On the Spatial Spread of Insect Pathogens: Theory and Experiment

Abstract

The mathematical theory of animal diseases has seen explosive growth in the past decade, yet most of the existing theory examines only temporal disease spread, ignoring the effects of patchy host or pathogen spatial distributions. Here I present a model for the within—season spatial spread of insect pathogens that incorporates host movement in an otherwise conventional insect host—pathogen model. Mathematical analysis of the model reveals that the pathogen will spread through the host population in a moving wave front of disease, known as a "travelling wave." This analysis shows how the spatial rate of spread of the pathogen depends upon the transmission rate of the disease, the rate of production of the pathogen by infected hosts, the initial population of the host, the decay rate of the pathogen, and the death rate of infected hosts. To test the predictions of the model, I performed a series of field experiments with the nuclear polyhedrosis virus (NPV) of Douglas—fir tussock moth, Orgyia pseudotsugata. First, I estimated each of the parameters of the model in the field with a series of small—scale experiments, and used the parameter estimates to predict the spatial rate of spread of the NPV through a population of tussock moth larvae (NPV diseases, like many insect pathogens, do not infect adults). To test this prediction, I then performed an experiment in which I measured the rate of spread of the NPV in an experimental population of tussock moth larvae on linear arrays of Douglas—fir seedlings. The model predicts the rate of spread of tussock moth NPV fairly accurately, suggesting that one can use this type of model to extrapolate individual behavior and localized transmission patterns to broader—scale spatial dynamics.

Effects of Host Variability on the Spread of Invasive Forest Diseases

“…In a forest stand, the epidemic spread rates are driven by the contacts between infected and healthy hosts or between vectors and infected/healthy hosts [71]. Both types of contact strongly depend on host density, which, in mixed forests, may vary significantly.…”

Free-living pathogens: Life-history constraints and strain competition

“…A free-living stage may possess morphological and physiological adaptations allowing it to endure lengthy periods without decaying (Anderson and May, 1981;Dwyer, 1992;Setlow, 2007); the pathogen consequently can persist through episodes of low host density (Dwyer, 1994;Bonhoeffer et al, 1996;Gandon 1998). Our paper asks how interactions between the decay rate of free-living infectious particles and other pathogen traits might affect the outcome of competition between different pathogen strains.…”

“…We make a simplification, common in models with free-living particles (e.g., Dwyer, 1992;Day, 2002), and assume that the rate of particle depletion by hosts has negligible impact on particle dynamics. Dwyer (1994), referring to Anderson and May (1981), offers justification for this assumption.…”

A model of insect—pathogen dynamics in which a pathogenic bacterium can also reproduce saprophytically

“…Unfortunately, insu¤cient data are currently available to construct such a model, although aspects of the within-season dynamics of the Serratia^grass grub interaction have been modelled without the additional complexity of saprophytism and bacterial competition (Barlow & Jackson 1992;Drummond et al 1996). Our intention here is to explore the population dynamics of the insect^pathogen^saprophyte interaction using the type of detail-independent model pioneered in insectp athogen studies by Anderson & May (1980, 1981; see also, for example, Begon et al 1992;Begon & Bowers 1994;Bowers & Begon 1991;Dwyer 1992;Dwyer & Elkinton 1993;Hochberg 1989Hochberg , 1991Thomas et al 1995;White et al 1996a). While such models are unable to make precise quantitative predictions about the population dynamics of speci¢c systems, they are often highly successful at predicting qualitative dynamic patterns (e.g.…”