All ecological and epidemiological systems are embedded in space and composed of individuals; these facts often have a profound effect on the dynamics and means many tools and definitions require reformulation. Modelling has always been about taking highly complex dynamical systems, such as the natural environment, and attempting to simplify them to a leve that can be conceptualised, in the process losing all the features that are not understood or not anticipated. The individual based spatial models which form the basis of this work start from the simple rules for individuals and build up to a complex system, allowing new, unexpected phenomenon to arise naturally.\ud The local interactions in spatial models lead to short scale correlations and self-induced spatial heterogeneity as the small fluctuations of environmental noise are amplified into macro-scale patterns. These spatial patterns can lead to ephemeral refuges for hosts from where they can disperse stabilising the dynamics.\ud After discussing the importance and variety of host-parasite interactions several techniques to be used in this work are developed and explained on simple examples. Chapters III and IV introduce a caricature host-pathogen model and how how this deviates from the standard mean field theory approximations. Attention is then turned to host-parasitoid systems and the spatially extended Nicholson-Bailey equations; probems with this coupled map lattice are highlighted and an alternative artificial ecology is formulated. Remaining with the Nicholson-Bailey equations these are forced to be integer based by utilising stochastic events, this greatly stabilises the dynamics hence the method was applied to the persistence of measles epidemics in small populations (=500000). Chapter VII demonstrates how the inclusion of space enhances the effects of parasitism in increasing the evolutionary advantage of sexual hosts over asexual ones. Finally general techniques are developed to implicitly model the effects of spatial correlations and stochastic individual based interactions
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