Nik J. Cunniffe

Epidemiological modeling of invasion in heterogeneous landscapes: spread of sudden oak death in California (1990–2030)

The spread of emerging infectious diseases (EIDs) in natural environments poses substantial risks to biodiversity and ecosystem function. As EIDs and their impacts grow, landscape- to regional-scale models of disease dynamics are increasingly needed for quantitative prediction of epidemic outcomes and design of practicable strategies for control. Here we use spatio-temporal, stochastic epidemiological modeling in combination with realistic geographical modeling to predict the spread of the sudden oak death pathogen (Phytophthora ramorum) through heterogeneous host populations in wildland forests, subject to fluctuating weather conditions. The model considers three stochastic processes: (1) the production of inoculum at a given site; (2) the chance that inoculum is dispersed within and among sites; and (3) the probability of infection following transmission to susceptible host vegetation. We parameterized the model using Markov chain Monte Carlo (MCMC) estimation from snapshots of local- and regional-scale data on disease spread, taking account of landscape heterogeneity and the principal scales of spread. Our application of the model to Californian landscapes over a 40-year period (1990–2030), since the approximate time of pathogen introduction, revealed key parameters driving the spatial spread of disease and the magnitude of stochastic variability in epidemic outcomes. Results show that most disease spread occurs via local dispersal (<250 m) but infrequent long-distance dispersal events can substantially accelerate epidemic spread in regions with high host availability and suitable weather conditions. In the absence of extensive control, we predict a ten-fold increase in disease spread between 2010 and 2030 with most infection concentrated along the north coast between San Francisco and Oregon. Long-range dispersal of inoculum to susceptible host communities in the Sierra Nevada foothills and coastal southern California leads to little secondary infection due to lower host availability and less suitable weather conditions. However, a shift to wetter and milder conditions in future years would double the amount of disease spread in California through 2030. This research illustrates how stochastic epidemiological models can be applied to realistic geographies and used to increase predictive understanding of disease dynamics in large, heterogeneous regions.

FUTURES: Multilevel Simulations of Emerging Urban–Rural Landscape Structure Using a Stochastic Patch-Growing Algorithm

We present a multilevel modeling framework for simulating the emergence of landscape spatial structure in urbanizing regions using a combination of field-based and object-based representations of land change. The FUTure Urban-Regional Environment Simulation (FUTURES) produces regional projections of landscape patterns using coupled submodels that integrate nonstationary drivers of land change: per capita demand, site suitability, and the spatial structure of conversion events. Patches of land change events are simulated as discrete spatial objects using a stochastic region-growing algorithm that aggregates cell-level transitions based on empirical estimation of parameters that control the size, shape, and dispersion of patch growth. At each time step, newly constructed patches reciprocally influence further growth, which agglomerates over time to produce patterns of urban form and landscape fragmentation. Multilevel structure in each submodel allows drivers of land change to vary in space (e.g., by jurisdiction), rather than assuming spatial stationarity across a heterogeneous region. We applied FUTURES to simulate land development dynamics in the rapidly expanding metropolitan region of Charlotte, North Carolina, between 1996 and 2030, and evaluated spatial variation in model outcomes along an urban–rural continuum, including assessments of cell- and patch-based correctness and error. Simulation experiments reveal that changes in per capita land consumption and parameters controlling the distribution of development affect the emergent spatial structure of forests and farmlands with unique and sometimes counterintuitive outcomes.

Thirteen challenges in modelling plant diseases

The underlying structure of epidemiological models, and the questions that models can be used to address, do not necessarily depend on the host organism in question. This means that certain preoccupations of plant disease modellers are similar to those of modellers of diseases in human, livestock and wild animal populations. However, a number of aspects of plant epidemiology are very distinctive, and this leads to specific challenges in modelling plant diseases, which in turn sets a certain agenda for modellers. Here we outline a selection of 13 challenges, specific to plant disease epidemiology, that we feel are important targets for future work.

Predicting the economic costs and property value losses attributed to sudden oak death damage in California (2010-2020).

Phytophthora ramorum, cause of sudden oak death, is a quarantined, non-native, invasive forest pathogen resulting in substantial mortality in coastal live oak (Quercus agrifolia) and several other related tree species on the Pacific Coast of the United States. We estimate the discounted cost of oak treatment, removal, and replacement on developed land in California communities using simulations of P. ramorum spread and infection risk over the next decade (2010-2020). An estimated 734 thousand oak trees occur on developed land in communities in the analysis area. The simulations predict an expanding sudden oak death (SOD) infestation that will likely encompass most of northwestern California and warrant treatment, removal, and replacement of more than 10 thousand oak trees with discounted cost of

The effect of landscape pattern on the optimal eradication zone of an invading epidemic.

7.5 million. In addition, we estimate the discounted property losses to single family homes of

A theoretical framework for biological control of soil-borne plant pathogens: Identifying effective strategies.

135 million. Expanding the land base to include developed land outside as well as inside communities doubles the estimates of the number of oak trees killed and the associated costs and losses. The predicted costs and property value losses are substantial, but many of the damages in urban areas (e.g. potential losses from increased fire and safety risks of the dead trees and the loss of ecosystem service values) are not included.

Optimising and Communicating Options for the Control of Invasive Plant Disease When There Is Epidemiological Uncertainty

A number of high profile eradication attempts on plant pathogens have recently been attempted in response to the increasing number of introductions of economically significant nonnative pathogen species. Eradication programs involve the removal of a large proportion of a host population and can thus lead to significant social and economic costs. In this paper we use a spatially explicit stochastic model to simulate an invading pathogen and show that it is possible to identify an optimal control radius, i.e., one that minimizes the total number of hosts removed during an eradication campaign that is effective in eradicating the pathogen. However, by simulating the epidemic and eradication processes in multiple landscapes, we demonstrate that the optimal radius depends critically on landscape pattern (i.e., the spatial configuration of hosts within the landscape). In particular, we find that the optimal radius, and also the number of host removals associated with it, increases with both the level of aggregation and the density of hosts in the landscape. The result is of practical significance and demonstrates that the location of an invading epidemic should be a key consideration in the design of future eradication strategies.

Invasion, persistence and control in epidemic models for plant pathogens: the effect of host demography.

We develop and analyse a flexible compartmental model of the interaction between a plant host, a soil-borne pathogen and a microbial antagonist, for use in optimising biological control. By extracting invasion and persistence thresholds of host, pathogen and biological control agent, performing an equilibrium analysis, and numerical investigation of sensitivity to parameters and initial conditions, we determine criteria for successful biological control. We identify conditions for biological control (i) to prevent a pathogen entering a system, (ii) to eradicate a pathogen that is already present and, if that is not possible, (iii) to reduce the density of the pathogen. Control depends upon the epidemiology of the pathogen and how efficiently the antagonist can colonise particular habitats (i.e. healthy tissue, infected tissue and/or soil-borne inoculum). A sharp transition between totally effective control (i.e. eradication of the pathogen) and totally ineffective control can follow slight changes in biologically interpretable parameters or to the initial amounts of pathogen and biological control agent present. Effective biological control requires careful matching of antagonists to pathosystems. For preventative/eradicative control, antagonists must colonise susceptible hosts. However, for reduction in disease prevalence, the range of habitat is less important than the antagonists bulking-up efficiency.

Cost-effective control of plant disease when epidemiological knowledge is incomplete: modelling Bahia bark scaling of citrus.

Although local eradication is routinely attempted following introduction of disease into a new region, failure is commonplace. Epidemiological principles governing the design of successful control are not well-understood. We analyse factors underlying the effectiveness of reactive eradication of localised outbreaks of invading plant disease, using citrus canker in Florida as a case study, although our results are largely generic, and apply to other plant pathogens (as we show via our second case study, citrus greening). We demonstrate how to optimise control via removal of hosts surrounding detected infection (i.e. localised culling) using a spatially-explicit, stochastic epidemiological model. We show how to define optimal culling strategies that take account of stochasticity in disease spread, and how the effectiveness of disease control depends on epidemiological parameters determining pathogen infectivity, symptom emergence and spread, the initial level of infection, and the logistics and implementation of detection and control. We also consider how optimal culling strategies are conditioned on the levels of risk acceptance/aversion of decision makers, and show how to extend the analyses to account for potential larger-scale impacts of a small-scale outbreak. Control of local outbreaks by culling can be very effective, particularly when started quickly, but the optimum strategy and its performance are strongly dependent on epidemiological parameters (particularly those controlling dispersal and the extent of any cryptic infection, i.e. infectious hosts prior to symptoms), the logistics of detection and control, and the level of local and global risk that is deemed to be acceptable. A version of the model we developed to illustrate our methodology and results to an audience of stakeholders, including policy makers, regulators and growers, is available online as an interactive, user-friendly interface at http://www.webidemics.com/. This version of our model allows the complex epidemiological principles that underlie our results to be communicated to a non-specialist audience.

Spatial Sampling to Detect an Invasive Pathogen Outside of an Eradication Zone

Many epidemiological models for plant disease include host demography to describe changes in the availability of susceptible tissue for infection. We compare the effects of using two commonly used formulations for host growth, one linear and the other nonlinear, upon the outcomes for invasion, persistence and control of pathogens in a widely used, generic model for botanical epidemics. The criterion for invasion, reflected in the basic reproductive number, R0, is unaffected by host demography: R0 is simply a function of epidemiological parameters alone. When, however, host growth is intrinsically nonlinear, unexpected results arise for persistence and the control of disease. The endemic level of infection (I∞) also depends upon R0. We show, however, that the sensitivity of I∞ to changes in R0 > 1 depends upon which underlying epidemiological parameter is changed. Increasing R0 by shortening the infectious period results in a monotonic increase in I∞. If, however, an increase in R0 is driven by increases in transmission rates or by decreases in the decay of free-living inoculum, I∞ first increases (R0 < 2), but then decreases (R0 > 2). This counterintuitive result means that increasing the intensity of control can result in more endemic infection.