An integrated model for pre- and post-harvest aflatoxin contamination in maize

Aflatoxin contamination caused by colonization of maize by Aspergillus flavus continues to pose a major human and livestock health hazard in the food chain. Increasing attention has been focused on the development of models to predict risk and to identify effective intervention strategies. Most risk prediction models have focused on elucidating weather and site variables on the pre-harvest dynamics of A. flavus growth and aflatoxin production. However fungal growth and toxin accumulation continue to occur after harvest, especially in countries where storage conditions are limited by logistical and cost constraints. In this paper, building on previous work, we introduce and test an integrated meteorology-driven epidemiological model that covers the entire supply chain from planting to delivery. We parameterise the model using approximate Bayesian computation with monthly time-series data over six years for contamination levels of aflatoxin in daily shipments received from up to three sourcing regions at a high-volume maize processing plant in South Central India. The time series for aflatoxin levels from the parameterised model successfully replicated the overall profile, scale and variance of the historical aflatoxin datasets used for fitting and validation. We use the model to illustrate the dynamics of A. flavus growth and aflatoxin production during the pre- and post-harvest phases in different sourcing regions, in short-term predictions to inform decision making about sourcing supplies and to compare intervention strategies to reduce the risks of aflatoxin contamination.

Developing a predictive model for an emerging epidemic on cassava in sub-Saharan Africa

The agricultural productivity of smallholder farmers in sub-Saharan Africa (SSA) is severely constrained by pests and pathogens, impacting economic stability and food security. An epidemic of cassava brown streak disease, causing significant yield loss, is spreading rapidly from Uganda into surrounding countries. Based on sparse surveillance data, the epidemic front is reported to be as far west as central DRC, the world's highest per capita consumer, and as far south as Zambia. Future spread threatens production in West Africa including Nigeria, the world's largest producer of cassava. Using innovative methods we develop, parameterise and validate a landscape-scale, stochastic epidemic model capturing the spread of the disease throughout Uganda. The model incorporates real-world management interventions and can be readily extended to make predictions for all 32 major cassava producing countries of SSA, with relevant data, and lays the foundations for a tool capable of informing policy decisions at a national and regional scale.

A new method for the analysis of access period experiments, illustrated with whitefly-borne cassava mosaic begomovirus

Reports of low transmission efficiency, of a cassava mosaic begomovirus (CMB) in Bemisia tabaci whitefly, diminished the perceived importance of whitefly in CMB epidemics. Studies indicating synergies between B. tabaci and CMB prompt a reconsideration of this assessment. In this paper, we analysed the retention period and infectiousness of CMB-carrying B. tabaci as well as B. tabaci susceptibility to CMB. We assessed the role of low laboratory insect survival in historic reports of a 9d virus retention period. To do this, we introduced Bayesian analyses to an important class of experiment in plant pathology. We were unable to reject a null hypothesis of life-long CMB retention when we accounted for low insect survival. Our analysis confirmed low insect survival, with insects surviving on average for around three days of transfers from the original infected plant to subsequent test plants. Use of the new analysis to account for insect death may lead to re-calibration of retention periods for other important insect-borne plant pathogens. In addition, we showed that B. tabaci susceptibility to CMB is substantially higher than previously thought. We also introduced a technique for high resolution analysis of retention period, showing that B. tabaci infectiousness with CMB was increasing over the first five days of infection.

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.

Rational design of a survey protocol for avocado sunblotch viroid in commercial orchards to demonstrate pest freedom

Avocado sunblotch viroid (ASBVd) is a subcellular pathogen of avocado that reduces yield from a tree, diminishes the appearance of the fruit by causing unsightly scarring and impedes trade because of quarantine conditions that are imposed to prevent spread of the pathogen via seed-borne inoculum. For countries where ASBVd is officially reported, permission to export fruit to another country may only be granted if an orchard can be demonstrated to be a pest free production site. The survey requirements to demonstrate pest freedom are usually defined in export protocols that have been mutually agreed upon by the trading partners. In this paper, we introduce a flexible statistical protocol for use in optimizing sampling strategies to establish pest free status from ASBVd in avocado orchards. The protocol, which is supported by an interactive app, integrates statistical considerations of multistage sampling of trees in orchards with a RT-qPCR assay allowing for detection of infection in pooled samples of leaves taken from multiple trees. While this study was motivated by a need to design a survey protocol for ASBVd, the theoretical framework and the accompanying app have broader applicability to a range of plant pathogens in which hierarchical sampling of a target population is coupled with pooling of material prior to diagnosis.

The role of pathogen-mediated insect superabundance in the East African emergence of a plant virus

One of the major crops for food security is cassava. Superabundant Bemisia tabaci whitefly, comprising unusually high landscape populations of the insect, have been implicated in cassava virus emergence. Studies have been unable to select from several hypotheses, however, as to the dynamic drivers of superabundant whitefly associated with the emergence in East Africa of severe cassava mosaic disease. One possibility is that pathogenic modification of infected plants can itself increase the growth of insect vector colonies on infected plants.Through the modelling of population processes at the landscape scale we introduce a framework for analysing patterns in the association of disease and insect waves.Our analyses demonstrate the role of pathogen-mediated insect superabundance in a plant disease invasion. Synthesis. An elevated abundance of insects at the landscape scale is frequently implicated in invasions of the plant pathogens that they carry. We advance ecological understanding of plant disease invasions by showing how landscape data can be used to investigate the causes of insect vector superabundance.

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.

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.

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.

When Does Spatial Diversification Usefully Maximize the Durability of Crop Disease Resistance?

Maximizing the durability of crop disease resistance genes in the face of pathogen evolution is a major challenge in modern agricultural epidemiology. Spatial diversification in the deployment of resistance genes, where susceptible and resistant fields are more closely intermixed, is predicted to drive lower epidemic intensities over evolutionary timescales. This is due to an increase in the strength of dilution effects, caused by pathogen inoculum challenging host tissue to which it is not well-specialized. The factors that interact with and determine the magnitude of this spatial suppressive effect are not currently well understood, however, leading to uncertainty over the pathosystems where such a strategy is most likely to be cost-effective. We model the effect on landscape scale disease dynamics of spatial heterogeneity in the arrangement of fields planted with either susceptible or resistant cultivars, and the way in which this effect depends on the parameters governing the pathosystem of interest. Our multiseason semidiscrete epidemiological model tracks spatial spread of wild-type and resistance-breaking pathogen strains, and incorporates a localized reservoir of inoculum, as well as the effects of within and between field transmission. The pathogen dispersal characteristics, any fitness cost(s) of the resistance-breaking trait, the efficacy of host resistance, and the length of the timeframe of interest all influence the strength of the spatial diversification effect. A key result is that spatial diversification has the strongest beneficial effect at intermediate fitness costs of the resistance-breaking trait, an effect driven by a complex set of nonlinear interactions. On the other hand, however, if the resistance-breaking strain is not fit enough to invade the landscape, then a partially effective resistance gene can result in spatial diversification actually worsening the epidemic. These results allow us to make general predictions of the types of system for which spatial diversification is most likely to be cost-effective, paving the way for potential economic modeling and pathosystem specific evaluation. These results highlight the importance of studying the effect of genetics on landscape scale spatial dynamics within host-pathogen disease systems.[Formula: see text] Copyright © 2020 The Author(s). This is an open access article distributed under the CC BY 4.0 International license.

What is pathogen-mediated insect superabundance?

When increasing abundance of insect vectors is manifest across multiple fields of a crop at the landscape scale, the phenomenon is sometimes referred to as insect superabundance. The phenomenon may reflect environmental factors (i.e. environmentally mediated insect superabundance, EMiS), including climatic change. A number of pathogens, however, are also known to modify the quality of infected plants as a resource for their insect vectors. In this paper, we term increasing vector abundance when associated with pathogen modification of plants as pathogen-mediated insect superabundance (henceforth PMiS). We investigate PMiS using a new epidemiological framework. We formalize a definition of PMiS and indicate the epidemiological mechanism by which it is most likely to arise. This study is motivated by the occurrence of a particularly destructive cassava virus epidemic that has been associated with superabundant whitefly populations in sub-Saharan Africa. Our results have implications for how PMiS can be distinguished from EMiS in field data. Above all, they represent a timely foundation for further investigations into the association between insect superabundance and plant pathogens.

Computational models to improve surveillance for cassava brown streak disease and minimize yield loss

Cassava brown streak disease (CBSD) is a rapidly spreading viral disease that affects a major food security crop in sub-Saharan Africa. Currently, there are several proposed management interventions to minimize loss in infected fields. Field-scale data comparing the effectiveness of these interventions individually and in combination are limited and expensive to collect. Using a stochastic epidemiological model for the spread and management of CBSD in individual fields, we simulate the effectiveness of a range of management interventions. Specifically we compare the removal of diseased plants by roguing, preferential selection of planting material, deployment of virus-free ‘clean seed’ and pesticide on crop yield and disease status of individual fields with varying levels of whitefly density crops under low and high disease pressure. We examine management interventions for sustainable production of planting material in clean seed systems and how to improve survey protocols to identify the presence of CBSD in a field or quantify the within-field prevalence of CBSD. We also propose guidelines for practical, actionable recommendations for the deployment of management strategies in regions of sub-Saharan Africa under different disease and whitefly pressure.

Cassava is the second largest source of calories in sub-Saharan Africa and is particularly important for the poorest farmers in the region. Cassava brown streak disease is a viral disease that causes cassava tubers to rot, rendering the roots inedible. Recently, the disease has begun to spread towards major cassava growing regions in West Africa from East Africa, where it continues to cause significant yield losses. Improved approaches for disease control are needed to enable small-holder farmers to prepare for and minimize the impact of the disease when their fields become infected. Using a combination of computational methods and mathematical models enables us to screen a much larger range of potential treatments for their likely effectiveness in managing disease and reducing crop loss than would be possible in conventional field trials, which are expensive and logistically difficult to conduct. Our results indicate that regularly planting part of the field with virus-free cassava greatly improves the yield. Removing visibly infected plants and replanting using visibly uninfected plants also improves yield, even when some of these plants may be infected but not yet showing symptoms. We also show how the survey protocol can be optimized to improve estimates of disease severity leading to more effective tailored advice to farmers in regions with different disease pressures.

A modelling framework to assess the likely effectiveness of facemasks in combination with 'lock-down' in managing the COVID-19 pandemic

COVID-19 is characterized by an infectious pre-symptomatic period, when newly infected individuals can unwittingly infect others. We are interested in what benefits facemasks could offer as a non-pharmaceutical intervention, especially in the settings where high-technology interventions, such as contact tracing using mobile apps or rapid case detection via molecular tests, are not sustainable. Here, we report the results of two mathematical models and show that facemask use by the public could make a major contribution to reducing the impact of the COVID-19 pandemic. Our intention is to provide a simple modelling framework to examine the dynamics of COVID-19 epidemics when facemasks are worn by the public, with or without imposed 'lock-down' periods. Our results are illustrated for a number of plausible values for parameter ranges describing epidemiological processes and mechanistic properties of facemasks, in the absence of current measurements for these values. We show that, when facemasks are used by the public all the time (not just from when symptoms first appear), the effective reproduction number, Re , can be decreased below 1, leading to the mitigation of epidemic spread. Under certain conditions, when lock-down periods are implemented in combination with 100% facemask use, there is vastly less disease spread, secondary and tertiary waves are flattened and the epidemic is brought under control. The effect occurs even when it is assumed that facemasks are only 50% effective at capturing exhaled virus inoculum with an equal or lower efficiency on inhalation. Facemask use by the public has been suggested to be ineffective because wearers may touch their faces more often, thus increasing the probability of contracting COVID-19. For completeness, our models show that facemask adoption provides population-level benefits, even in circumstances where wearers are placed at increased risk. At the time of writing, facemask use by the public has not been recommended in many countries, but a recommendation for wearing face-coverings has just been announced for Scotland. Even if facemask use began after the start of the first lock-down period, our results show that benefits could still accrue by reducing the risk of the occurrence of further COVID-19 waves. We examine the effects of different rates of facemask adoption without lock-down periods and show that, even at lower levels of adoption, benefits accrue to the facemask wearers. These analyses may explain why some countries, where adoption of facemask use by the public is around 100%, have experienced significantly lower rates of COVID-19 spread and associated deaths. We conclude that facemask use by the public, when used in combination with physical distancing or periods of lock-down, may provide an acceptable way of managing the COVID-19 pandemic and re-opening economic activity. These results are relevant to the developed as well as the developing world, where large numbers of people are resource poor, but fabrication of home-made, effective facemasks is possible. A key message from our analyses to aid the widespread adoption of facemasks would be: 'my mask protects you, your mask protects me'.

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'.

Estimating epidemiological parameters from experiments in vector access to host plants, the method of matching gradients

Estimation of pathogenic life-history values, for instance the duration a pathogen is retained in an insect vector (i.e., retention period) is of particular importance for understanding plant disease epidemiology. How can we extract values for these epidemiological parameters from conventional small-scale laboratory experiments in which transmission success is measured in relation to durations of vector access to host plants? We provide a solution to this problem by deriving formulae for the empirical curves that these experiments produce, called access period response curves (i.e., transmission success vs access period). We do this by writing simple equations for the fundamental life-cycle components of insect vectors in the laboratory. We then infer values of epidemiological parameters by matching the theoretical and empirical gradients of access period response curves. Using the example of Cassava brown streak virus (CBSV), which has emerged in sub-Saharan Africa and now threatens regional food security, we illustrate the method of matching gradients. We show how applying the method to published data produces a new understanding of CBSV through the inference of retention period, acquisition period and inoculation period parameters. We found that CBSV is retained for a far shorter duration in its insect vector (Bemisia tabaci whitefly) than had previously been assumed. Our results shed light on a number of critical factors that may be responsible for the transition of CBSV from sub- to super-threshold R₀ in sub-Saharan Africa. The method is applicable to plant pathogens in general, to supply epidemiological parameter estimates that are crucial for practical management of epidemics and prediction of pandemic risk.

Cassava brown streak virus (CBSV), which was confined to coastal East Africa and the shores of Lake Malawi, has rapidly expanded its geographic range and now threatens regional food security. A recent laboratory experiment, in which vector access to plants infected with CBSV is varied, has provided plausible ranges for epidemiological parameters such as pathogen retention period (i.e., the duration that the pathogen is retained by the vector). In this work we introduce a new computational and mathematical framework for estimating epidemiological parameter values, instead of plausible ranges, from experiments in vector access to host plants. Since long distance carriage of insect vectors occurs within atmospheric air flows, the duration that the vector retains the pathogen (i.e., retention period) indirectly limits the scale of epidemics. Using our methods, we found that CBSV is retained for a far shorter duration than had previously been assumed. Our methods can be applied to the many experiments in vector access to host plants that have been conducted for numerous arthropod-transmitted plant pathogens across a range of genera. The ensuing epidemiological parameter estimates can be used in landscape computer simulations to predict epidemic risk and the prospects for control.

Different Plant Viruses Induce Changes in Feeding Behavior of Specialist and Generalist Aphids on Common Bean That Are Likely to Enhance Virus Transmission

Bean common mosaic virus (BCMV), bean common mosaic necrosis virus (BCMNV), and cucumber mosaic virus (CMV) cause serious epidemics in common bean (Phaseolus vulgaris), a vital food security crop in many low-to-medium income countries, particularly in Sub-Saharan Africa. Aphids transmit these viruses "non-persistently," i.e., virions attach loosely to the insects' stylets. Viruses may manipulate aphid-host interactions to enhance transmission. We used direct observation and electrical penetration graph measurements to see if the three viruses induced similar or distinct changes in feeding behaviors of two aphid species, Aphis fabae and Myzus persicae. Both aphids vector BCMV, BCMNV, and CMV but A. fabae is a legume specialist (the dominant species in bean fields) while M. persicae is a generalist that feeds on and transmits viruses to diverse plant hosts. Aphids of both species commenced probing epidermal cells (behavior optimal for virus acquisition and inoculation) sooner on virus-infected plants than on mock-inoculated plants. Infection with CMV was especially disruptive of phloem feeding by the bean specialist aphid A. fabae. A. fabae also experienced mechanical stylet difficulty when feeding on virus-infected plants, and this was also exacerbated for M. persicae. Overall, feeding on virus-infected host plants by specialist and generalist aphids was affected in different ways but all three viruses induced similar effects on each aphid type. Specifically, non-specialist (M. persicae) aphids encountered increased stylet difficulties on plants infected with BCMV, BCMNV, or CMV, whereas specialist aphids (A. fabae) showed decreased phloem ingestion on infected plants. Probing and stylet pathway activity (which facilitate virus transmission) were not decreased by any of the viruses for either of the aphid species, except in the case of A. fabae on CMV-infected bean, where these activities were increased. Overall, these virus-induced changes in host-aphid interactions are likely to enhance non-persistent virus transmission, and data from this work will be useful in epidemiological modeling of non-persistent vectoring of viruses by aphids.

Three Aphid-Transmitted Viruses Encourage Vector Migration From Infected Common Bean (Phaseolus vulgaris) Plants Through a Combination of Volatile and Surface Cues

Bean common mosaic virus (BCMV), bean common mosaic necrosis virus (BCMNV), and cucumber mosaic virus (CMV) are important pathogens of common bean (Phaseolus vulgaris), a crop vital for food security in sub-Saharan Africa. These viruses are vectored by aphids non-persistently, with virions bound loosely to stylet receptors. These viruses also manipulate aphid-mediated transmission by altering host properties. Virus-induced effects on host-aphid interactions were investigated using choice test (migration) assays, olfactometry, and analysis of insect-perceivable volatile organic compounds (VOCs) using gas chromatography (GC)-coupled mass spectrometry, and GC-coupled electroantennography. When allowed to choose freely between infected and uninfected plants, aphids of the legume specialist species Aphis fabae, and of the generalist species Myzus persicae, were repelled by plants infected with BCMV, BCMNV, or CMV. However, in olfactometer experiments with A. fabae, only the VOCs emitted by BCMNV-infected plants repelled aphids. Although BCMV, BCMNV, and CMV each induced distinctive changes in emission of aphid-perceivable volatiles, all three suppressed emission of an attractant sesquiterpene, α-copaene, suggesting these three different viruses promote migration of virus-bearing aphids in a similar fashion.

Modelling and manipulation of aphid-mediated spread of non-persistently transmitted viruses

Aphids vector many plant viruses in a non-persistent manner i.e., virus particles bind loosely to the insect mouthparts (stylet). This means that acquisition of virus particles from infected plants, and inoculation of uninfected plants by viruliferous aphids, are rapid processes that require only brief probes of the plant's epidermal cells. Virus infection alters plant biochemistry, which causes changes in emission of volatile organic compounds and altered accumulation of nutrients and defence compounds in host tissues. These virus-induced biochemical changes can influence the migration, settling and feeding behaviours of aphids. Working mainly with cucumber mosaic virus and several potyviruses, a number of research groups have noted that in some plants, virus infection engenders resistance to aphid settling (sometimes accompanied by emission of deceptively attractive volatiles, that can lead to exploratory penetration by aphids without settling). However, in certain other hosts, virus infection renders plants more susceptible to aphid colonisation. It has been suggested that induction of resistance to aphid settling encourages transmission of non-persistently transmitted viruses, while induction of susceptibility to settling retards transmission. However, recent mathematical modelling indicates that both virus-induced effects contribute to epidemic development at different scales. We have also investigated at the molecular level the processes leading to induction, by cucumber mosaic virus, of feeding deterrence versus susceptibility to aphid infestation. Both processes involve complex interactions between specific viral proteins and host factors, resulting in manipulation or suppression of the plant's immune networks.

Expansion of the cassava brown streak pandemic in Uganda revealed by annual field survey data for 2004 to 2017

Cassava brown streak disease (CBSD) is currently the most devastating cassava disease in eastern, central and southern Africa affecting a staple crop for over 700 million people on the continent. A major outbreak of CBSD in 2004 near Kampala rapidly spread across Uganda. In the following years, similar CBSD outbreaks were noted in countries across eastern and central Africa, and now the disease poses a threat to West Africa including Nigeria - the biggest cassava producer in the world. A comprehensive dataset with 7,627 locations, annually and consistently sampled between 2004 and 2017 was collated from historic paper and electronic records stored in Uganda. The survey comprises multiple variables including data for incidence and symptom severity of CBSD and abundance of the whitefly vector (Bemisia tabaci). This dataset provides a unique basis to characterize the epidemiology and dynamics of CBSD spread in order to inform disease surveillance and management. We also describe methods used to integrate and verify extensive field records for surveys typical of emerging epidemics in subsistence crops.

An early warning system to predict and mitigate wheat rust diseases in Ethiopia

Wheat rust diseases pose one of the greatest threats to global food security, including subsistence farmers in Ethiopia. The fungal spores transmitting wheat rust are dispersed by wind and can remain infectious after dispersal over long distances. The emergence of new strains of wheat rust has exacerbated the risks of severe crop loss. We describe the construction and deployment of a near realtime early warning system (EWS) for two major wind-dispersed diseases of wheat crops in Ethiopia that combines existing environmental research infrastructures, newly developed tools and scientific expertise across multiple organisations in Ethiopia and the UK. The EWS encompasses a sophisticated framework that integrates field and mobile phone surveillance data, spore dispersal and disease environmental suitability forecasting, as well as communication to policy-makers, advisors and smallholder farmers. The system involves daily automated data flow between two continents during the wheat season in Ethiopia. The framework utilises expertise and environmental research infrastructures from within the cross-disciplinary spectrum of biology, agronomy, meteorology, computer science and telecommunications. The EWS successfully provided timely information to assist policy makers formulate decisions about allocation of limited stock of fungicide during the 2017 and 2018 wheat seasons. Wheat rust alerts and advisories were sent by short message service and reports to 10 000 development agents and approximately 275 000 smallholder farmers in Ethiopia who rely on wheat for subsistence and livelihood security. The framework represents one of the first advanced crop disease EWSs implemented in a developing country. It provides policy-makers, extension agents and farmers with timely, actionable information on priority diseases affecting a staple food crop. The framework together with the underpinning technologies are transferable to forecast wheat rusts in other regions and can be readily adapted for other wind-dispersed pests and disease of major agricultural crops.

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'.

Pathogenic modification of plants enhances long-distance dispersal of nonpersistently transmitted viruses to new hosts

Aphids spread the majority of plant viruses through nonpersistent transmission (NPT), whereby virus particles attach transiently to these insects’ probing mouthparts. Virus acquisition from infected plants and inoculation to healthy host plants is favored when aphids briefly probe plant epidermal cells. It is well established that NPT virus infection can alter plant–vector interactions, and, moreover, such pathogen modifications are found in a range of plant and animal systems. In particular, viruses can make plants more attractive to aphids but inhibit aphid settling on infected plants. It is hypothesized that this viral “reprogramming” of plants promotes virus acquisition and encourages dispersal of virus‐bearing aphids to fresh hosts. In contrast, it is hypothesized that virus‐induced biochemical changes encouraging prolonged feeding on infected hosts inhibit NPT. To understand how these virus‐induced modifications affect epidemics, we developed a modeling framework accounting for important but often neglected factors, including feeding behaviors (probing or prolonged feeding) and distinct spatial scales of transmission (as conditioned by wingless or winged aphids). Analysis of our models confirmed that when viruses inhibit aphid settling on infected plants this initially promotes virus transmission. However, initially enhanced transmission is self‐limiting because it decreases vector density. Another important finding is that virus‐induced changes encouraging settling will stimulate birth of winged aphids, which promotes epidemics of NPT viruses over greater distances. Thus our results illustrate how plant virus modifications influence epidemics by altering vector distribution, density, and even vector form. Our insights are important for understanding how pathogens in general propagate through natural plant communities and crops.

Resource Allocation for Epidemic Control Across Multiple Sub-populations

The number of pathogenic threats to plant, animal and human health is increasing. Controlling the spread of such threats is costly and often resources are limited. A key challenge facing decision makers is how to allocate resources to control the different threats in order to achieve the least amount of damage from the collective impact. In this paper we consider the allocation of limited resources across n independent target populations to treat pathogens whose spread is modelled using the susceptible–infected–susceptible model. Using mathematical analysis of the systems dynamics, we show that for effective disease control, with a limited budget, treatment should be focused on a subset of populations, rather than attempting to treat all populations less intensively. The choice of populations to treat can be approximated by a knapsack-type problem. We show that the knapsack closely approximates the exact optimum and greatly outperforms a number of simpler strategies. A key advantage of the knapsack approximation is that it provides insight into the way in which the economic and epidemiological dynamics affect the optimal allocation of resources. In particular using the knapsack approximation to apportion control takes into account two important aspects of the dynamics: the indirect interaction between the populations due to the shared pool of limited resources and the dependence on the initial conditions.

Variability in commercial demand for tree saplings affects the probability of introducing exotic forest diseases

Several devastating forest pathogens are suspected or known to have entered the UK through imported planting material. The nursery industry is a key business of the tree trade network. Variability in demand for trees makes it difficult for nursery owners to predict how many trees to produce in their nursery. When in any given year, the demand for trees is larger than the production, nursery owners buy trees from foreign sources to match market demand. These imports may introduce exotic diseases.

We have developed a model of the dynamics of plant production linked to an economic model. We have used this to quantify the effect of demand variability on the risk of introducing an exotic disease.

We find that: (a) When the cost of producing a tree in a UK nursery is considerably smaller than the cost of importing a tree (in the example presented, less than half the importing cost), the risk of introducing an exotic disease is hardly affected by an increase in demand variability. (b) When the cost of producing a tree in the nursery is smaller than, but not very different from the cost of importing a tree, the risk of importing exotic diseases increases with increasing demand variability.

Synthesis and applications. Our model and results demonstrate how a balanced management of demand variability and costs can reduce the risk of importing an exotic forest disease according to the management strategy adopted. For example, a management strategy that can reduce the demand variability, the ratio of production to import cost or both, optimizes the nursery gross margin when mainly own‐produced trees are commercialized. This can also translate into a reduction of the risk of introducing exotic forest diseases due to the small number of imported trees for sale.

Our model and results demonstrate how a balanced management of demand variability and costs can reduce the risk of importing an exotic forest disease according to the management strategy adopted. For example, a management strategy that can reduce the demand variability, the ratio of production to import cost or both, optimizes the nursery gross margin when mainly own‐produced trees are commercialized. This can also translate into a reduction of the risk of introducing exotic forest diseases due to the small number of imported trees for sale.

Microsatellite Analysis and Urediniospore Dispersal Simulations Support the Movement of Puccinia graminis f. sp. tritici from Southern Africa to Australia

The Australian wheat stem rust (Puccinia graminis f. sp. tritici) population was shaped by the introduction of four exotic incursions into the country. It was previously hypothesized that at least two of these (races 326-1,2,3,5,6 and 194-1,2,3,5,6 first detected in 1969) had an African origin and moved across the Indian Ocean to Australia on high-altitude winds. We provide strong supportive evidence for this hypothesis by combining genetic analyses and complex atmospheric dispersion modeling. Genetic analysis of 29 Australian and South African P. graminis f. sp. tritici races using microsatellite markers confirmed the close genetic relationship between the South African and Australian populations, thereby confirming previously described phenotypic similarities. Lagrangian particle dispersion model simulations using finely resolved meteorological data showed that long distance dispersal events between southern Africa and Australia are indeed possible, albeit rare. Simulated urediniospore transmission events were most frequent from central South Africa (viable spore transmission on approximately 7% of all simulated release days) compared with other potential source regions in southern Africa. The study acts as a warning of possible future P. graminis f. sp. tritici dispersal events from southern Africa to Australia, which could include members of the Ug99 race group, emphasizing the need for continued surveillance on both continents.

Viral Manipulation of Plant Stress Responses and Host Interactions With Insects

Do the alterations in plant defensive signaling and metabolism that occur in susceptible hosts following virus infection serve any purpose beyond directly aiding viruses to replicate and spread? Or indeed, are these modifications to host phenotype purely incidental consequences of virus infection? A growing body of data, in particular from studies of viruses vectored by whiteflies and aphids, indicates that viruses influence the efficiency of their own transmission by insect vectors and facilitate mutualistic relationships between viruses and their insect vectors. Furthermore, it appears that viruses may be able to increase the opportunity for transmission in the long term by providing reward to the host plants that they infect. This may be conditional, for example, by aiding host survival under conditions of drought or cold or, more surprisingly, by helping plants attract beneficial insects such as pollinators. In this chapter, we cover three main areas. First, we describe the molecular-level interactions governing viral manipulation of host plant biology. Second, we review evidence that virus-induced changes in plant phenotype enhance virus transmission. Finally, we discuss how direct and indirect manipulation of insects and plants might impact on the evolution of viruses and their hosts.

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

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

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.

Quantifying airborne dispersal routes of pathogens over continents to safeguard global wheat supply

Infectious crop diseases spreading over large agricultural areas pose a threat to food security. Aggressive strains of the obligate pathogenic fungus Puccinia graminis f.sp. tritici (Pgt), causing the crop disease wheat stem rust, have been detected in East Africa and the Middle East, where they lead to substantial economic losses and threaten livelihoods of farmers. The majority of commercially grown wheat cultivars worldwide are susceptible to these emerging strains, which pose a risk to global wheat production, because the fungal spores transmitting the disease can be wind-dispersed over regions and even continents ^1-11 . Targeted surveillance and control requires knowledge about airborne dispersal of pathogens, but the complex nature of long-distance dispersal poses significant challenges for quantitative research ^12-14 . We combine international field surveys, global meteorological data, a Lagrangian dispersion model and high-performance computational resources to simulate a set of disease outbreak scenarios, tracing billions of stochastic trajectories of fungal spores over dynamically changing host and environmental landscapes for more than a decade. This provides the first quantitative assessment of spore transmission frequencies and amounts amongst all wheat producing countries in Southern/East Africa, the Middle East and Central/South Asia. We identify zones of high air-borne connectivity that geographically correspond with previously postulated wheat rust epidemiological zones (characterized by endemic disease and free movement of inoculum) ^10,15 , and regions with genetic similarities in related pathogen populations ^16,17 . We quantify the circumstances (routes, timing, outbreak sizes) under which virulent pathogen strains such as 'Ug99' ^5,6 pose a threat from long-distance dispersal out of East Africa to the large wheat producing areas in Pakistan and India. Long-term mean spore dispersal trends (predominant direction, frequencies, amounts) are summarized for all countries in the domain (Supplementary Data). Our mechanistic modelling framework can be applied to other geographic areas, adapted for other pathogens and used to provide risk assessments in real-time ³ .

Large-Scale Atmospheric Dispersal Simulations Identify Likely Airborne Incursion Routes of Wheat Stem Rust Into Ethiopia

In recent years, severe wheat stem rust epidemics hit Ethiopia, sub-Saharan Africa's largest wheat-producing country. These were caused by race TKTTF (Digalu race) of the pathogen Puccinia graminis f. sp. tritici, which, in Ethiopia, was first detected at the beginning of August 2012. We use the incursion of this new pathogen race as a case study to determine likely airborne origins of fungal spores on regional and continental scales by means of a Lagrangian particle dispersion model (LPDM). Two different techniques, LPDM simulations forward and backward in time, are compared. The effects of release altitudes in time-backward simulations and P. graminis f. sp. tritici urediniospore viability functions in time-forward simulations are analyzed. Results suggest Yemen as the most likely origin but, also, point to other possible sources in the Middle East and the East African Rift Valley. This is plausible in light of available field surveys and phylogenetic data on TKTTF isolates from Ethiopia and other countries. Independent of the case involving TKTTF, we assess long-term dispersal trends (>10 years) to obtain quantitative estimates of the risk of exotic P. graminis f. sp. tritici spore transport (of any race) into Ethiopia for different 'what-if' scenarios of disease outbreaks in potential source countries in different months of the wheat season.

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.

Market analyses of livestock trade networks to inform the prevention of joint economic and epidemiological risks

Conventional epidemiological studies of infections spreading through trade networks, e.g. via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic–epidemiological risks in networks underlying pathogen propagation and trade.

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.

Modeling when, where, and how to manage a forest epidemic, motivated by sudden oak death in California

Sudden oak death, caused by Phytophthora ramorum, has killed millions of oak and tanoak in California since its first detection in 1995. Despite some localized small-scale management, there has been no large-scale attempt to slow the spread of the pathogen in California. Here we use a stochastic spatially explicit model parameterized using data on the spread of P. ramorum to investigate whether and how the epidemic can be controlled. We find that slowing the spread of P. ramorum is now not possible, and has been impossible for a number of years. However, despite extensive cryptic (i.e., presymptomatic) infection and frequent long-range transmission, effective exclusion of the pathogen from large parts of the state could, in principle, have been possible were it to have been started by 2002. This is the approximate date by which sufficient knowledge of P. ramorum epidemiology had accumulated for large-scale management to be realistic. The necessary expenditure would have been very large, but could have been greatly reduced by optimizing the radius within which infected sites are treated and careful selection of sites to treat. In particular, we find that a dynamic strategy treating sites on the epidemic wave front leads to optimal performance. We also find that "front loading" the budget, that is, treating very heavily at the start of the management program, would greatly improve control. Our work introduces a framework for quantifying the likelihood of success and risks of failure of management that can be applied to invading pests and pathogens threatening forests worldwide.

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.

Phenotypic and Genotypic Characterization of Race TKTTF of Puccinia graminis f. sp. tritici that Caused a Wheat Stem Rust Epidemic in Southern Ethiopia in 2013-14

A severe stem rust epidemic occurred in southern Ethiopia during November 2013 to January 2014, with yield losses close to 100% on the most widely grown wheat cultivar, 'Digalu'. Sixty-four stem rust samples collected from the regions were analyzed. A meteorological model for airborne spore dispersal was used to identify which regions were most likely to have been infected from postulated sites of initial infection. Based on the analyses of 106 single-pustule isolates derived from these samples, four races of Puccinia graminis f. sp. tritici were identified: TKTTF, TTKSK, RRTTF, and JRCQC. Race TKTTF was found to be the primary cause of the epidemic in the southeastern zones of Bale and Arsi. Isolates of race TKTTF were first identified in samples collected in early October 2013 from West Arsi. It was the sole or predominant race in 31 samples collected from Bale and Arsi zones after the stem rust epidemic was established. Race TTKSK was recovered from 15 samples from Bale and Arsi zones at low frequencies. Genotyping indicated that isolates of race TKTTF belongs to a genetic lineage that is different from the Ug99 race group and is composed of two distinct genetic types. Results from evaluation of selected germplasm indicated that some cultivars and breeding lines resistant to the Ug99 race group are susceptible to race TKTTF. Appearance of race TKTTF and the ensuing epidemic underlines the continuing threats and challenges posed by stem rust not only in East Africa but also to wider-scale wheat production.

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.

Cost-effective control of plant disease when epidemiological knowledge is incomplete: modelling Bahia bark scaling of citrus

A spatially-explicit, stochastic model is developed for Bahia bark scaling, a threat to citrus production in north-eastern Brazil, and is used to assess epidemiological principles underlying the cost-effectiveness of disease control strategies. The model is fitted via Markov chain Monte Carlo with data augmentation to snapshots of disease spread derived from a previously-reported multi-year experiment. Goodness-of-fit tests strongly supported the fit of the model, even though the detailed etiology of the disease is unknown and was not explicitly included in the model. Key epidemiological parameters including the infection rate, incubation period and scale of dispersal are estimated from the spread data. This allows us to scale-up the experimental results to predict the effect of the level of initial inoculum on disease progression in a typically-sized citrus grove. The efficacies of two cultural control measures are assessed: altering the spacing of host plants, and roguing symptomatic trees. Reducing planting density can slow disease spread significantly if the distance between hosts is sufficiently large. However, low density groves have fewer plants per hectare. The optimum density of productive plants is therefore recovered at an intermediate host spacing. Roguing, even when detection of symptomatic plants is imperfect, can lead to very effective control. However, scouting for disease symptoms incurs a cost. We use the model to balance the cost of scouting against the number of plants lost to disease, and show how to determine a roguing schedule that optimises profit. The trade-offs underlying the two optima we identify-the optimal host spacing and the optimal roguing schedule-are applicable to many pathosystems. Our work demonstrates how a carefully parameterised mathematical model can be used to find these optima. It also illustrates how mathematical models can be used in even this most challenging of situations in which the underlying epidemiology is ill-understood.

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 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.

Optimal control of disease infestations on a lattice

The design of durable and sustainable strategies for the control of plant diseases is not possible without due consideration of landscape structure and economic factors. However, many studies on control strategies of plant infestation have overlooked these considerations. In this paper, we address the problem of how best to deploy resources for the control of disease outbreaks during a single agricultural season. We consider a spatial model for the spread of a plant pathogen over an agricultural region, and model the effect of control on disease dynamics. We associate with a control strategy a 'costs function' that balances amount invested for treatment to the cost incurred by disease infestation. Our objective is to minimize the level of disease infestation and the effort of control. We prove the existence of a solution to the optimal control problem, and devise a numerical algorithm to compute it. We present results of our numerical studies, and show that the solution depends on the interplay between economic and epidemiological factors, as well as the nature of the control agent.

Interference with jasmonic acid-regulated gene expression is a general property of viral suppressors of RNA silencing but only partly explains virus-induced changes in plant-aphid interactions

The cucumber mosaic virus (CMV) 2b viral suppressor of RNA silencing (VSR) inhibits host responses to jasmonic acid (JA), a chemical signal regulating resistance to insects. Previous experiments with a CMV subgroup IA strain and its 2b gene deletion mutant suggested that VSRs might neutralize aphid (Myzus persicae) resistance by inhibiting JA-regulated gene expression. To further investigate this, we examined JA-regulated gene expression and aphid performance in Nicotiana benthamiana infected with Potato virus X, Potato virus Y, Tobacco mosaic virus and a subgroup II CMV strain, as well as in transgenic plants expressing corresponding VSRs (p25, HC-Pro, 126 kDa and 2b). All the viruses or their VSRs inhibited JA-induced gene expression. However, this did not always correlate with enhanced aphid performance. Thus, VSRs are not the sole viral determinants of virus-induced changes in host-aphid interactions and interference with JA-regulated gene expression cannot completely explain enhanced aphid performance on virus-infected plants.

Estimating the delay between host infection and disease (incubation period) and assessing its significance to the epidemiology of plant diseases

Knowledge of the incubation period of infectious diseases (time between host infection and expression of disease symptoms) is crucial to our epidemiological understanding and the design of appropriate prevention and control policies. Plant diseases cause substantial damage to agricultural and arboricultural systems, but there is still very little information about how the incubation period varies within host populations. In this paper, we focus on the incubation period of soilborne plant pathogens, which are difficult to detect as they spread and infect the hosts underground and above-ground symptoms occur considerably later. We conducted experiments on Rhizoctonia solani in sugar beet, as an example patho-system, and used modelling approaches to estimate the incubation period distribution and demonstrate the impact of differing estimations on our epidemiological understanding of plant diseases. We present measurements of the incubation period obtained in field conditions, fit alternative probability models to the data, and show that the incubation period distribution changes with host age. By simulating spatially-explicit epidemiological models with different incubation-period distributions, we study the conditions for a significant time lag between epidemics of cryptic infection and the associated epidemics of symptomatic disease. We examine the sensitivity of this lag to differing distributional assumptions about the incubation period (i.e. exponential versus Gamma). We demonstrate that accurate information about the incubation period distribution of a pathosystem can be critical in assessing the true scale of pathogen invasion behind early disease symptoms in the field; likewise, it can be central to model-based prediction of epidemic risk and evaluation of disease management strategies. Our results highlight that reliance on observation of disease symptoms can cause significant delay in detection of soil-borne pathogen epidemics and mislead practitioners and epidemiologists about the timing, extent, and viability of disease control measures for limiting economic loss.

Quantitative resistance can lead to evolutionary changes in traits not targeted by the resistance QTLs

This paper addresses the general concern in plant pathology that the introduction of quantitative resistance in the landscape can lead to increased pathogenicity. Hereto, we study the hypothetical case of a quantitative trait loci (QTL) acting on pathogen spore production per unit lesion area. To regain its original fitness, the pathogen can break the QTL, restoring its spore production capacity leading to an increased spore production per lesion. Or alternatively, it can increase its lesion size, also leading to an increased spore production per lesion. A data analysis shows that spore production per lesion (affected by the resistance QTL) and lesion size (not targeted by the QTL) are positively correlated traits, suggesting that a change in magnitude of a trait not targeted by the QTL (lesion size) might indirectly affect the targeted trait (spore production per lesion). Secondly, we model the effect of pathogen adaptation towards increased lesion size and analyse its consequences for spore production per lesion. The model calculations show that when the pathogen is unable to overcome the resistance associated QTL, it may compensate for its reduced fitness by indirect selection for increased pathogenicity on both the resistant and susceptible cultivar, but whereby the QTLs remain effective.

The consequence of tree pests and diseases for ecosystem services

Trees and forests provide a wide variety of ecosystem services in addition to timber, food, and other provisioning services. New approaches to pest and disease management are needed that take into account these multiple services and the different stakeholders they benefit, as well as the likelihood of greater threats in the future resulting from globalization and climate change. These considerations will affect priorities for both basic and applied research and how trade and phytosanitary regulations are formulated.

Percolation-based risk index for pathogen invasion: application to soilborne disease in propagation systems

Propagation systems for seedling growth play a major role in agriculture, and in notable cases (such as organic systems), are under constant threat from soil and seedborne fungal plant pathogens such as Rhizoctonia solani or Pythium spp. Yet, to date little is known that links the risk of disease invasion to the host density, which is an agronomic characteristic that can be readily controlled. We introduce here, for the first time in an agronomic system, a percolation framework to analyze the link. We set up an experiment to study the spread of the ubiquitous fungus R. solani in replicated propagation systems with different planting densities, and fit a percolation-based epidemiological model to the data using Bayesian inference methods. The estimated probability of pathogen transmission between infected and susceptible plants is used to calculate the risk of invasion. By comparing the transmission probability and the risk values obtained for different planting densities, we are able to give evidence of a nonlinear relationship between disease invasion and the inter-plant spacing, hence to demonstrate the existence of a spatial threshold for epidemic invasion. The implications and potential use of our methods for the evaluation of disease control strategies are discussed.

Host growth can cause invasive spread of crops by soilborne pathogens

Invasive soilborne plant pathogens cause substantial damage to crops and natural populations, but our understanding of how to prevent their epidemics or reduce their damage is limited. A key and experimentally-tested concept in the epidemiology of soilborne plant diseases is that of a threshold spacing between hosts below which epidemics (invasive spread) can occur. We extend this paradigm by examining how plant-root growth may alter the conditions for occurrence of soilborne pathogen epidemics in plant populations. We hypothesise that host-root growth can 1) increase the probability of pathogen transmission between neighbouring plants and, consequently, 2) decrease the threshold spacing for epidemics to occur. We predict that, in systems initially below their threshold conditions, root growth can trigger soilborne pathogen epidemics through a switch from non-invasive to invasive behaviour, while in systems above threshold conditions root growth can enhance epidemic development. As an example pathosystem, we studied the fungus Rhizoctonia solani on sugar beet in field experiments. To address hypothesis 1, we recorded infections within inoculum-donor and host-recipient pairs of plants with differing spacing. We translated these observations into the individual-level concept of pathozone, a host-centred form of dispersal kernel. To test hypothesis 2 and our prediction, we used the pathozone to parameterise a stochastic model of pathogen spread in a host population, contrasting scenarios of spread with and without host growth. Our results support our hypotheses and prediction. We suggest that practitioners of agriculture and arboriculture account for root system expansion in order to reduce the risk of soilborne-disease epidemics. We discuss changes in crop design, including increasing plant spacing and using crop mixtures, for boosting crop resilience to invasion and damage by soilborne pathogens. We speculate that the disease-induced root growth observed in some pathosystems could be a pathogen strategy to increase its population through host manipulation.

Prediction of invasion from the early stage of an epidemic

Predictability of undesired events is a question of great interest in many scientific disciplines including seismology, economy and epidemiology. Here, we focus on the predictability of invasion of a broad class of epidemics caused by diseases that lead to permanent immunity of infected hosts after recovery or death. We approach the problem from the perspective of the science of complexity by proposing and testing several strategies for the estimation of important characteristics of epidemics, such as the probability of invasion. Our results suggest that parsimonious approximate methodologies may lead to the most reliable and robust predictions. The proposed methodologies are first applied to analysis of experimentally observed epidemics: invasion of the fungal plant pathogen Rhizoctonia solani in replicated host microcosms. We then consider numerical experiments of the susceptible-infected-removed model to investigate the performance of the proposed methods in further detail. The suggested framework can be used as a valuable tool for quick assessment of epidemic threat at the stage when epidemics only start developing. Moreover, our work amplifies the significance of the small-scale and finite-time microcosm realizations of epidemics revealing their predictive power.