1. Long-term pathogen control or eradication in wildlife is rare and represents a major challenge in conservation. Control is particularly difficult for environmentally transmitted pathogens, including some of the most conservation-critical wildlife diseases. 2. We undertook a treatment program aimed at population-scale eradication of the environmentally transmitted Sarcoptes scabiei mite (causative agent of sarcoptic mange) during an epizootic in bare-nosed wombats (Vombatus ursinus). Field trial results were used to parameterize a mechanistic host-disease model that explicitly described indirect-transmission, host behaviour, and viable disease intervention methods. 3. Model analysis shows that elimination of S. scabiei in the wild is most sensitive to the success of treatment delivery, and duration of the program. In addition, we found the frequency that wombats switch burrows was an important positive driver of mite persistence. 4. Synthesis and applications: This research emphasises the utility of applying model-guided management techniques in order to achieve practical solutions in the field. Our approach and findings have applicability to other species affected by S. scabiei (e.g., wolves, red foxes, Spanish ibex, and American black bear), as well as other conservation-critical systems involving environmental transmission (e.g., bat white-nose syndrome and amphibian chytridiomycosis).