Network models for spread and control of soil-borne epidemics

Lead Research Organisation: University of Cambridge
Department Name: Plant Sciences


There is an urgent need for reliable control strategies for epidemics caused by soil-borne plant pathogens. In particular for root-diseases, a fundamental approach is lacking. Susceptible plants or roots are spatially separated in a heterogeneous, dynamically changing soil environment through which pathogens spread. The opacity and heterogeneity of soil makes it difficult to deliver control agents. Currently, there is no coherent theoretical framework available that can deal with such a complicated and heterogeneous system. Hence practitioners and scientist are still applying biological and chemical control strategies empirically. This proposal is set out to change this, by developing and testing a theory for soil-borne epidemics. The main aims of this project are to link developments from non-equilibrium statistical physics with epidemiological theory and experimentation in order: 1. to model and analyse the spread of soil-borne diseases through inherently heterogeneous systems at microscopic and macroscopic scales, using theory of non-equilibrium phase transition in complex networks; 2. to analyse the efficiency of control strategies on such disordered networks. In previous work we have shown that a small change in environmental conditions can induce a switch from non-invasive to invasive spread for soil-borne pathogens, and that this behaviour is consistent with thresholds predicted from percolation theory for networks. Experimentation, however, was conducted in artificial systems, and the concept of sudden changes to ecosystems remains counterintuitive and subject of debate amongst biologists. Experimental verification of model predictions under realistic scenarios is therefore important. Moreover, a close interaction between experimentation and modelling such as we propose will lead to appropriate model parameterisation and to testing of the robustness of predictions under realistic heterogeneous conditions. Despite these undisputed benefits, experimental testing of theoretical predictions is rare. We propose that network models offer a way forward for soil-borne epidemics in that testable hypotheses related to invasion and persistence can be formulated. Susceptible sites in soil-borne epidemics can be identified as roots or plants, in various spatial arrangements, analogous to networks. The connections between sites may be weak or strong (depending on mode of dispersal (propagation)), permanent or temporal (depending on soil physical conditions, host growth, recovery, and changes in susceptibility), with sites spatially arranged either in lines (crops grown in rows), regular lattice (crops or propagation trays), or off-lattice (e.g. spatial distribution of roots). The spread of epidemics on complex networks has been the topic of intensive investigation, yet the inherent heterogeneity typical for epidemics is often omitted in these models. Such heterogeneity, however, can appreciably affect the behaviour of networks. In this proposal we will tackle this by extending the theory for network models to heterogeneous systems making use and building upon our expertise in non-equilibrium statistical physics. Our experimental and theoretical expertise in soil physics and soil-borne epidemics will enable us to identify ways to manipulate the network topology and the network parameters (transmission and recovery), and to collect data on replicated epidemics, which allows for testing of model prediction on invasion and extinction. By linking our expertises in non-equilibrium statistical physics with epidemiological theory and experimentation we will formulate and test appropriate models, and use these to identify those conditions that can significantly change epidemics (make epidemics invade and persist), and will hence identify control strategies that are most likely to be successful in such a complex environment.

Technical Summary

The spread of epidemics in complex networks exemplified by biological populations including animals, human and plants is a very important area of research from both fundamental and practical viewpoints. Real epidemics spread in networks which are inherently disordered with network parameters including recovery and transmission rates varying throughout populations. Such disorders can influence crucially the behaviour within a network and understanding the role of disorder in the dynamical properties of epidemics within realistic disordered biological networks is of major significance for the control of epidemics. The main aims of this project are to link developments from non-equilibrium statistical physics with epidemiological theory and experimentation in order: 1. to model and analyse the spread of soil-borne diseases through inherently heterogeneous systems at microscopic and macroscopic scales, using theory of non-equilibrium phase transition in complex networks; 2. to analyse the efficiency of control strategies on such disordered systems. We will develop and experimentally test this theory for contrasting epidemiological systems, namely (a) root systems, and (b) plants on lattices. In each system we will consider the spread of selected pathogens with different mode of dispersal. Our approach is motivated by recent work in the PI's group where we validated the existence of theoretical thresholds for invasion empirically, the expertise of the CI in theoretical analysis of complex networks, which now makes it possible to develop and test network-based models for soil-borne epidemics in inherently heterogeneous environments. The findings will have applicability to a broad range of eidemics and will identify criteria for invasion (e.g. plant densities or dispersal distance of pathogens) and will provide guidance for the deployment of control strategies in heterogeneous environments.


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Fallert SV (2008) Contact process in disordered and periodic binary two-dimensional lattices. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Fallert SV (2009) Scaling behavior of the disordered contact process. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Fallert SV (2008) Simulating the contact process in heterogeneous environments. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Gilligan CA (2008) Sustainable agriculture and plant diseases: an epidemiological perspective. in Philosophical transactions of the Royal Society of London. Series B, Biological sciences

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Gilligan CA (2008) Epidemiological models for invasion and persistence of pathogens. in Annual review of phytopathology

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Handford TP (2011) Epidemics in networks of spatially correlated three-dimensional root-branching structures. in Journal of the Royal Society, Interface

Description This project has delivered (i) various novel analytical tools for analysis of invasion in heterogeneous populations, novel concepts for control strategies for epidemics and tools for statistical inference. i. Analytical tools: We have developed several analytical tools for invasion in heterogeneous root, crop and soil environments. These tools include: a. A method to account for the morphological complexity of hosts (comprising plant root systems) in epidemiological models. Our analysis has revealed that disorder expressed in the host morphology and anisotropy has important effects on the ability of pathogens to invade a population [Refs. 1,2,15]. We have developed simplified 'toy' models that capture the main morphological features of hosts influencing the spread of epidemics. Such models are prototypes for epidemics in populations of morphologically complex hosts, and the estimates for invasion thresholds can be linked to morphological characteristics that can be used for invasions in practical models. b. Models that analyse invasion of SIS and SIR epidemics in populations with different types of hosts (comprising single plants, root systems, and exceptionally fields) regularly or randomly placed on lattices (e.g. hosts belonging to two different classes with different infectivity and susceptibility) [Refs. 4-9]. Based on a theoretical analysis of SIR epidemics with heterogeneity, we showed for the first time that the resilience of such systems to invasion can be suitably described by two control parameters, the mean and variance of the transmissibility [Ref. 9]. c. Experimental systems: We designed experimental systems and protocols that enable practical testing of the effect of host heterogeneity on the development of epidemics and the thresholds for invasion [Ref. 13]. d. Models for biological invasion in soils: We developed methods to derive networks from the pore network in soils obtained with X-ray Computed Tomography and developed mathematical models to analyse biological invasion on these 3-D networks [Ref. Conf paper with two further papers in advanced draft] e. Models including synergistic effects: For many epidemics, the transmission of the pathogens between any pair ofhosts in a population is affected by the presence of other colonised hosts nearby but has till now been routinely ignored in models for epidemic spread. We have developed theoretical methods to analyse and describe such synergistic effects in epidemics. Our results show that synergy can significantly affect important features of invasions, including the patch-size distribution and the time-scales for invasion [Ref. 10]. ii. Novel insights for Control strategies: a. Control of epidemics spreading through heterogeneous populations of hosts: having initially analysed the effects of host heterogeneity on the transmission of disease and the probability of invasion, we have identified strategies that exploit the degree of heterogeneity in a population in order to enhance the effectiveness of control. We have also identified criteria to distinguish when complete or partial control is sufficient to prevent invasion [Ref 9]. These methods have direct application to a range of host-pathogen systems as well as the soil-borne based systems for which they have been developed [Ref 9]. b. The methodology in (a) has been tested in experimental systems involving spread of R. solani on cauliflower in the presence and absence of the biocontrol agent, T. viride. [Paper in preparation]. c. We have demonstrated how changes in the morphology of root systems (that could in principle be affected by plant breeding or crop nutrition) could affect pathogen invasion [Refs. 1,2,15]. iii. Methods for statistical inference and prediction: A new method adapted from Approximate Bayesian Computation has been developed to predict the evolution of the epidemics from a limited number of observations at the start of an epidemic.
Exploitation Route The experimental, mathematical and statistical methods are clearly documented in the papers associated with this project and could be used by other researchers to apply in new soil systems with different host pathogens or to continue further development of the research.
Sectors Agriculture, Food and Drink,Environment

Description 1. Spread of disease in morphologically complex hosts. We have identified morphological parameters of complex root systems that affect the transmission of soil-borne plant pathogens, showing, in particular, the quantitative effect of such parameters on the threshold for invasion of the pathogen, and hence, disease. 2. Effect of heterogeneity on invasion and control of disease. We have shown rigorously for the first time how heterogeneity in host populations affects the probability of invasion of soil-borne plant pathogens, and we have identified disease control strategies that make use of inherent heterogeneity, typical of most plant populations. 3. Modelling epidemic spread on soil networks. We have derived 3-D network models that represent soil structure from 3-D X-ray CT data and used epidemiological models to show the impact of soil heterogeneity in the pore network on the probability of invasive spread of pathogens through soil.
First Year Of Impact 2010
Sector Agriculture, Food and Drink