methods. Bootstrap analysis indicated that, among experienced raters, precision (r) and agreement (ρc) were often reduced when using the H-B scale compared with NPEs. There was no consistent effect of converting NPEs to NPEH-B midpoint values compared with actual H-B values. Inter-rater reliability using the H-B scale was never better than NPEs. Bootstrap analysis indicated no difference in the length of time needed to assess disease but regression analysis suggested that raters who were inherently fast in assessing disease with NPEs were often slower when using the H-B scale; conversely, raters who were slow assessing with NPEs were often faster when using the H-B scale. Thus, there appears to be no advantage in accuracy or reliability or reduction in time when inexperienced or experienced raters used a category rating scale to assess pecan scab.

Efficacy of Area-Wide Inoculum Reduction and Vector Control on Temporal Progress of Huanglongbing in Young Sweet Orange Plantings.

Huanglongbing (HLB), caused by 'Candidatus Liberibacter' spp. and transmitted by the Asian citrus psyllid Diaphorina citri (ACP), is an important threat to citrus industries worldwide, causing significant yield loss. The current recommended strategies to manage HLB are to eliminate HLB-symptomatic trees to reduce sources of bacterial inoculum and to apply insecticides to reduce psyllid vector populations. The objective of this study was to assess the effectiveness and the importance of both strategies applied within young citrus plots (local management), in different frequencies and combinations, on HLB temporal progress. Two factorial field experiments, E1 and E2, were initiated in a new plantation of sweet orange in an HLB epidemic region of Sao Paulo, Brazil, in October 2005 and May 2006, respectively. Local inoculum reduction (tree removal) intervals for E1 were every 4, 8, and 16 weeks and, for E2, every 2, 4, 12, and 26 weeks. Local vector control strategies for E1 were no control, program A (PA), and program B (PB); and, for E2, no control and program C (PC), as follows. Psyllids were controlled with two 56-day-interval soil or drench applications of systemic insecticides concurrently with the rainy season each year and, during the rest of the year, with insecticide sprays every 28 days for PA and every 14 days for PB and PC. Regional HLB management was present for E1 and absent for E2. The beginning of the HLB epidemic was delayed for 10 months in E1 compared with appearance of the first diseased tree in E2 but wasn't affected by different local strategies in either experiment. After 60 (E1) and 53 (E2) months, the HLB incidence and progress rates were not affected by different frequencies of local inoculum reduction in either experiment, and were different only in plots with and without local vector control in E2. In E1, the disease incidence was reduced by 90% and the disease progress rate by 50% in plots both with and without vector control. These reductions were explained by smaller psyllid populations and lower frequency of bacterialiferous psyllids in E1 compared with E2. Annual productivity increased over time in E1, as expected for young plantings, but remained stable or decreased in E2. These results confirm that immigration of bacterialiferous ACP vectors plays a critical role in HLB epidemics and suggest that area-wide inoculum reduction and ACP management strongly affect HLB control.

The Effect of Horsfall-Barratt Category Size on the Accuracy and Reliability of Estimates of Pecan Scab Severity.

Pecan scab (Fusicladium effusum) is a destructive pecan disease. Disease assessments may be made using interval-scale-based methods or estimates of severity to the nearest percent area diseased. To explore the effects of rating method-Horsfall-Barratt (H-B) scale estimates versus nearest percent estimates (NPEs)-on the accuracy and reliability of severity estimates over different actual pecan scab severity ranges on fruit valves, raters assessed two cohorts of images with actual area (0 to 6, 6+ to 25%, and 25+ to 75%) diseased. Mean estimated disease within each actual disease severity range varied substantially. Means estimated by NPE within each actual disease severity range were not necessarily good predictors of the H-B scale estimate at <25% severity. H-B estimates by raters most often placed severity in the wrong category compared with actual disease. Measures of bias, accuracy, precision, and agreement using Lin's concordance correlation depended on the range of actual severity, with improvements increasing with actual disease severity category (from 0 to 6 through 25+ to 75%); however, the improvement was unaffected by the H-B assessments. Bootstrap analysis indicated that NPEs provided either equally good or more accurate and precise estimate of disease compared with the H-B scale at severities of 25+ to 75%. Inter-rater reliability using NPEs was greater at 25+ to 75% actual disease severity compared with using the H-B scale. Using NPEs compared with the H-B scale will more often result in more precise and accurate estimates of pecan scab severity, particularly when estimating actual disease severities of 25+ to 75%.