Mathematical models have proven useful in planning conservation efforts for threatened species. In this paper, we develop a model based on the Macquarie Island ecosystem, where native seabirds were threatened by invasive pest species. In particular, European rabbits (Oryctolagus cuniculus) destroyed seabird nesting sites, while feral cats (Felis catus) preferentially hunted rabbits but also consumed seabirds. Management strategies included releasing a rabbit-killing disease and shooting feral cats. We investigate the interactions between species in the ecosystem as well as conservation practices using analytical techniques such as the basic reproductive ratio (R0) and partial rank correlation coefficient analysis. The results of this study reveal that the important factors to disease establishment change depending on the ecological interactions present in the system. Additionally, we show that the interaction between disease and predation sometimes produces surprising outcomes. Overall, the results of the study demonstrate the need for mathematical modelling in the conservation process in order to anticipate the complex responses of an ecosystem to management practices. We conclude with a brief list of considerations for conservation planners dealing with ecologically complex systems in the future.