On 'Analytical models for the patchy spread of plant disease'.

Epidemiologists are interested in using models that incorporate the effects of clustering in the spatial pattern of disease on epidemic dynamics. Bolker (1999, Bull. Math. Biol. 61, 849-874) has developed an approach to study such models based on a moment closure assumption. We show that the assumption works above a threshold initial level of disease that depends on the spatial dispersal of the pathogen. We test an alternative assumption and show that it does not have this limitation. We examine the relation between lattice and continuous-medium implementations of the approach

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'

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.FMN gratefully acknowledges financial support from BBSRC, USDA-ARS, USDA-Aphis PPQ, Citrus Research and Development Foundation. CAG gratefully acknowledges the support of a BBSRC Professorial Fellowship, with additional support from USDA and Defra. ARC was supported by BBSRC, USDA, the National University of Singapore, and NMRC. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

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.FFL was funded via a CNPq Fellowship (Brazil's National Council for Scientific and Technological Development, see http://memoria.cnpq.br/english/cnpq/index.htm). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Software testing in a scientific research group

Scientific software is more difficult to test than many other software products, but scientists are not usually trained in software engineering techniques. Considering how often software is used to produce scientific results, how can we be sure the predictions made from these results are correct? Software engineering techniques should be useful for computational scientists. The problem is they find it difficult to know how to apply domain-independent techniques to the specific problems they face in their work. Nevertheless, we have discovered scientists use their own intuition to reinvent techniques surprisingly similar to those in software engineering. This seems like a good place to start our training.This work was supported by the University of Cambridge/ Wellcome Trust Junior Interdisciplinary Fellowship “Making scientific software easier to understand, test and communicate through modern advances in software engineering”.This is the author accepted manuscript. The final version is available from the Association for Computing Machinery via http://dx.doi.org/10.1145/2851613.285178

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. © 2013 Leclerc et al.ML thanks the Institut Technique franc¸ais de la Betterave industrielle (ITB) for funding this project. CAG and JANF were funded by the UK’s Biotechnology and Biological Sciences Research Council (BBSRC). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Testing stochastic software using Pseudo-oracles

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.Wellcome TrustThis is the author accepted manuscript. The final version is available from the Association for Computing Machinery via http://dx.doi.org/10.1145/2931037.293106

The Effect of Forest Management Options on Forest Resilience to Pathogens

Invasive pathogens threaten the ability of forests globally to produce a range of valuable ecosystem services over time. However, the ability to detect such pathogen invasions—and thus to produce appropriate and timely management responses—is relatively low. We argue that a promising approach is to plan and manage forests in a way that increases their resilience to invasive pathogens not yet present or ubiquitous in the forest. This paper is based on a systematic search and critical review of empirical evidence of the effect of a wide range of forest management options on the primary and secondary infection rates of forest pathogens, and on subsequent forest recovery. Our goals are to inform forest management decision making to increase forest resilience, and to identify the most important evidence gaps for future research. The management options for which there is the strongest evidence that they increase forest resilience to pathogens are: reduced forest connectivity, removal or treatment of inoculum sources such as cut stumps, reduced tree density, removal of diseased trees and increased tree species diversity. In all cases the effect of these options on infection dynamics differs greatly amongst tree and pathogen species and between forest environments. However, the lack of consistent effects of silvicultural systems or of thinning, pruning or coppicing treatments is notable. There is also a lack of evidence of how the effects of treatments are influenced by the scale at which they are applied, e.g., the mixture of tree species. An overall conclusion is that forest managers often need to trade-off increased resilience to tree pathogens against other benefits obtained from forests

Estimating expansion of the range of oak processionary moth (Thaumetopoea processionea) in the UK from 2006 to 2019

1. The expansion of oak processionary moth (OPM) in South-East England continues despite ongoing efforts to control the pest since its introduction in 2006. 2. Using locations of OPM larval nests, supplied by the Forestry Commission and recorded as part of ongoing surveillance and control measures from 2006 onwards, we show that the expansion of the range of OPM in South-East England up to 2019 was biphasic with a higher rate of expansion from 2015 onwards. 3. The maximum rate of OPM range expansion in the United Kingdom from 2006 to 2014 was estimated as 1.66 km/year (95% CI = [1.22, 2.09]), whereas the 2015–2019 expansion rate was estimated as 6.17 km/year (95% CI = [5.49, 6.84]). This corresponds to an estimated species range distribution area of 7077 km2 in 2019. 4. To explain the faster expansion of OPM range from 2015 onwards, we discuss potential reasons that include: natural capability of species of both short- and long-distance dispersal; external factors such as environmental heterogeneity; a reduction of active control