Cassava viral diseases, including Cassava Mosaic Disease (CMD) and Cassava Brown Streak Disease (CBSD), pose significant threats to global food security, particularly in sub-Saharan Africa. This study explores the potential of varietal mixtures as a sustainable disease management strategy by introducing CropMix, a novel web-based application. The application encodes a flexible insect-borne plant pathogen transmission model to predict and optimize yields under scenarios of varietal mixtures. For instance, we use the application to evaluate the ability of virus-resistant cassava varieties (which may have lower yields in the absence of disease) to protect more susceptible varieties against CMD and CBSD, and we also consider mixtures involving tolerant varieties and non-host crops. For CMD, the high transmission rates of cassava mosaic virus (genus Begomovirus) limits the efficacy of mixtures, with susceptible monocultures emerging as more productive than susceptible-resistant mixtures whatever the whitefly pressure. In contrast, for CBSD, varietal mixtures demonstrate substantial benefits, with resistant varieties shielding susceptible ones and mitigating severe yield losses under moderate or high insect pressure. Management strategies involving non-host crops and complementary control measures, such as roguing, can further enhance outcomes. The model's simplicity and adaptability make it suitable for tailoring recommendations to diverse insect-borne crop viral diseases and agroecological contexts. The study emphasizes the need for integrating real-world data and participatory frameworks to refine and implement disease management strategies. We discuss the critical balance between agronomic potential and farmer acceptability, underscoring the importance of collaborative efforts to ensure sustainable cassava production.

There is an urgent need for mathematical models that can be used to inform the deployment of surveillance, early warning and management systems for transboundary pest invasions. This is especially important for desert locust, one of the most dangerous migratory pests for smallholder farmers. During periods of desert locust upsurges and plagues, gregarious adult locusts form into swarms that are capable of long-range dispersal. Here we introduce a novel integrated modelling framework for use in predicting gregarious locust populations. The framework integrates the selection of breeding sites, maturation through egg, hopper and adult stages and swarm dispersal in search of areas suitable for feeding and breeding. Using a combination of concepts from epidemiological modelling, weather and environment data, together with an atmospheric transport model for swarm movement we provide a tool to forecast short- and long-term swarm movements. A principal aim of the framework is to provide a practical starting point for use in the next upsurge.

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.

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.

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 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.

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.

Stochastic simulations are developed and employed across many fields, to advise governmental policy decisions and direct future research. Faulty simulation software can have serious consequences, but its correctness is difficult to determine due to complexity and random behaviour. Stochastic simulations may output a different result each time they are run, whereas most testing techniques are designed for programs which (for a given set of inputs) always produce the same behaviour. In this paper, we introduce a new approach towards testing stochastic simulations using statistical oracles and transition probabilities. Our approach was implemented as a toolkit, which allows the frequency of state transitions to be tested, along with their final output distribution. We evaluated our toolkit on eight simulation programs from a variety fields and found it can detect errors at least three times smaller (and in one case, over 1000 times smaller) than a conventional (tolerance threshold) approach.

Trade or sharing that moves infectious planting material between farms can, for vertically-transmitted plant diseases, act as a significant force for dispersal of pathogens, particularly where the extent of material movement may be greater than that of infected vectors or inoculum. The network over which trade occurs will then effect dispersal, and is important to consider when attempting to control the disease. We consider the difference that planting material exchange can make to successful control of cassava brown streak disease, an important viral disease affecting one of Africa's staple crops. We use a mathematical model of smallholders' fields to determine the effect of informal trade on both the spread of the pathogen and its control using clean-seed systems, determining aspects that could limit the damage caused by the disease. In particular, we identify the potentially detrimental effects of markets, and the benefits of a community-based approach to disease control.

Stochastic models can be difficult to test due to their complexity and randomness, yet their predictions are often used to make important decisions, so they need to be correct. We introduce a new search-based technique for testing implementations of stochastic models by maximising the differences between the implementation and a pseudo-oracle. Our technique reduces testing effort and enables discrepancies to be found that might otherwise be overlooked. We show the technique can identify differences challenging for humans to observe, and use it to help a new user understand implementation differences in a real model of a citrus disease (Huanglongbing) used to inform policy and research.

It is difficult to test programs that input images, due to the large number of (pixel) values that must be chosen and the complex ways these values interact. Typically, such programs are tested manually, using images that have known results. However, this is a laborious process and limited in the range of tests that can be applied. We introduce a new approach for testing programs that input images automatically, using procedural noise and spatial statistics to create inputs that are both realistic and can easily be tuned to have specific properties. The effectiveness of our approach is illustrated on an epidemiological simulation of a recently introduced tree pest in Great Britain: Oriental Chestnut Gall Wasp. Our approach produces images that match the real landscapes more closely than other techniques and can be used (alongside metamorphic relations) to detect smaller (artificially introduced) errors with greater accuracy.

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.

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.

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.

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.

Increasing the durability of crop resistance to plant pathogens is one of the key goals of virulence management. Despite the recognition of the importance of demographic and environmental stochasticity on the dynamics of an epidemic, their effects on the evolution of the pathogen and durability of resistance has not received attention. We formulated a stochastic epidemiological model, based on the Kramer-Moyal expansion of the Master Equation, to investigate how random fluctuations affect the dynamics of an epidemic and how these effects feed through to the evolution of the pathogen and durability of resistance. We focused on two hypotheses: firstly, a previous deterministic model has suggested that the effect of cropping ratio (the proportion of land area occupied by the resistant crop) on the durability of crop resistance is negligible. Increasing the cropping ratio increases the area of uninfected host, but the resistance is more rapidly broken; these two effects counteract each other. We tested the hypothesis that similar counteracting effects would occur when we take account of demographic stochasticity, but found that the durability does depend on the cropping ratio. Secondly, we tested whether a superimposed external source of stochasticity (for example due to environmental variation or to intermittent fungicide application) interacts with the intrinsic demographic fluctuations and how such interaction affects the durability of resistance. We show that in the pathosystem considered here, in general large stochastic fluctuations in epidemics enhance extinction of the pathogen. This is more likely to occur at large cropping ratios and for particular frequencies of the periodic external perturbation (stochastic resonance). The results suggest possible disease control practises by exploiting the natural sources of stochasticity.

Exotic pathogens and pests threaten ecosystem service, biodiversity, and crop security globally. If an invasive agent can disperse asymptomatically over long distances, multiple spatial and temporal scales interplay, making identification of effective strategies to regulate, monitor, and control disease extremely difficult. The management of outbreaks is also challenged by limited data on the actual area infested and the dynamics of spatial spread, due to financial, technological, or social constraints. We examine principles of landscape epidemiology important in designing policy to prevent or slow invasion by such organisms, and use Phytophthora ramorum, the cause of sudden oak death, to illustrate how shortfalls in their understanding can render management applications inappropriate. This pathogen has invaded forests in coastal California, USA, and an isolated but fast-growing epidemic focus in northern California (Humboldt County) has the potential for extensive spread. The risk of spread is enhanced by the pathogen's generalist nature and survival. Additionally, the extent of cryptic infection is unknown due to limited surveying resources and access to private land. Here, we use an epidemiological model for transmission in heterogeneous landscapes and Bayesian Markov-chain-Monte-Carlo inference to estimate dispersal and life-cycle parameters of P. ramorum and forecast the distribution of infection and speed of the epidemic front in Humboldt County. We assess the viability of management options for containing the pathogen's northern spread and local impacts. Implementing a stand-alone host-free "barrier" had limited efficacy due to long-distance dispersal, but combining curative with preventive treatments ahead of the front reduced local damage and contained spread. While the large size of this focus makes effective control expensive, early synchronous treatment in newly-identified disease foci should be more cost-effective. We show how the successful management of forest ecosystems depends on estimating the spatial scales of invasion and treatment of pathogens and pests with cryptic long-distance dispersal.

Heterogeneity in host populations is an important factor affecting the ability of a pathogen to invade, yet the quantitative investigation of its effects on epidemic spread is still an open problem. In this paper, we test recent theoretical results, which extend the established "percolation paradigm" to the spread of a pathogen in discrete heterogeneous host populations. In particular, we test the hypothesis that the probability of epidemic invasion decreases when host heterogeneity is increased. We use replicated experimental microcosms, in which the ubiquitous pathogenic fungus Rhizoctonia solani grows through a population of discrete nutrient sites on a lattice, with nutrient sites representing hosts. The degree of host heterogeneity within different populations is adjusted by changing the proportion and the nutrient concentration of nutrient sites. The experimental data are analysed via Bayesian inference methods, estimating pathogen transmission parameters for each individual population. We find a significant, negative correlation between heterogeneity and the probability of pathogen invasion, thereby validating the theory. The value of the correlation is also in remarkably good agreement with the theoretical predictions. We briefly discuss how our results can be exploited in the design and implementation of disease control strategies.