Parasitic diseases of animals place a large constraint on livestock production worldwide. The parasite Theileria parva, and the disease East Coast fever it produces, are responsible for the deaths of thousands of cattle each year in central and eastern Africa. Disease control is one way in which agricultural production can be improved, and is a matter of fundamental importance to developing countries where levels of nutrient intake are dangerously low over the majority of the population. This thesis presents computer simulation models to study East Coast fever and its control. Models are constructed based on expert rules extracted from over 80 years of scientific literature concerning the disease. Rules are translated into programming code, and their outcome investigated by computer experimentation. The models are climate driven, and one chapter of this thesis concerns the development of a model to generate sequences of daily weather data from minimal datasets. This thesis also contains deterministic models studying the dynamics of other, more general, parasitic diseases, and also the competition between similar species of parasite. These models are constructed using difference equations and analysed analytically and by simulation. This approach is adopted further to specifically consider the behaviour of the level of Theileria parva infection amongst vector and host populations.