Modelling wildlife disease poses some unique challenges. Wildlife disease systems are data poor in comparison with human or livestock disease systems, and the impact of disease on population size is often the key question of interest. This review concentrates specifically on the application of dynamic models to evaluate and guide management strategies. Models have proved useful particularly in two areas. They have been widely used to evaluate vaccination strategies, both for protecting endangered species and for preventing spillover from wildlife to humans or livestock. They have also been extensively used to evaluate culling strategies, again both for diseases in species of conservation interest and to prevent spillover. In addition, models are important to evaluate the potential of parasites and pathogens as biological control agents. The review concludes by identifying some key research gaps, which are further development of models of macroparasites, deciding on appropriate levels of complexity, modelling genetic management and connecting models to data.

A susceptible–exposed–infectious theoretical model describing Tasmanian devil population and disease dynamics is presented and mathematically analysed using a dynamical systems approach to determine its behaviour under a range of scenarios. The steady states of the system are calculated and their stability analysed. Closed forms for the bifurcation points between these steady states are found using the rate of removal of infected individuals as a bifurcation parameter. A small-amplitude Hopf region, in which the populations oscillate in time, is shown to be present and subjected to numerical analysis. The model is then studied in detail in relation to an unfolding parameter which describes the disease latent period. The model’s behaviour is found to be biologically reasonable for Tasmanian devils and potentially applicable to other species.