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In this paper we introduce a method to analyze the inter- and intraspecies transmission rates and contact structure between susceptible and infected plants in epidemics in mixed plant populations. Using spatiotemporal maps of damping-off epidemics caused by Rhizoctonia solani in replicated microcosms of >400 randomly mixed radish and mustard seedlings, we first show that as an epidemic progresses through a mixed plant population it changes the contact structure between infected (I) and susceptible (S) plants, so that resistant plants are challenged progressively more frequently, thereby slowing the epidemic. We estimate the transmission rates for each of the four S-I pair combinations. All transmission rates rose initially with time and then declined, with overall lower rates for the more resistant mustard species. However, the interspecies transmission rates were unexpectedly high. We show how these rates relate to relative changes in infectivity and susceptibility of each host species, and how a species that is weakly susceptible in a pure stand can still act as a strong donor of disease in a mixture, thereby lowering the efficacy of the mixture to reduce disease. We discuss the broader consequences for the dynamics of disease in natural and managed populations. Key words: disease control; mixed host populations; primary and secondary infection; Rhizoctonia solani; soil-borne diseases; transmission of infection.

The rates of transmission of infection from inoculum or infecteds to susceptible hosts are critical determinants of epidemics, yet no formal experimental methods have been described for their quantification and analysis in spatially explicit epidemics. Replicated microcosms of >400 radish seedlings and with tight control of environmental conditions were exposed to known amounts of inoculum of the fungal plant pathogen Rhizoctonia solani. Spatiotemporal maps of disease progress were used to distinguish between primary and secondary infections and to count changes with time in the number of infected plants and the number of contacts between susceptible and neighboring infected plants. Transmission rates were defined within a compartmental S-I (susceptible-infected) model for plant epidemics and estimated empirically using counts from spatial maps. The transmission rate for primary infection declined with time; the transmission rate for secondary infection rose initially and then declined. We discuss the mechanisms contributing to the changes in transmission rates with time and show that spatial mapping combined with an epidemiological analysis provides accurate empirical estimates of transmission rates. Key words: demographic variability; invasion; primary and secondary infection; Rhizoctonia solani; soilborne diseases; transmission of infection.

Abstract: Bystander effects, whereby cells that are not directly exposed to ionizing radiation exhibit adverse biological effects, have been observed in a number of experimental systems. A novel stochastic model of the radiation-induced bystander effect is developed that takes account of spatial location, cell killing and repopulation. The ionizing radiation dose- and time-responses of this model are explored, and it is shown to exhibit pronounced downward curvature in the high dose-rate region, similar to that observed in many experimental systems, reviewed in the paper. It is also shown to predict the augmentation of effect after fractionated delivery of dose that has been observed in certain experimental systems. It is shown that the generally intractable solution of the full stochastic system can be considerably simplified by assumption of pairwise conditional dependence that varies exponentially over time. [Copyright &y& Elsevier]

Epidemiologists are interested in using models that incorporate the effects of clustering in the spatial pattern of disease on epidemic dynamics. Bolker (1999, Bull. Math. Biol. 61, 849–874) has developed an approach to study such models based on a moment closure assumption. We show that the assumption works above a threshold initial level of disease that depends on the spatial dispersal of the pathogen. We test an alternative assumption and show that it does not have this limitation. We examine the relation between lattice and continuous-medium implementations of the approach. [Copyright &y& Elsevier]

Spatial interactions are key determinants in the dynamics of many epidemiological and ecological systems; therefore it is important to use spatio-temporal models to estimate essential parameters. However, spatially-explicit data sets are rarely available; moreover, fitting spatially-explicit models to such data can be technically demanding and computationally intensive. Thus non-spatial models are often used to estimate parameters from temporal data. We introduce a method for fitting models to temporal data in order to estimate parameters which characterise spatial epidemics. The method uses semi-spatial models and pair approximation to take explicit account of spatial clustering of disease without requiring spatial data. The approach is demonstrated for data from experiments with plant populations invaded by a common soilborne fungus, Rhizoctonia solani. Model inferences concerning the number of sources of disease and primary and secondary infections are tested against independent measures from spatio-temporal data. The applicability of the method to a wide range of host–pathogen systems is discussed. [Copyright &y& Elsevier]

The nature of pathogen transport mechanisms strongly determines the spatial pattern of disease and, through this, the dynamics and persistence of epidemics in plant populations. Up to recently, the range of possible mechanisms or interactions assumed by epidemic models has been limited: either independent of the location of individuals (mean-field models) or restricted to local contacts (between nearest neighbours or decaying exponentially with distance). Real dispersal processes are likely to lie between these two extremes, and many are well described by long-tailed contact kernels such as power laws. We investigate the effect of different spatial dispersal mechanisms on the spatio-temporal spread of disease epidemics by simulating a stochastic Susceptible-infective model motivated by previous data analyses. Both long-term stationary behaviour (in the presence of a control or recovery process) and transient behaviour (which varies widely within and between epidemics) are examined. We demonstrate the relationship between epidemic size and disease pattern (characterized by spatial autocorrelation), and its dependence on dispersal and infectivity parameters. Special attention is given to boundary effects, which can decrease disease levels significantly relative to standard, periodic geometries in cases of long-distance dispersal. We propose and test a definition of transient duration which captures the dependence of transients on dispersal mechanisms. We outline an analytical approach that represents the behaviour of the spatially-explicit model, and use it to prove that the epidemic size is predicted exactly by the mean-field model (in the limit of an infinite system) when dispersal is sufficiently long ranged (i.e. when the power-law exponent a⩽2). [Copyright &y& Elsevier]