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.

Identifying potential significant factors impacting zero-inflated proportion data.

Classical supervised methods like linear regression and decision trees are not completely adapted for identifying impacting factors on a response variable corresponding to zero-inflated proportion data (ZIPD) that are dependent, continuous and bounded. In this article we propose a within-block permutation-based methodology to identify factors (discrete or continuous) that are significantly correlated with ZIPD, we propose a performance indicator quantifying the percentage of correlation explained by the subset of significant factors, and we show how to predict the ranks of the response variables conditionally on the observation of these factors. The methodology is illustrated on simulated data and on two real data sets dealing with epidemiology. In the first data set, ZIPD correspond to probabilities of transmission of Influenza between horses. In the second data set, ZIPD correspond to probabilities that geographic entities (eg, states and countries) have the same COVID-19 mortality dynamics.

Characterizing viral within-host diversity in fast and non-equilibrium demo-genetic dynamics.

High-throughput sequencing has opened the route for a deep assessment of within-host genetic diversity that can be used, e.g., to characterize microbial communities and to infer transmission links in infectious disease outbreaks. The performance of such characterizations and inferences cannot be analytically assessed in general and are often grounded on computer-intensive evaluations. Then, being able to simulate within-host genetic diversity across time under various demo-genetic assumptions is paramount to assess the performance of the approaches of interest. In this context, we built an original model that can be simulated to investigate the temporal evolution of genotypes and their frequencies under various demo-genetic assumptions. The model describes the growth and the mutation of genotypes at the nucleotide resolution conditional on an overall within-host viral kinetics, and can be tuned to generate fast non-equilibrium demo-genetic dynamics. We ran simulations of this model and computed classic diversity indices to characterize the temporal variation of within-host genetic diversity (from high-throughput amplicon sequences) of virus populations under three demographic kinetic models of viral infection. Our results highlight how demographic (viral load) and genetic (mutation, selection, or drift) factors drive variations in within-host diversity during the course of an infection. In particular, we observed a non-monotonic relationship between pathogen population size and genetic diversity, and a reduction of the impact of mutation on diversity when a non-specific host immune response is activated. The large variation in the diversity patterns generated in our simulations suggests that the underlying model provides a flexible basis to produce very diverse demo-genetic scenarios and test, for instance, methods for the inference of transmission links during outbreaks.

Strain Diversity and Spatial Distribution Are Linked to Epidemic Dynamics in Host Populations.

AbstractThe inherently variable nature of epidemics renders predictions of when and where infection is expected to occur challenging. Differences in pathogen strain composition, diversity, fitness, and spatial distribution are generally ignored in epidemiological modeling and are rarely studied in natural populations, yet they may be important drivers of epidemic trajectories. To examine how these factors are linked to epidemics in natural host populations, we collected epidemiological and genetic data from 15 populations of the powdery mildew fungus, Podosphaera plantaginis, on Plantago lanceolata in the Åland Islands, Finland. In each population, we tracked spatiotemporal disease progression throughout one epidemic season and coupled our survey of infection with intensive field sampling of the pathogen. We found that strain composition varied greatly among populations in the landscape. Within populations, strain composition was driven by the sequence of strain activity: early-active strains reached higher abundances, leading to consistent strain compositions over time. Co-occurring strains also varied in their contribution to the growth of the local epidemic, and these fitness inequalities were linked to epidemic dynamics: a higher proportion of hosts became infected in populations containing strains that were more similar in fitness. Epidemic trajectories in the populations were also linked to strain diversity and spatial dynamics: higher infection rates occurred in populations containing higher strain diversity, while spatially clustered epidemics experienced lower infection rates. Together, our results suggest that spatial and/or temporal variation in the strain composition, diversity, and fitness of pathogen populations are important factors generating variation in epidemiological trajectories among infected host populations.

Correction: Estimation of the dispersal distances of an aphid-borne virus in a patchy landscape.

[This corrects the article DOI: 10.1371/journal.pcbi.1006085.].

To Treat or Not to Treat Bees? Handy VarLoad: A Predictive Model for Varroa destructor Load.

The parasitic Varroa destructor is considered a major pathogenic threat to honey bees and to beekeeping. Without regular treatment against this mite, honey bee colonies can collapse within a 2-3-year period in temperate climates. Beyond this dramatic scenario, Varroa induces reductions in colony performance, which can have significant economic impacts for beekeepers. Unfortunately, until now, it has not been possible to predict the summer Varroa population size from its initial load in early spring. Here, we present models that use the Varroa load observed in the spring to predict the Varroa load one or three months later by using easily and quickly measurable data: phoretic Varroa load and capped brood cell numbers. Built on 1030 commercial colonies located in three regions in the south of France and sampled over a three-year period, these predictive models are tools designed to help professional beekeepers' decision making regarding treatments against Varroa. Using these models, beekeepers will either be able to evaluate the risks and benefits of treating against Varroa or to anticipate the reduction in colony performance due to the mite during the beekeeping season.

Inferring long-distance connectivity shaped by air-mass movement for improved experimental design in aerobiology.

The collection and analysis of air samples for the study of microbial airborne communities or the detection of airborne pathogens is one of the few insights that we can grasp of a continuously moving flux of microorganisms from their sources to their sinks through the atmosphere. For large-scale studies, a comprehensive sampling of the atmosphere is beyond the scopes of any reasonable experimental setting, making the choice of the sampling locations and dates a key factor for the representativeness of the collected data. In this work we present a new method for revealing the main patterns of air-mass connectivity over a large geographical area using the formalism of spatio-temporal networks, that are particularly suitable for representing complex patterns of connection. We use the coastline of the Mediterranean basin as an example. We reveal a temporal pattern of connectivity over the study area with regions that act as strong sources or strong receptors according to the season of the year. The comparison of the two seasonal networks has also allowed us to propose a new methodology for comparing spatial weighted networks that is inspired from the small-world property of non-spatial networks.

When the average hides the risk of Bt-corn pollen on non-target Lepidoptera: Application to Aglais io in Catalonia.

Field cultivation of Genetically Modified (GM) Bt-plants has a potential environmental risk toward non-target Lepidoptera (NTLs) larvae through the consumption of Bt-maize pollen. The Bt-maize Cry protein targeting Lepidoptera species detrimental to the crop is also expressed in pollen which is dispersed by wind and can thus reach habitats of NTLs. To better assess the current ecological risk of Bt-maize at landscape scales, we developed a spatially-explicit exposure-hazard model considering (i) the dynamics of pollen dispersal obtained by convolving GM plants emission with a dispersal kernel and (ii) a toxicokinetic-toxicodynamic (TKTD) model accounting for the impact of toxin ingestion on individual lethal effects. We simulated the model using real landscape observations in Catalonia (Spain): GM-maize locations, flowering dates, rainfall time series and larvae emergence date of the European peacock butterfly Aglais io. While in average, the additional mortality appears to be negligible, we show significant additional mortality at sub-population level, with for instance a mortality higher than 40% within the 10m for the 10% most Bt-sensitive individuals. Also, using Pareto optimality we capture the best trade-off between isolation distance and additional mortality: up to 50 m are required to significantly buffer Bt-pollen impact on NTLs survival at the individual level. Our study clears up the narrow line between diverging conclusions: those claiming no risk by only looking at the average regional effect of Bt on NTLs survival and those pointing out a significant threaten when considering the variability of individuals mortality.

Towards unified and real-time analyses of outbreaks at country-level during pandemics.

The management of public health and the preparedness for health emergencies partly rely on the collection and analysis of surveillance data, which become crucial in the context of an emergency such as the pandemic caused by COVID-19. For COVID-19, typically, numerous national and global initiatives have been set up from this perspective. Here, we propose to develop a shared vision of the country-level outbreaks during a pandemic, by enhancing, at the international scale, the foundations of the analysis of surveillance data and by adopting a unified and real-time approach to monitor and forecast the outbreak across time and across the world. This proposal, rolled out as a web platform, should contribute to strengthen epidemiological understanding, sanitary democracy as well as global and local responses to pandemics.

COVID-19 mortality dynamics: The future modelled as a (mixture of) past(s).

Discrepancies in population structures, decision making, health systems and numerous other factors result in various COVID-19-mortality dynamics at country scale, and make the forecast of deaths in a country under focus challenging. However, mortality dynamics of countries that are ahead of time implicitly include these factors and can be used as real-life competing predicting models. We precisely propose such a data-driven approach implemented in a publicly available web app timely providing mortality curves comparisons and real-time short-term forecasts for about 100 countries. Here, the approach is applied to compare the mortality trajectories of second-line and front-line European countries facing the COVID-19 epidemic wave. Using data up to mid-April, we show that the second-line countries generally followed relatively mild mortality curves rather than fast and severe ones. Thus, the continuation, after mid-April, of the COVID-19 wave across Europe was likely to be mitigated and not as strong as it was in most of the front-line countries first impacted by the wave (this prediction is corroborated by posterior data).

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.

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%).

Analyzing the Influence of Landscape Aggregation on Disease Spread to Improve Management Strategies.

Epidemiological models are increasingly used to predict epidemics and improve management strategies. However, they rarely consider landscape characteristics although such characteristics can influence the epidemic dynamics and, thus, the effectiveness of disease management strategies. Here, we present a generic in silico approach which assesses the influence of landscape aggregation on the costs associated with an epidemic and on improved management strategies. We apply this approach to sharka, one of the most damaging diseases of Prunus trees, for which a management strategy is already applied in France. Epidemic simulations were carried out with a spatiotemporal stochastic model under various management strategies in landscapes differing in patch aggregation. Using sensitivity analyses, we highlight the impact of management parameters on the economic output of the model. We also show that the sensitivity analysis can be exploited to identify several strategies that are, according to the model, more profitable than the current French strategy. Some of these strategies are specific to a given aggregation level, which shows that management strategies should generally be tailored to each specific landscape. However, we also identified a strategy that is efficient for all levels of landscape aggregation. This one-size-fits-all strategy has important practical implications because of its simple applicability at a large scale.

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

Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in particular in the intents of reconstructing the past dynamics of the alien organisms and predicting their future spatial extents. Partial differential equations offer a rich and flexible modeling framework that has been applied to a large number of invasions. In this article, we are specifically interested in dating and localizing the introduction that led to an invasion using mathematical modeling, post-introduction data and an adequate statistical inference procedure. We adopt a mechanistic-statistical approach grounded on a coupled reaction-diffusion-absorption model representing the dynamics of an organism in an heterogeneous domain with respect to growth. Initial conditions (including the date and site of the introduction) and model parameters related to diffusion, reproduction and mortality are jointly estimated in the Bayesian framework by using an adaptive importance sampling algorithm. This framework is applied to the invasion of Xylella fastidiosa, a phytopathogenic bacterium detected in South Corsica in 2015, France.

Improving Management Strategies of Plant Diseases Using Sequential Sensitivity Analyses.

Improvement of management strategies of epidemics is often hampered by constraints on experiments at large spatiotemporal scales. A promising approach consists of modeling the biological epidemic process and human interventions, which both impact disease spread. However, few methods enable the simultaneous optimization of the numerous parameters of sophisticated control strategies. To do so, we propose a heuristic approach (i.e., a practical improvement method approximating an optimal solution) based on sequential sensitivity analyses. In addition, we use an economic improvement criterion based on the net present value, accounting for both the cost of the different control measures and the benefit generated by disease suppression. This work is motivated by sharka (caused by Plum pox virus), a vector-borne disease of prunus trees (especially apricot, peach, and plum), the management of which in orchards is mainly based on surveillance and tree removal. We identified the key parameters of a spatiotemporal model simulating sharka spread and control and approximated optimal values for these parameters. The results indicate that the current French management of sharka efficiently controls the disease, but it can be economically improved using alternative strategies that are identified and discussed. The general approach should help policy makers to design sustainable and cost-effective strategies for disease management.

A Spatio-Temporal Exposure-Hazard Model for Assessing Biological Risk and Impact.

We developed a simulation model for quantifying the spatio-temporal distribution of contaminants (e.g., xenobiotics) and assessing the risk of exposed populations at the landscape level. The model is a spatio-temporal exposure-hazard model based on (i) tools of stochastic geometry (marked polygon and point processes) for structuring the landscape and describing the exposed individuals, (ii) a dispersal kernel describing the dissemination of contaminants from polygon sources, and (iii) an (eco)toxicological equation describing the toxicokinetics and dynamics of contaminants in affected individuals. The model was implemented in the briskaR package (biological risk assessment with R) of the R software. This article presents the model background, the use of the package in an illustrative example, namely, the effect of genetically modified maize pollen on nontarget Lepidoptera, and typical comparisons of landscape configurations that can be carried out with our model (different configurations lead to different mortality rates in the treated example). In real case studies, parameters and parametric functions encountered in the model will have to be precisely specified to obtain realistic measures of risk and impact and accurate comparisons of landscape configurations. Our modeling framework could be applied to study other risks related to agriculture, for instance, pathogen spread in crops or livestock, and could be adapted to cope with other hazards such as toxic emissions from industrial areas having health effects on surrounding populations. Moreover, the R package has the potential to help risk managers in running quantitative risk assessments and testing management strategies.

Identifying Lookouts for Epidemio-Surveillance: Application to the Emergence of Xylella fastidiosa in France.

Recent detections of Xylella fastidiosa in Corsica Island, France, has raised concerns on its possible spread to mainland France and the rest of the Mediterranean Basin. Early detection of infected plants is paramount to prevent the spread of the bacteria, but little is known about this pathosystem in European environments, hence standard surveillance strategies may be ineffective. We present a new methodological approach for the design of risk-based surveillance strategies, adapted to the emerging risk caused by X. fastidiosa. Our proposal is based on a combination of machine learning techniques and network analysis that aims at understanding the main abiotic drivers of the infection, produce risk maps and identify lookouts for the design of future surveillance plans. The identified drivers coincide with known results in laboratory studies about the correlation between environmental variables, such as water stress and temperature, and the presence of the bacterium in plants. Furthermore, the produced risk maps overlap nicely with detected foci of infection, while they also highlight other susceptible regions where X. fastidiosa has not been found yet. We conclude the paper presenting a list of recommended regions for a risk-based surveillance campaign based on the predicted spread and probability of early detection of the disease.

Measuring biological age to assess colony demographics in honeybees.

Honeybee colonies are increasingly exposed to environmental stress factors, which can lead to their decline or failure. However, there are major gaps in stressor risk assessment due to the difficulty of assessing the honeybee colony state and detecting abnormal events. Since stress factors usually induce a demographic disturbance in the colony (e.g. loss of foragers, early transition from nurse to forager state), we suggest that disturbances could be revealed indirectly by measuring the age- and task-related physiological state of bees, which can be referred to as biological age (an indicator of the changes in physiological state that occur throughout an individual lifespan). We therefore estimated the biological age of bees from the relationship between age and biomarkers of task specialization (vitellogenin and the adipokinetic hormone receptor). This relationship was determined from a calibrated sample set of known-age bees and mathematically modelled for biological age prediction. Then, we determined throughout the foraging season the evolution of the biological age of bees from colonies with low (conventional apiary) or high Varroa destructor infestation rates (organic apiary). We found that the biological age of bees from the conventional apiary progressively decreased from the spring (17 days) to the fall (6 days). However, in colonies from the organic apiary, the population aged from spring (13 days) to summer (18.5 days) and then rejuvenated in the fall (13 days) after Varroa treatment. Biological age was positively correlated with the amount of brood (open and closed cells) in the apiary with low Varroa pressure, and negatively correlated with Varroa infestation level in the apiary with high Varroa pressure. Altogether, these results show that the estimation of biological age is a useful and effective method for assessing colony demographic state and likely detrimental effects of stress factors.

Assessing the Aerial Interconnectivity of Distant Reservoirs of Sclerotinia sclerotiorum.

Many phytopathogenic fungi are disseminated as spores via the atmosphere from short to long distances. The distance of dissemination determines the extent to which plant diseases can spread and novel genotypes of pathogens can invade new territories. Predictive tools including models that forecast the arrival of spores in areas where susceptible crops are grown can help to more efficiently manage crop health. However, such models are difficult to establish for fungi with broad host ranges because sources of inoculum cannot be readily identified. Sclerotinia sclerotiorum, the pandemic agent of white mold disease, can attack >400 plant species including economically important crops. Monitoring airborne inoculum of S. sclerotiorum in several French cropping areas has shown that viable ascospores are present in the air almost all the time, even when no susceptible crops are nearby. This raises the hypothesis of a distant origin of airborne inoculum. The objective of the present study was to determine the interconnectivity of reservoirs of S. sclerotiorum from distant regions based on networks of air mass movement. Viable airborne inoculum of S. sclerotiorum was collected in four distinct regions of France and 498 strains were genotyped with 16 specific microsatellite markers and compared among the regions. Air mass movements were inferred using the HYSPLIT model and archived meteorological data from the global data assimilation system (GDAS). The results show that up to 700 km could separate collection sites that shared the same haplotypes. There was low or no genetic differentiation between strains collected from the four sites. The rate of aerial connectivity between two sites varied according to the direction considered. The results also show that the aerial connectivity between sites is a better indicator of the probability of the incoming component (PIC) of inoculum at a given site from another one than is geographic distance. We identified the links between specific sites in the trajectories of air masses and we quantified the frequencies at which the directional links occurred as a proof-of-concept for an operational method to assess the arrival of airborne inoculum in a given area from distant origins.

Estimation of the dispersal distances of an aphid-borne virus in a patchy landscape.

Characterising the spatio-temporal dynamics of pathogens in natura is key to ensuring their efficient prevention and control. However, it is notoriously difficult to estimate dispersal parameters at scales that are relevant to real epidemics. Epidemiological surveys can provide informative data, but parameter estimation can be hampered when the timing of the epidemiological events is uncertain, and in the presence of interactions between disease spread, surveillance, and control. Further complications arise from imperfect detection of disease and from the huge number of data on individual hosts arising from landscape-level surveys. Here, we present a Bayesian framework that overcomes these barriers by integrating over associated uncertainties in a model explicitly combining the processes of disease dispersal, surveillance and control. Using a novel computationally efficient approach to account for patch geometry, we demonstrate that disease dispersal distances can be estimated accurately in a patchy (i.e. fragmented) landscape when disease control is ongoing. Applying this model to data for an aphid-borne virus (Plum pox virus) surveyed for 15 years in 605 orchards, we obtain the first estimate of the distribution of flight distances of infectious aphids at the landscape scale. About 50% of aphid flights terminate beyond 90 m, which implies that most infectious aphids leaving a tree land outside the bounds of a 1-ha orchard. Moreover, long-distance flights are not rare-10% of flights exceed 1 km. By their impact on our quantitative understanding of winged aphid dispersal, these results can inform the design of management strategies for plant viruses, which are mainly aphid-borne.