Applications of percolation theory to fungal spread with synergy

There is increasing interest in the use of the percolation paradigm to analyze and predict the progress of disease spreading in spatially-structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is in uenced only by that of its neighbours. In a recent paper the percolation paradigm has been generalised to incorporate synergistic interactions in host infectivity and susceptibility and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by rst formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently tting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model tting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease control strategies that de ect epidemics from invasive to non-invasive regimes are discussed

The effect of heterogeneity on invasion in spatial epidemics: from theory to experimental evidence in a model system

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

A Bayesian space-time model for discrete spread processes on a lattice

Funding for this work was provided by GEOIDE through the Government of Canada’s Networks for Centres of Excellence program.In this article we present a Bayesian Markov model for investigating environmental spread processes. We formulate a model where the spread of a disease over a heterogeneous landscape through time is represented as a probabilistic function of two processes: local diffusion and random-jump dispersal. This formulation represents two mechanisms of spread which result in highly peaked and long-tailed distributions of dispersal distances (i.e., local and long-distance spread), commonly observed in the spread of infectious diseases and biological invasions. We demonstrate the properties of this model using a simulation experiment and an empirical case study - the spread of mountain pine beetle in western Canada. Posterior predictive checking was used to validate the number of newly inhabited regions in each time period. The model performed well in the simulation study in which a goodness-of-fit statistic measuring the number of newly inhabited regions in each time interval fell within the 95% posterior predictive credible interval in over 97% of simulations. The case study of a mountain pine beetle infestation in western Canada (1999-2009) extended the base model in two ways. First, spatial covariates thought to impact the local diffusion parameters, elevation and forest cover, were included in the model. Second, a refined definition for translocation or jump-dispersal based on mountain pine beetle ecology was incorporated improving the fit of the model. Posterior predictive checks on the mountain pine beetle model found that the observed goodness-of-fit test statistic fell within the 95% posterior predictive credible interval for 8 out of 10. years. The simulation study and case study provide evidence that the model presented here is both robust and flexible; and is therefore appropriate for a wide range of spread processes in epidemiology and ecology.PostprintPeer reviewe

Complexity and anisotropy in host morphology make populations safer against epidemic outbreaks

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to analyse separately the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.Comment: 21 pages, 8 figure

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

Inference and experimental design for percolation and random graph models.

The problem of optimal arrangement of nodes of a random weighted graph is studied in this thesis. The nodes of graphs under study are fixed, but their edges are random and established according to the so called edge-probability function. This function is assumed to depend on the weights attributed to the pairs of graph nodes (or distances between them) and a statistical parameter. It is the purpose of experimentation to make inference on the statistical parameter and thus to extract as much information about it as possible. We also distinguish between two different experimentation scenarios: progressive and instructive designs. We adopt a utility-based Bayesian framework to tackle the optimal design problem for random graphs of this kind. Simulation based optimisation methods, mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We study optimal design problem for the inference based on partial observations of random graphs by employing data augmentation technique. We prove that the infinitely growing or diminishing node configurations asymptotically represent the worst node arrangements. We also obtain the exact solution to the optimal design problem for proximity graphs (geometric graphs) and numerical solution for graphs with threshold edge-probability functions. We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice Zd and derive a range of both numerical and analytical results for these graphs. We introduce inner-outer plots by deleting some of the lattice nodes and show that the ‘mostly populated’ designs are not necessarily optimal in the case of incomplete observations under both progressive and instructive design scenarios. Finally, we formulate a problem of approximating finite point sets with lattice nodes and describe a solution to this problem

Characterising Livestock System Zoonoses Hotspots

A systematic review of the published literature was undertaken, to explore the ability of different types of model to help identify the relative importance of different drivers leading to the development of zoonoses hotspots. We estimated that out of 373 papers we included in our review, 108 papers touched upon the objective of 'Assessment of interventions and intervention policies', 75 addressed the objective of 'Analysis of economic aspects of disease outbreaks and interventions', 67 the objective of 'Prediction of future outbreaks', but only 37 broadly addressed the objective of 'Sensitivity analysis to identify criteria leading to enhanced risk'. Most models of zoonotic diseases are currently capturing outbreaks over relatively short time and largely ignoring socio-economic drivers leading to pathogen emergence, spill-over and spread. In order to study long-term changes we need to understand how socio-economic and climatic changes affect structure of livestock production and how these in turn affect disease emergence and spread. Models capable of describing this processes do not appear to exist, although some progress has been made in linking social and economical aspects of livestock production and in linking economics to disease dynamics. Henceforth we conclude that a new modelling framework is required that expands and formalises the 'one world, one health' strategy, enabling its deployment in the re-thinking of prevention and control strategies. Although modelling can only provide means to identify risks associated with socio-economic changes, it can never be a substitute for data collection. Finally, we note that uncertainty analysis and uncertainty communication form a key element of modelling process and yet are rarely addressed