This thesis investigates epidemics with specific reference to Rabbit Haemorrhagic Disease (RHD) in Australia and New Zealand. Different models will be investigated to find critical parameters that are responsible for creating an epidemic. The models to be analysed are the Classic SIR model, 1 dimensional diffusion models, an endemic model with disease related deaths and the extended SIR model. The critical parameters for each of the models can be used to determine the severity of the epidemic and also the minimum speed with which the infection must travel through a population in order for the propagation of disease. The accuracy and limitations of such models will also be discussed
A variety of mathematical techniques will be employed so that both qualitative and quantitative analysis is able to be carried out on various models in order to assess their accuracy and limitations. This thesis also provides the mathematical grounding to further analyse different aspects of each of the models, and develop the extended SIR model in a manner which has not yet been investigated.