Christopher A. Gilligan

Metapopulation dynamics of bubonic plague.

Bubonic plague is widely regarded as a disease of mainly historical importance; however, with increasing reports of incidence and the discovery of antibiotic-resistant strains of the plague bacterium Yersinia pestis, it is re-emerging as a significant health concern. Here we bypass the conventional human-disease models, and propose that bubonic plague is driven by the dynamics of the disease in the rat population. Using a stochastic, spatial metapopulation model, we show that bubonic plague can persist in relatively small rodent populations from which occasional human epidemics arise, without the need for external imports. This explains why historically the plague persisted despite long disease-free periods, and how the disease re-occurred in cities with tight quarantine control. In a contemporary setting, we show that human vaccination cannot eradicate the plague, and that culling of rats may prevent or exacerbate human epidemics, depending on the timing of the cull. The existence of plague reservoirs in wild rodent populations has important public-health implications for the transmission to urban rats and the subsequent risk of human outbreaks.

Bubonic plague: a metapopulation model of a zoonosis

Bubonic plague (Yersinia pestis) is generally thought of as a historical disease; however, it is still responsible for around 1000–3000 deaths each year worldwide. This paper expands the analysis of a model for bubonic plague that encompasses the disease dynamics in rat, flea and human populations. Some key variables of the deterministic model, including the force of infection to humans, are shown to be robust to changes in the basic parameters, although variation in the flea searching efficiency, and the movement rates of rats and fleas will be considered throughout the paper. The stochastic behaviour of the corresponding metapopulation model is discussed, with attention focused on the dynamics of rats and the force of infection at the local spatial scale. Short–lived local epidemics in rats govern the invasion of the disease and produce an irregular pattern of human cases similar to those observed. However, the endemic behaviour in a few rat subpopulations allows the disease to persist for many years. This spatial stochastic model is also used to identify the criteria for the spread to human populations in terms of the rat density. Finally, the full stochastic model is reduced to the form of a probabilistic cellular automaton, which allows the analysis of a large number of replicated epidemics in large populations. This simplified model enables us to analyse the spatial properties of rat epidemics and the effects of movement rates, and also to test whether the emergent metapopulation behaviour is a property of the local dynamics rather than the precise details of the model.

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.

Effect of bulk density on the spatial organisation of the fungus Rhizoctonia solani in soil

Abstract The mycelial growth form of eucarpic fungi allows for a highly effective spatial exploration of the soil habitat. However, understanding mycelial spread through soil has been limited by difficulties of observation and quantification of fungi as they spread through this matrix. We report on a study on the effects of soil structure by altering the soil bulk density, on the spatial exploration of soil by the fungus Rhizoctonia solani using a soil thin-sectioning technique. First we quantified fungal densities in microscopic images (0.44 mm(2)). At this scale, hyphae were either absent, or present as minor fragments, typically occupying less than 1% surface area of the thin section. From contiguous microscopic images we then produced large-scale (6.21 cm(2)) spatial distribution maps of fungal hyphae. These maps were superimposed onto soil structural maps, which quantify the degree of porosity in each microscopic image. Alterations in soil structure by changing the bulk density are shown to affect the distribution of the fungus within the soil. The volume of soil explored by the fungus increased with increasing bulk density. This was associated with a shift from a few large pore spaces to more evenly distributed small-scale pores. Fungal hyphae were present in all porosity classes within each bulk density, including areas that contain less than 5% visible pore space. However, fungal hyphae were more often found in areas with a higher porosity, in particular at low soil bulk densities. The results show that soil structure is a major component in the spatial exploration of soil by fungi.

Landscape epidemiology and control of pathogens with cryptic and long-distance dispersal: Sudden oak death in northern Californian forests

Exotic pathogens and pests threaten ecosystem service, biodiversity, and crop security globally. If an invasive agent can disperse asymptomatically over long distances, multiple spatial and temporal scales interplay, making identification of effective strategies to regulate, monitor, and control disease extremely difficult. The management of outbreaks is also challenged by limited data on the actual area infested and the dynamics of spatial spread, due to financial, technological, or social constraints. We examine principles of landscape epidemiology important in designing policy to prevent or slow invasion by such organisms, and use Phytophthora ramorum, the cause of sudden oak death, to illustrate how shortfalls in their understanding can render management applications inappropriate. This pathogen has invaded forests in coastal California, USA, and an isolated but fast-growing epidemic focus in northern California (Humboldt County) has the potential for extensive spread. The risk of spread is enhanced by the pathogens generalist nature and survival. Additionally, the extent of cryptic infection is unknown due to limited surveying resources and access to private land. Here, we use an epidemiological model for transmission in heterogeneous landscapes and Bayesian Markov-chain-Monte-Carlo inference to estimate dispersal and life-cycle parameters of P. ramorum and forecast the distribution of infection and speed of the epidemic front in Humboldt County. We assess the viability of management options for containing the pathogens northern spread and local impacts. Implementing a stand-alone host-free “barrier” had limited efficacy due to long-distance dispersal, but combining curative with preventive treatments ahead of the front reduced local damage and contained spread. While the large size of this focus makes effective control expensive, early synchronous treatment in newly-identified disease foci should be more cost-effective. We show how the successful management of forest ecosystems depends on estimating the spatial scales of invasion and treatment of pathogens and pests with cryptic long-distance dispersal.

Models of Fungicide Resistance Dynamics

We describe two classes of models used for fungicide and antibiotic resistance dynamics. One class assumes that the density of the pathogen (or severity of the disease caused by the pathogen) has no feedback effects on the rate at which new infections arise. The second class does not make this assumption. A quantitative relationship between these two classes is derived. We then discuss the two sets of assumptions made in the literature about initial conditions: either both the fungicide-sensitive strain and the -resistant strain are initially at low density, or the sensitive strain is resident at nonlow density and the resistant strain is initially at low density. We show that models of fungicide resistance dynamics with and without density-dependent feedback give contrasting predictions on the effects of pathogen life-cycle parameters and the effects of the fungicide (dose, frequency, use of mixtures, spatial usage restrictions) on the evolution, invasion, and spread of fungicide resistance. We further show that the evaluation of a resistance management strategy requires a very precise definition of what constitutes a good strategy.

Optimal control of epidemics in metapopulations.

Little is known about how best to deploy scarce resources for disease control when epidemics occur in different but interconnected regions. We use a combination of optimal control methods and epidemiological theory for metapopulations to address this problem. We consider what strategy should be used if the objective is to minimize the discounted number of infected individuals during the course of an epidemic. We show, for a system with two interconnected regions and an epidemic in which infected individuals recover and can be reinfected, that equalizing infection in the two regions is the worst possible strategy in minimizing the total level of infection. Treatment should instead be preferentially directed at the region with the lower level of infection, treating the other subpopulation only when there is resource left over. The same strategy holds with preferential treatments of regions with lower levels of infection when quarantine is introduced.

Sustainable agriculture and plant diseases: an epidemiological perspective.

The potential for modern biology to identify new sources for genetical, chemical and biological control of plant disease is remarkably high. Successful implementation of these methods within globally and locally changing agricultural environments demands new approaches to durable control. This, in turn, requires fusion of population genetics and epidemiology at a range of scales from the field to the landscape and even to continental deployment of control measures. It also requires an understanding of economic and social constraints that influence the deployment of control. Here I propose an epidemiological framework to model invasion, persistence and variability of epidemics that encompasses a wide range of scales and topologies through which disease spreads. By considering how to map control methods onto epidemiological parameters and variables, some new approaches towards optimizing the efficiency of control at the landscape scale are introduced. Epidemiological strategies to minimize the risks of failure of chemical and genetical control are presented and some consequences of heterogeneous selection pressures in time and space on the persistence and evolutionary changes of the pathogen population are discussed. Finally, some approaches towards embedding epidemiological models for the deployment of control in an economically plausible framework are presented.

Measures of durability of resistance.

ABSTRACT Conventional models for the durability of resistant cultivars focus on the dynamics of the frequency of resistance genes. This leads to a definition of the durability of resistance as the time from introduction of the cultivar to the time when the frequency of the virulence gene reaches a preset threshold. It is questionable whether this is the most appropriate way to measure durability. Here we use a simple epidemiological model to link population dynamics and population genetics to compare three measures of durability: (i) the expected time until invasion of the virulent genotype, by mutation or immigration, and subsequent establishment of a population (T(invasion)); (ii) the virulence frequency related measure of the time for the virulent genotype to take-over the pathogen population ( T(take-over)); and (iii) the additional yield, measured by the additional number of uninfected host growth days (T(additional)). Specifically, we show how the measures of durability are affected by deployment and epidemiological parameters. We use a combination of numerical solution and analytical approximation of a model for the population dynamics of avirulent and virulent genotypes of a pathogen growing in dynamically changing populations of resistant and susceptible cultivars. The three measures of durability are compared. Some consequences of the results for durable resistance in multilines and mixtures and the regional deployment of resistant cultivars are discussed.

Optimizing the control of disease infestations at the landscape scale

Using a contact-process model for the spread of crop disease over a regional scale, we examine the importance of the time scale for control with respect to the cost of the epidemic. The costs include the direct cost of treating infected sites as well as the indirect costs incurred through lost yield. We first use a mean-field approximation to derive analytical results for the optimal treatment regimes that minimize the total cost of the epidemic. We distinguish short- and long-term epidemics. and show that seasonal control (short time scale) requires extreme treatment, either treating all sites or none or switching between the two at some stage during the season. The optimal long-term strategy requires an intermediate level of control that results in near eradication of the disease. We also demonstrate the importance of incorporating economic constraints by deriving a critical relationship between the epidemiological and economic parameters that determine the qualitative nature of the optimal treatment strategy. The set of optimal strategies is summarized in a policy plot, which can be used to determine the nature of the optimal treatment regime given prior knowledge of the epidemiological and economic parameters. Finally, we test the robustness of the analytical results, derived from the mean-field approximation, on the spatially explicit contact process and demonstrate robustness to implementation errors and misestimation of crucial parameters.