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.

Wheat rust epidemics damage Ethiopian wheat production: A decade of field disease surveillance reveals national-scale trends in past outbreaks.

Wheat rusts are the key biological constraint to wheat production in Ethiopia-one of Africa's largest wheat producing countries. The fungal diseases cause economic losses and threaten livelihoods of smallholder farmers. While it is known that wheat rust epidemics have occurred in Ethiopia, to date no systematic long-term analysis of past outbreaks has been available. We present results from one of the most comprehensive surveillance campaigns of wheat rusts in Africa. More than 13,000 fields have been surveyed during the last 13 years. Using a combination of spatial data-analysis and visualization, statistical tools, and empirical modelling, we identify trends in the distribution of wheat stem rust (Sr), stripe rust (Yr) and leaf rust (Lr). Results show very high infection levels (mean incidence for Yr: 44%; Sr: 34%; Lr: 18%). These recurrent rust outbreaks lead to substantial economic losses, which we estimate to be of the order of 10s of millions of US-D annually. On the widely adopted wheat variety, Digalu, there is a marked increase in disease prevalence following the incursion of new rust races into Ethiopia, which indicates a pronounced boom-and-bust cycle of major gene resistance. Using spatial analyses, we identify hotspots of disease risk for all three rusts, show a linear correlation between altitude and disease prevalence, and find a pronounced north-south trend in stem rust prevalence. Temporal analyses show a sigmoidal increase in disease levels during the wheat season and strong inter-annual variations. While a simple logistic curve performs satisfactorily in predicting stem rust in some years, it cannot account for the complex outbreak patterns in other years and fails to predict the occurrence of stripe and leaf rust. The empirical insights into wheat rust epidemiology in Ethiopia presented here provide a basis for improving future surveillance and to inform the development of mechanistic models to predict disease spread.

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.

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'.

What a Difference a Stochastic Process Makes: Epidemiological-Based Real Options Models of Optimal Treatment of Disease.

The real options approach has been used within environmental economics to investigate the impact of uncertainty on the optimal timing of control measures to minimise the impacts of invasive species, including pests and diseases. Previous studies typically model the growth in infected area using geometric Brownian motion (GBM). The advantage of this simple approach is that it allows for closed form solutions. However, such a process does not capture the mechanisms underlying the spread of infection. In particular the GBM assumption does not respect the natural upper boundary of the system, which is determined by the maximum size of the host species, nor the deceleration in the rate of infection as this boundary is approached. We show how the stochastic process describing the growth in infected area can be derived from the characteristics of the spread of infection. If the model used does not appropriately capture uncertainty in infection dynamics, then the excessive delay before treatment implies that the full value of the option to treat is not realised. Indeed, when uncertainty is high or the disease is fast spreading, ignoring the mechanisms of infection spread can lead to control never being deployed. Thus the results presented here have important implications for the way in which the real options approach is applied to determine optimal timing of disease control given uncertainty in future disease progression.

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.

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.

Prominent effect of soil network heterogeneity on microbial invasion.

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil.

Time-dependent infectivity and flexible latent and infectious periods in compartmental models of plant disease.

Compartmental models have become the dominant theoretical paradigm in mechanistic modeling of plant disease and offer well-known advantages in terms of analytic tractability, ease of simulation, and extensibility. However, underlying assumptions of constant rates of infection and of exponentially distributed latent and infectious periods are difficult to justify. Although alternative approaches, including van der Plank's seminal discrete time model and models based on the integro-differential formulation of Kermack and McKendrick's model, have been suggested for plant disease and relax these unrealistic assumptions, they are challenging to implement and to analyze. Here, we propose an extension to the susceptible, exposed, infected, and removed (SEIR) compartmental model, splitting the latent and infection compartments and thereby allowing time-varying infection rates and more realistic distributions of latent and infectious periods to be represented. Although the model is, in fact, more general, we specifically target plant disease by demonstrating how it can represent both the van der Plank model and the most commonly used variant of the Kermack and McKendrick (K & M) model (in which the infectivity response is delay Gamma distributed). We show how our reformulation retains the numeric and analytic tractability of SEIR models, and how it can be used to replicate earlier analyses of the van der Plank and K & M models. Our reformulation has the advantage of using elementary mathematical techniques, making implementation easier for the nonspecialist. We show a practical implication of these results for disease control. By taking advantage of the easy extensibility characteristic of compartmental models, we also investigate the effects of including additional biological realism. As an example, we show how the more realistic infection responses we consider interact with host demography and lead to divergent invasion thresholds when compared with the "standard" SEIR model. An ever-increasing number of analyses purportedly extract more biologically realistic invasion thresholds by adding additional biological detail to the SEIR model framework; we contend that our results demonstrate that extending a model that has such a simplistic representation of the infection dynamics may not, in fact, lead to more accurate results. Therefore, we suggest that modelers should carefully consider the underlying assumptions of the simplest compartmental models in their future work.

Spatial sampling to detect an invasive pathogen outside of an eradication zone.

Invasive pathogens are known to cause major damage to the environments they invade. Effective control of such invasive pathogens depends on early detection. In this paper we focus on sampling with the aim of detecting an invasive pathogen. To that end, we introduce the concept of optimized spatial sampling, using spatial simulated annealing, to plant pathology. It has been mathematically proven (15) that this optimization method converges to the optimum allocation of sampling points that give the largest detection probability. We show the benefits of the method to plant pathology by (i) first illustrating that optimized spatial sampling can easily be applied for disease detection, and then we show that (ii) combining it with a spatially explicit epidemic model, we can develop optimum sample schemes, i.e., optimum locations to sample that maximize the probability of detecting an invasive pathogen. This method is then used as baseline against which other sampling methods can be tested for their accuracy. For the specific example case of this paper, we test (i) random sampling, (ii) stratified sampling as well as (iii) sampling based on the output of the simulation model (using the most frequently infected hosts as sample points), and (iv) sampling the hosts closest to the outbreak point.

Epidemics in networks of spatially correlated three-dimensional root-branching structures.

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected-recovered ('SIR') epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.

Periodicity in host availability does not account for evolutionary branching as observed in many plant pathogens: an application to Gaeumannomyces graminis var. tritici.

Periodicity in host availability is common in agricultural systems. Although it is known to have profound effects on plant pathogen abundance, the evolutionary consequences of periodicity for the pathogen population have not previously been analyzed. An epidemiological model incorporating periodic absence of the host crop is combined with the theory of adaptive dynamics to determine whether or not seasonality in host presence plays a role in the occurrence of evolutionary branching, leading to coexisting yet genetically distinct pathogen phenotypes. The study is motivated and illustrated by the specific example of take-all disease of wheat, caused by the pathogen Gaeumannomyces graminis var. tritici, for which two coexisting but genetically distinct types and a trade-off related to seasonality in host presence have been identified. Numerical simulations are used to show that a trade-off between the pathogen transmission rate and the survival of the pathogen between cropping seasons cannot account for the evolutionary branching observed in many pathogens. Model elaborations show that this conclusion holds for a broad range of putative mechanisms. Although the analysis is motivated and illustrated by the specific example of take-all of wheat, the results apply to a broad range of pathogens.

The effect of landscape pattern on the optimal eradication zone of an invading epidemic.

A number of high profile eradication attempts on plant pathogens have recently been attempted in response to the increasing number of introductions of economically significant nonnative pathogen species. Eradication programs involve the removal of a large proportion of a host population and can thus lead to significant social and economic costs. In this paper we use a spatially explicit stochastic model to simulate an invading pathogen and show that it is possible to identify an optimal control radius, i.e., one that minimizes the total number of hosts removed during an eradication campaign that is effective in eradicating the pathogen. However, by simulating the epidemic and eradication processes in multiple landscapes, we demonstrate that the optimal radius depends critically on landscape pattern (i.e., the spatial configuration of hosts within the landscape). In particular, we find that the optimal radius, and also the number of host removals associated with it, increases with both the level of aggregation and the density of hosts in the landscape. The result is of practical significance and demonstrates that the location of an invading epidemic should be a key consideration in the design of future eradication strategies.

Optimal strategies for the eradication of asiatic citrus canker in heterogeneous host landscapes.

ABSTRACT The eradication of nonnative plant pathogens is a key challenge in plant disease epidemiology. Asiatic citrus canker is an economically significant disease of citrus caused by the bacterial plant pathogen Xanthomonas citri subsp. citri. The pathogen is a major exotic disease problem in many citrus producing areas of the world including the United States, Brazil, and Australia. Various eradication attempts have been made on the disease but have been associated with significant social and economic costs due to the necessary removal of large numbers of host trees. In this paper, a spatially explicit stochastic simulation model of Asiatic citrus canker is introduced that describes an epidemic of the disease in a heterogeneous host landscape. We show that an optimum eradication strategy can be determined that minimizes the adverse costs associated with eradication. In particular, we show how the optimum strategy and its total cost depend on the topological arrangement of the host landscape. We discuss the implications of the results for invading plant disease epidemics in general and for historical and future eradication attempts on Asiatic citrus canker.

Epidemiological analysis of take-all decline in winter wheat.

Take-all dynamics within crops differing in cropping history (the number of previous consecutive wheat crops) were analyzed using an epidemiological model to determine the processes affected during take-all decline. The model includes terms for primary infection, secondary infection, inoculum decay, and root growth. The average rates of root production did not vary with cropping history. The force of primary infection increased from a low level in 1st wheat crops, to a maximum in 2nd to 4th wheat crops, and then to intermediate levels thereafter. The force of secondary infection was low but increased steadily during the season in first wheat crops, was delayed but rose and fell sharply in 2nd to 4th wheat crops, and for 5th and 7th wheat crops returned to similar dynamics as that for 1st wheat crops. Chemical seed treatment with silthiofam had no consistent effect on the take-all decline process. We conjecture that these results are consistent with (i) low levels of particulate inoculum prior to the first wheat crop leading to low levels of primary infection, low levels of secondary infection, and little disease suppression; (ii) net amplification of inoculum during the first wheat crop and intercrop period; (iii) increased levels of primary and secondary infection in subsequent crops, but higher levels of disease suppression; and (iv) an equilibrium between the pathogen and antagonist populations by the 5th wheat, reflected by lower overall rates of primary infection, secondary infection, disease suppression and hence, disease severity.

A fungal growth model fitted to carbon-limited dynamics of Rhizoctonia solani.

Here, a quasi-steady-state approximation was used to simplify a mathematical model for fungal growth in carbon-limiting systems, and this was fitted to growth dynamics of the soil-borne plant pathogen and saprotroph Rhizoctonia solani. The model identified a criterion for invasion into carbon-limited environments with two characteristics driving fungal growth, namely the carbon decomposition rate and a measure of carbon use efficiency. The dynamics of fungal spread through a population of sites with either low (0.0074 mg) or high (0.016 mg) carbon content were well described by the simplified model with faster colonization for the carbon-rich environment. Rhizoctonia solani responded to a lower carbon availability by increasing the carbon use efficiency and the carbon decomposition rate following colonization. The results are discussed in relation to fungal invasion thresholds in terms of carbon nutrition.

Constructing the effect of alternative intervention strategies on historic epidemics.

Data from historical epidemics provide a vital and sometimes under-used resource from which to devise strategies for future control of disease. Previous methods for retrospective analysis of epidemics, in which alternative interventions are compared, do not make full use of the information; by using only partial information on the historical trajectory, augmentation of control may lead to predictions of a paradoxical increase in disease. Here we introduce a novel statistical approach that takes full account of the available information in constructing the effect of alternative intervention strategies in historic epidemics. The key to the method lies in identifying a suitable mapping between the historic and notional outbreaks, under alternative control strategies. We do this by using the Sellke construction as a latent process linking epidemics. We illustrate the application of the method with two examples. First, using temporal data for the common human cold, we show the improvement under the new method in the precision of predictions for different control strategies. Second, we show the generality of the method for retrospective analysis of epidemics by applying it to a spatially extended arboreal epidemic in which we demonstrate the relative effectiveness of host culling strategies that differ in frequency and spatial extent. Some of the inferential and philosophical issues that arise are discussed along with the scope of potential application of the new method.