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The number of pathogenic threats to plant, animal and human health is increasing. Controlling the spread of such threats is costly and often resources are limited. A key challenge facing decision makers is how to allocate resources to control the different threats in order to achieve the least amount of damage from the collective impact. In this paper we consider the allocation of limited resources across n independent target populations to treat pathogens whose spread is modelled using the susceptible-infected-susceptible model. Using mathematical analysis of the systems dynamics, we show that for effective disease control, with a limited budget, treatment should be focused on a subset of populations, rather than attempting to treat all populations less intensively. The choice of populations to treat can be approximated by a knapsack-type problem. We show that the knapsack closely approximates the exact optimum and greatly outperforms a number of simpler strategies. A key advantage of the knapsack approximation is that it provides insight into the way in which the economic and epidemiological dynamics affect the optimal allocation of resources. In particular using the knapsack approximation to apportion control takes into account two important aspects of the dynamics: the indirect interaction between the populations due to the shared pool of limited resources and the dependence on the initial conditions.

Resistance to chemical control is a major impediment to combating many socially and economically important diseases. Theoretical and experimental studies have shown that reducing the intensity of treatment can slow, or even prevent, the invasion of resistance, yet reducing treatment levels also results in a net increase in disease severity. Clearly there is a need to identify control strategies that balance the conflicting aims of resistance management and disease suppression. Using a mathematical model for the dynamics of fungicide resistance in crop pathogens, we present a broadly applicable measure of the performance of chemical control in the presence of resistant pathogen strains. We illustrate how to optimise fungicide performance with respect to the intensity of treatment as a function of the duration of treatment and the fitness of the resistant strain. We find that in the short term, fungicide performance is optimised at high levels of treatment despite rapid selection for resistance, while the long-term optimum performance is achieved when treatment renders the fungicide-sensitive and fungicide-resistant pathogens equally fit. We further present evidence that under prescribed conditions, the ratio of dose size and frequency, and the fungicide mode of action, can have a significant effect on fungicide performance.

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.

Drug and pesticide resistance are among the most pressing problems facing public, animal and plant health today. In order to design effective resistance management strategies it is imperative to identify criteria for the invasion of resistant forms. Two key determinants of the ability of a resistant pest or pathogen to invade are any inherent fitness costs to the resistant subpopulation, and the effect of treatment on the sensitive and resistant subpopulations. For two generic classes of model which encompass many of the standard models in this field, we summarize relative fitness and treatment efficacy via two simple parameters, and demonstrate that invasion of resistance depends critically on a trade-off between them. Thresholds for invasion are derived when the effect of treatment is a constant reduction in the life-history parameters of the pathogen, and when treatment efficacy varies periodically with the repeated application and subsequent decay of the chemical.

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.

Models of particular epidemiological systems can rapidly become complicated by biological detail which can obscure their essential features and behaviour. In general, we wish to retain only those components and processes that contribute to the dynamics of the system. In this paper, we apply asymptotic techniques to an SEI-type model with primary and secondary infection in order to reduce it to a much simpler form. This allows the identification of parameter groupings discriminating between regions of contrasting dynamics and leads to simple approximations for the model's transient behaviour. These can be used to follow the evolution of the developing infection process. The techniques examined in this paper will be applicable to a large number of similar models.