Understanding, predicting and managing the spread of plant pathogens is crucial given the economic, societal and climatic benefits of plants, including crops and trees. Mathematical models have long been used to investigate disease dynamics in plants. An important component of such models is to account for spatial structure, since plant hosts are immobile and a majority of disease spread will often be localised. Here we apply a lattice-based mathematical modelling approach, a pair approximation, to model disease spread. While this method has previously been used to develop epidemiological theory, it has not been used to predict spread in a specific pathosystem. We fit our lattice-based epidemiological model to experimental data relating to Bahia bark scaling of citrus, an economically-important disease in north-eastern Brazil, and compare its performance to a more commonly used dispersal-kernel modelling approach. We show that the lattice-based model fits the data well, predicting a significant degree of near-neighbour infections, with similar estimated values of epidemiologically-meaningful parameters to the dispersal model. We highlight the pros and cons of the lattice-based approach and discuss how it may be used to predict disease spread and optimise control of plant diseases.

The resources available for managing disease epidemics - whether in animals, plants or humans - are limited by a range of practical and financial constraints. Optimal control has been widely explored for optimising allocation of these resources to maximise their impact. The most common approach assumes a deterministic, continuous model to approximate the epidemic dynamics. However, real systems are stochastic and so a range of outcomes are possible for any given epidemic situation. The deterministic models are also known to be poor approximations in cases where the number of infected hosts is low - either globally or within a subset of the population - and these cases are highly relevant in the context of control. Hence, this work explores the effectiveness of disease management strategies derived using optimal control theory when applied to a more realistic, stochastic form of disease model. We demonstrate that the deterministic optimal control solutions are not optimal in cases where the disease is eradicated or close to eradication. The range of potential outcomes in the stochastic models means that optimising the deterministic case will not reliably eradicate disease - the required rate of control is higher than the deterministic optimal control would predict. Using Model Predictive Control, in which the optimisation is performed repeatedly as the system evolves to correct for deviations from the optimal control predictions, improves performance but the level of control calculated at each repeated optimisation is still insufficient. To demonstrate this, we present several simple heuristics to allocate control resources across different locations which can outperform the strategies calculated by MPC when the control budget is sufficient for eradication. Our illustration uses examples based on simulation of the spatial spread of plant disease but similar issues would be expected in any deterministic model where infection is driven close to zero.

Plant viruses threaten food security and are often transmitted by insect vectors. Non-persistently transmitted (NPT) plant viruses are transmitted almost exclusively by aphids. Because virions attach to the aphid's stylet (mouthparts) and are acquired and inoculated via brief epidermal probes, the aphid-virus interaction is highly transient, with a very short aphid virus retention time. Many NPT viruses manipulate their host plant's phenotype to change aphid behaviour to optimise virus transmission. Epidemiological models of this have overlooked a key feature of aphid NPT virus retention: probing or feeding on a plant causes aphids to lose the virus. Furthermore, experimental studies suggest aphids could possibly inoculate multiple healthy plants within one infective period if they do not feed. Consequences of this for virus manipulation of host plant phenotype have not been explored. Our new compartmental epidemiological model includes both behaviour-based aphid dispersal and infectivity loss rates, and the ability of infective aphids to probe multiple plants before virus loss. We use our model to explore how NPT virus-induced host phenotypes affect epidemic outcomes, comparing these results to representative previous models. We find that previous models behave fundamentally differently and underestimate the benefit of an 'attract-and-deter' phenotype, where the virus induces increased aphid attraction to infected plants but deters them from prolonged feeding. Our results also highlight the importance of characterising NPT virus retention upon the aphid during probing. Allowing for multiple infective probes increases disease incidence and the effectiveness of virus manipulation, with implications for epidemic prediction and control.

Infectious diseases of plants present an ongoing and increasing threat to international biosecurity, with wide-ranging implications. An important challenge in plant disease management is achieving early detection of invading pathogens, which requires effective surveillance through the implementation of appropriate monitoring programmes. However, when monitoring relies on visual inspection as a means of detection, surveillance is often hindered by a long incubation period (delay from infection to symptom onset) during which plants may be infectious but not displaying visible symptoms. 'Sentinel' plants-alternative susceptible host species that display visible symptoms of infection more rapidly-could be introduced to at-risk populations and included in monitoring programmes to act as early warning beacons for infection. However, while sentinel hosts exhibit faster disease progression and so allow pathogens to be detected earlier, this often comes at a cost: faster disease progression typically promotes earlier onward transmission. Here, we construct a computational model of pathogen transmission to explore this trade-off and investigate how including sentinel plants in monitoring programmes could facilitate earlier detection of invasive plant pathogens. Using Xylella fastidiosa infection in Olea europaea (European olive) as a current high profile case study, for which Catharanthus roseus (Madagascan periwinkle) is a candidate sentinel host, we apply a Bayesian optimisation algorithm to determine the optimal number of sentinel hosts to introduce for a given sampling effort, as well as the optimal division of limited surveillance resources between crop and sentinel plants. Our results demonstrate that including sentinel plants in monitoring programmes can reduce the expected prevalence of infection upon outbreak detection substantially, increasing the feasibility of local outbreak containment.

Plant pathogens respond to selection pressures exerted by disease management strategies. This can lead to fungicide resistance and/or the breakdown of disease-resistant cultivars, each of which significantly threaten food security. Both fungicide resistance and cultivar breakdown can be characterised as qualitative or quantitative. Qualitative (monogenic) resistance/breakdown involves a step change in the characteristics of the pathogen population with respect to disease control, often caused by a single genetic change. Quantitative (polygenic) resistance/breakdown instead involves multiple genetic changes, each causing a smaller shift in pathogen characteristics, leading to a gradual alteration in the effectiveness of disease control over time. Although resistance/breakdown to many fungicides/cultivars currently in use is quantitative, the overwhelming majority of modelling studies focus on the much simpler case of qualitative resistance. Further, those very few models of quantitative resistance/breakdown which do exist are not fitted to field data. Here we present a model of quantitative resistance/breakdown applied to Zymoseptoria tritici, which causes Septoria leaf blotch, the most prevalent disease of wheat worldwide. Our model is fitted to data from field trials in the UK and Denmark. For fungicide resistance, we show that the optimal disease management strategy depends on the timescale of interest. Greater numbers of fungicide applications per year lead to greater selection for resistant strains, although over short timescales this can be oset by the increased control oered by more sprays. However, over longer timescales higher yields are attained using fewer fungicide applications per year. Deployment of disease-resistant cultivars is not only a valuable disease management strategy, but also oers the secondary benefit of protecting fungicide effectiveness by delaying the development of fungicide resistance. However, disease-resistant cultivars themselves erode over time. We show how an integrated disease management strategy with frequent replacement of disease-resistant cultivars can give a large improvement in fungicide durability and yields.

While the spread of plant disease depends strongly on biological factors driving transmission, it also has a human dimension. Disease control depends on decisions made by individual growers, who are in turn influenced by a broad range of factors. Despite this, human behaviour has rarely been included in plant epidemic models. Considering Cassava Brown Streak Disease, we model how the perceived increase in profit due to disease management influences participation in clean seed systems (CSS). Our models are rooted in game theory, with growers making strategic decisions based on the expected profitability of different control strategies. We find that both the information used by growers to assess profitability and the perception of economic and epidemiological parameters influence long-term participation in the CSS. Over-estimation of infection risk leads to lower participation in the CSS, as growers perceive that paying for the CSS will be futile. Additionally, even though good disease management can be achieved through the implementation of CSS, and a scenario where all controllers use the CSS is achievable when growers base their decision on the average of their entire strategy, CBSD is rarely eliminated from the system. These results are robust to stochastic and spatial effects. Our work highlights the importance of including human behaviour in plant disease models, but also the significance of how that behaviour is included.

Many plant viruses are transmitted by insect vectors. Transmission can be described as persistent or non-persistent depending on rates of acquisition, retention, and inoculation of virus. Much experimental evidence has accumulated indicating vectors can prefer to settle and/or feed on infected versus noninfected host plants. For persistent transmission, vector preference can also be conditional, depending on the vector's own infection status. Since viruses can alter host plant quality as a resource for feeding, infection potentially also affects vector population dynamics. Here we use mathematical modelling to develop a theoretical framework addressing the effects of vector preferences for landing, settling and feeding-as well as potential effects of infection on vector population density-on plant virus epidemics. We explore the consequences of preferences that depend on the host (infected or healthy) and vector (viruliferous or nonviruliferous) phenotypes, and how this is affected by the form of transmission, persistent or non-persistent. We show how different components of vector preference have characteristic effects on both the basic reproduction number and the final incidence of disease. We also show how vector preference can induce bistability, in which the virus is able to persist even when it cannot invade from very low densities. Feedbacks between plant infection status, vector population dynamics and virus transmission potentially lead to very complex dynamics, including sustained oscillations. Our work is supported by an interactive interface https://plantdiseasevectorpreference.herokuapp.com/. Our model reiterates the importance of coupling virus infection to vector behaviour, life history and population dynamics to fully understand plant virus epidemics.

Aphids are the primary vector of plant viruses. Transient aphids, which probe several plants per day, are considered to be the principal vectors of non-persistently transmitted (NPT) viruses. However, resident aphids, which can complete their life cycle on a single host and are affected by agronomic practices, can transmit NPT viruses as well. Moreover, they can interfere both directly and indirectly with transient aphids, eventually shaping plant disease dynamics. By means of an epidemiological model, originally accounting for ecological principles and agronomic practices, we explore the consequences of fertilization and irrigation, pesticide deployment and roguing of infected plants on the spread of viral diseases in crops. Our results indicate that the spread of NPT viruses can be i) both reduced or increased by fertilization and irrigation, depending on whether the interference is direct or indirect; ii) counter-intuitively increased by pesticide application and iii) reduced by roguing infected plants. We show that a better understanding of vectors' interactions would enhance our understanding of disease transmission, supporting the development of disease management strategies.

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 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.

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.