Dating and localizing an invasion from post-introduction data and a coupled reaction-diffusion-absorption model

A Compartmental Model for Xylella fastidiosa Diseases with Explicit Vector Seasonal Dynamics

The bacterium Xylella fastidiosa is mainly transmitted by the meadow spittlebug Philaenus spumarius in Europe, where it has caused significant economic damage to olive and almond trees. Understanding the factors that determine disease dynamics in pathosystems that share similarities can help to design control strategies focused on minimizing transmission chains. Here, we introduce a compartmental model for X. fastidiosa-caused diseases in Europe that accounts for the main relevant epidemiological processes, including the seasonal dynamics of P. spumarius. The model was confronted with epidemiological data from the two major outbreaks of X. fastidiosa in Europe, the olive quick disease syndrome in Apulia, Italy, caused by the subspecies pauca, and the almond leaf scorch disease in Mallorca, Spain, caused by subspecies multiplex and fastidiosa. Using a Bayesian inference framework, we show how the model successfully reproduces the general field data in both diseases. In a global sensitivity analysis, the vector-to-plant and plant-to-vector transmission rates, together with the vector removal rate, were the most influential parameters in determining the time of the infectious host population peak, the incidence peak, and the final number of dead hosts. We also used our model to check different vector-based control strategies, showing that a joint strategy focused on increasing the rate of vector removal while lowering the number of annual newborn vectors is optimal for disease control. [Formula: see text] Copyright © 2023 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license.

Forecasting Pathogen Dynamics with Bayesian Model-Averaging: Application to Xylella fastidiosa

Forecasting invasive-pathogen dynamics is paramount to anticipate eradication and containment strategies. Such predictions can be obtained using a model grounded on partial differential equations (PDE; often exploited to model invasions) and fitted to surveillance data. This framework allows the construction of phenomenological but concise models relying on mechanistic hypotheses and real observations. However, it may lead to models with overly rigid behavior and possible data-model mismatches. Hence, to avoid drawing a forecast grounded on a single PDE-based model that would be prone to errors, we propose to apply Bayesian model averaging (BMA), which allows us to account for both parameter and model uncertainties. Thus, we propose a set of different competing PDE-based models for representing the pathogen dynamics, we use an adaptive multiple importance sampling algorithm (AMIS) to estimate parameters of each competing model from surveillance data in a mechanistic-statistical framework, we evaluate the posterior probabilities of models by comparing different approaches proposed in the literature, and we apply BMA to draw posterior distributions of parameters and a posterior forecast of the pathogen dynamics. This approach is applied to predict the extent of Xylella fastidiosa in South Corsica, France, a phytopathogenic bacterium detected in situ in Europe less than 10 years ago (Italy 2013, France 2015). Separating data into training and validation sets, we show that the BMA forecast outperforms competing forecast approaches.

Optimal spatial monitoring of populations described by reaction-diffusion models

Using spatialised population measurements and related geographic habitat data, it is feasible nowadays to derive parsimonious spatially explicit population models and to carry on their parameter estimation. To achieve such goal, reaction-diffusion models are common in conservation biology and agricultural plant health where they are used, for example, for landscape planning or epidemiological surveillance. Unfortunately, if the mathematical methods and computational power are readily available, biological measurements are not. Despite the high throughput of some habitat related remote sensors, the experimental cost of biological measurements are one of the worst bottleneck against a widespread usage of reaction-diffusion models. Hence we will recall some classical methods for optimal experimental design that we deem useful to spatial ecologist. Using two case studies, one in landscape ecology and one in conservation biology, we will show how to construct a priori experimental design minimizing variance of parameter estimates, enabling optimal experimental setup under constraints.

Parameter Estimation in a PDE Model for the Spatial Spread of Cocoa Black Pod Disease

In this paper, we develop an epidemiological model with both environmental (primary infection from the environmental spores reservoir) and direct transmission (secondary infection from an infected host to a susceptible pod). This model simulates the spatiotemporal evolution of cocoa black pod disease caused by Phytophthora megakarya. Since reliable parameter estimation is a central issue for modeling realistic biological systems, we used a mechanistic-statistical approach to estimate model parameters from real observations of a specific cocoa plot. In addition, to refine numerical simulations of the pathosystem, data describing the shade intensity all over the plot were exploited and led to increased model predictions accuracy and also highlighted a higher number of infected pods located in areas of the plot with higher shading intensity. Recommendations in terms of promoting cocoa farming in systems with low shading intensity may be evident if these results are confirmed. Our results also highlight the importance of the environmental spore reservoir in black pod disease dynamics.

COVID-19 mortality analysis from soft-data multivariate curve regression and machine learning

A multiple objective space-time forecasting approach is presented involving cyclical curve log-regression, and multivariate time series spatial residual correlation analysis. Specifically, the mean quadratic loss function is minimized in the framework of trigonometric regression. While, in our subsequent spatial residual correlation analysis, maximization of the likelihood allows us to compute the posterior mode in a Bayesian multivariate time series soft-data framework. The presented approach is applied to the analysis of COVID-19 mortality in the first wave affecting the Spanish Communities, since March 8, 2020 until May 13, 2020. An empirical comparative study with Machine Learning (ML) regression, based on random k-fold cross-validation, and bootstrapping confidence interval and probability density estimation, is carried out. This empirical analysis also investigates the performance of ML regression models in a hard- and soft-data frameworks. The results could be extrapolated to other counts, countries, and posterior COVID-19 waves.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00477-021-02021-0.

Emerging strains of watermelon mosaic virus in Southeastern France: model-based estimation of the dates and places of introduction

Where and when alien organisms are successfully introduced are central questions to elucidate biotic and abiotic conditions favorable to the introduction, establishment and spread of invasive species. We propose a modelling framework to analyze multiple introductions by several invasive genotypes or genetic variants, in competition with a resident population, when observations provide knowledge on the relative proportions of each variant at some dates and places. This framework is based on a mechanistic-statistical model coupling a reaction–diffusion model with a probabilistic observation model. We apply it to a spatio-temporal dataset reporting the relative proportions of five genetic variants of watermelon mosaic virus (WMV, genus Potyvirus, family Potyviridae) in infections of commercial cucurbit fields. Despite the parsimonious nature of the model, it succeeds in fitting the data well and provides an estimation of the dates and places of successful introduction of each emerging variant as well as a reconstruction of the dynamics of each variant since its introduction.

Metapopulation Structure Predicts Population Dynamics in the Cakile maritima-Alternaria brassicicola Host-Pathogen Interaction

AbstractIn symbiotic interactions, spatiotemporal variation in the distribution or population dynamics of one species represents spatial and temporal heterogeneity of the landscape for the other. Such interdependent demographic dynamics result in situations where the relative importance of biotic and abiotic factors in determining ecological processes is complicated to decipher. Using a detailed survey of three metapopulations of the succulent plant Cakile maritima and the necrotrophic fungus Alternaria brassicicola located along the southeastern Australian coast, we developed a series of statistical analyses-namely, synchrony analysis, patch occupancy dynamics, and a spatially explicit metapopulation model-to understand how habitat quality, weather conditions, dispersal, and spatial structure determine metapopulation dynamics. Climatic conditions are important drivers, likely explaining the high synchrony among populations. Host availability, landscape features facilitating dispersal, and habitat conditions also impact the occurrence and spread of disease. Overall, we show that the collection of extensive data on host and pathogen population dynamics, in combination with spatially explicit epidemiological modeling, makes it possible to accurately predict disease dynamics-even when there is extreme variability in host population dynamics. Finally, we discuss the importance of genetic information for predicting demographic dynamics in this pathosystem.

Shape and rate of movement of the invasion front of Xylella fastidiosa spp. pauca in Puglia

In 2013, Xylella fastidiosa spp. pauca was first reported in Puglia, Italy, causing the olive quick decline syndrome (OQDS). Since then the disease has spread, prompting the initiation of management measures to contain the outbreak. Estimates of the shape of the disease front and the rate of area expansion are needed to inform management, e.g. the delineation of buffer zones. However, empirical estimates of the invasion front and the rate of spread of OQDS are not available. Here, we analysed the hundreds of thousands of records of monitoring data on disease occurrence in Puglia to estimate the shape of the invasion front and the rate of movement of the front. The robustness of estimation was checked using simulation. The shape of the front was best fitted by a logistic function while using a beta-binomial error distribution to model variability around the expected proportion of infected trees. The estimated rate of movement of the front was 10.0 km per year (95% confidence interval: 7.5-12.5 km per year). This rate of movement is at the upper limit of previous expert judgements. The shape of the front was flatter than expected. The fitted model indicates that the disease spread started approximately in 2008. This analysis underpins projections of further disease spread and the need for preparedness in areas that are still disease free.

Spatial Bayesian Modeling Applied to the Surveys of Xylella fastidiosa in Alicante (Spain) and Apulia (Italy)

The plant-pathogenic bacterium Xylella fastidiosa was first reported in Europe in 2013, in the province of Lecce, Italy, where extensive areas were affected by the olive quick decline syndrome, caused by the subsp. pauca. In Alicante, Spain, almond leaf scorch, caused by X. fastidiosa subsp. multiplex, was detected in 2017. The effects of climatic and spatial factors on the geographic distribution of X. fastidiosa in these two infested regions in Europe were studied. The presence/absence data of X. fastidiosa in the official surveys were analyzed using Bayesian hierarchical models through the integrated nested Laplace approximation (INLA) methodology. Climatic covariates were obtained from the WorldClim v.2 database. A categorical variable was also included according to Purcell's minimum winter temperature thresholds for the risk of occurrence of Pierce's disease of grapevine, caused by X. fastidiosa subsp. fastidiosa. In Alicante, data were presented aggregated on a 1 km grid (lattice data), where the spatial effect was included in the model through a conditional autoregressive structure. In Lecce, data were observed at continuous locations occurring within a defined spatial domain (geostatistical data). Therefore, the spatial effect was included via the stochastic partial differential equation approach. In Alicante, the pathogen was detected in all four of Purcell's categories, illustrating the environmental plasticity of the subsp. multiplex. Here, none of the climatic covariates were retained in the selected model. Only two of Purcell's categories were represented in Lecce. The mean diurnal range (bio2) and the mean temperature of the wettest quarter (bio8) were retained in the selected model, with a negative relationship with the presence of the pathogen. However, this may be due to the heterogeneous sampling distribution having a confounding effect with the climatic covariates. In both regions, the spatial structure had a strong influence on the models, but not the climatic covariates. Therefore, pathogen distribution was largely defined by the spatial relationship between geographic locations. This substantial contribution of the spatial effect in the models might indicate that the current extent of X. fastidiosa in the study regions had arisen from a single focus or from several foci, which have been coalesced.

Impact of Lockdown on the Epidemic Dynamics of COVID-19 in France

The COVID-19 epidemic was reported in the Hubei province in China in December 2019 and then spread around the world reaching the pandemic stage at the beginning of March 2020. Since then, several countries went into lockdown. Using a mechanistic-statistical formalism, we estimate the effect of the lockdown in France on the contact rate and the effective reproduction number R e of the COVID-19. We obtain a reduction by a factor 7 (R e = 0.47, 95%-CI: 0.45-0.50), compared to the estimates carried out in France at the early stage of the epidemic. We also estimate the fraction of the population that would be infected by the beginning of May, at the official date at which the lockdown should be relaxed. We find a fraction of 3.7% (95%-CI: 3.0-4.8%) of the total French population, without taking into account the number of recovered individuals before April 1st, which is not known. This proportion is seemingly too low to reach herd immunity. Thus, even if the lockdown strongly mitigated the first epidemic wave, keeping a low value of R e is crucial to avoid an uncontrolled second wave (initiated with much more infectious cases than the first wave) and to hence avoid the saturation of hospital facilities.

From Nucleotides to Satellite Imagery: Approaches to Identify and Manage the Invasive Pathogen Xylella fastidiosa and Its Insect Vectors in Europe

Biological invasions represent some of the most severe threats to local communities and ecosystems. Among invasive species, the vector-borne pathogen Xylella fastidiosa is responsible for a wide variety of plant diseases and has profound environmental, social and economic impacts. Once restricted to the Americas, it has recently invaded Europe, where multiple dramatic outbreaks have highlighted critical challenges for its management. Here, we review the most recent advances on the identification, distribution and management of X. fastidiosa and its insect vectors in Europe through genetic and spatial ecology methodologies. We underline the most important theoretical and technological gaps that remain to be bridged. Challenges and future research directions are discussed in the light of improving our understanding of this invasive species, its vectors and host–pathogen interactions. We highlight the need of including different, complimentary outlooks in integrated frameworks to substantially improve our knowledge on invasive processes and optimize resources allocation. We provide an overview of genetic, spatial ecology and integrated approaches that will aid successful and sustainable management of one of the most dangerous threats to European agriculture and ecosystems.

Using Early Data to Estimate the Actual Infection Fatality Ratio from COVID-19 in France

The number of screening tests carried out in France and the methodology used to target the patients tested do not allow for a direct computation of the actual number of cases and the infection fatality ratio (IFR). The main objective of this work is to estimate the actual number of people infected with COVID-19 and to deduce the IFR during the observation window in France. We develop a `mechanistic-statistical' approach coupling a SIR epidemiological model describing the unobserved epidemiological dynamics, a probabilistic model describing the data acquisition process and a statistical inference method. The actual number of infected cases in France is probably higher than the observations: we find here a factor ×8 (95%-CI: 5-12) which leads to an IFR in France of 0.5% (95%-CI: 0.3-0.8) based on hospital death counting data. Adjusting for the number of deaths in nursing homes, we obtain an IFR of 0.8% (95%-CI: 0.45-1.25). This IFR is consistent with previous findings in China (0.66%) and in the UK (0.9%) and lower than the value previously computed on the Diamond Princess cruse ship data (1.3%).

Update of the Scientific Opinion on the risks to plant health posed by Xylella fastidiosa in the EU territory

EFSA was asked to update the 2015 EFSA risk assessment on Xylella fastidiosa for the territory of the EU. In particular, EFSA was asked to focus on potential establishment, short- and long-range spread, the length of the asymptomatic period, the impact of X. fastidiosa and an update on risk reduction options. EFSA was asked to take into account the different subspecies and Sequence Types of X. fastidiosa. This was attempted throughout the scientific opinion but several issues with data availability meant that this could only be partially achieved. Models for risk of establishment showed most of the EU territory may be potentially suitable for X. fastidiosa although southern EU is most at risk. Differences in estimated areas of potential establishment were evident among X. fastidiosa subspecies, particularly X. fastidiosa subsp. multiplex which demonstrated areas of potential establishment further north in the EU. The model of establishment could be used to develop targeted surveys by Member States. The asymptomatic period of X. fastidiosa varied significantly for different host and pathogen subspecies combinations, for example from a median of approximately 1 month in ornamental plants and up to 10 months in olive, for pauca. This variable and long asymptomatic period is a considerable limitation to successful detection and control, particularly where surveillance is based on visual inspection. Modelling suggested that local eradication (e.g. within orchards) is possible, providing sampling intensity is sufficient for early detection and effective control measures are implemented swiftly (e.g. within 30 days). Modelling of long-range spread (e.g. regional scale) demonstrated the important role of long-range dispersal and the need to better understand this. Reducing buffer zone width in both containment and eradication scenarios increased the area infected. Intensive surveillance for early detection, and consequent plant removal, of new outbreaks is crucial for both successful eradication and containment at the regional scale, in addition to effective vector control. The assessment of impacts indicated that almond and Citrus spp. were at lower impact on yield compared to olive. Although the lowest impact was estimated for grapevine, and the highest for olive, this was based on several assumptions including that the assessment considered only Philaenus spumarius as a vector. If other xylem-feeding insects act as vectors the impact could be different. Since the Scientific Opinion published in 2015, there are still no risk reduction options that can remove the bacterium from the plant in open field conditions. Short- and long-range spread modelling showed that an early detection and rapid application of phytosanitary measures, consisting among others of plant removal and vector control, are essential to prevent further spread of the pathogen to new areas. Further data collection will allow a reduction in uncertainty and facilitate more tailored and effective control given the intraspecific diversity of X. fastidiosa and wide host range.