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Using a combination of mathematical analysis, model fitting and parameter estimation, this thesis examines the dynamics and control of host-parasite systems in heterogeneous and disturbed environments. The first chapter introduces and tests models for the population dynamics of <I>Sclerotinia minor, </I>an economically important fungal plant parasite, and the fungal hyperparasite <I>Sporidesmium sclerotivorum </I>in a closed system from which any host of <I>S. minor </I>is excluded. Model structures are identified that reflect experimental data rather than models that are simply mathematical abstractions. Various elaborations of this simple model are discussed in the next chapter and, specifically, the effect of a latent period of infection and the influence of differentiating between primary and secondary infections are considered. In the following chapter, models are developed in which the dynamics of a host crop (lettuce) of <I>S. minor </I>are included. Various mechanisms that contribute to the observed persistence of the parasite are examined and, in particular, the roles played by discontinuities due to planting and harvesting of the lettuce crop, spatial heterogeneity and changes in environmental conditions are considered. Although the models discussed in the first three chapters are developed with close reference to the <I>S. minor-S. sclerotivorum </I>system, they are of broad applicability. In the remaining largely theoretical chapters, the population dynamics of the models are analysed, paying particular attention to thresholds for invasion and persistence. The persistence of host-parasite interactions in disturbed environments (where the host is not continuously present or does not continuously reproduce) is considered first. In the penultimate chapter, thresholds for invasion in plant-parasite systems are derived. These systems are characterised by dual sources of inoculum (primary and secondary infection) and a host response to infection load. Finally, the simple model fitted to the <I>S. minor-S. sclerotivorum </I>data is used to examine the effects of heterogeneous mixing on invasion and persistence.

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