Disease modelling is one approach for providing new insights into wildlife disease epidemiology. This paper describes a spatio-temporal, stochastic, susceptible- exposed-infected-recovered process model that simulates the potential spread of classical swine fever through a documented, large and free living wild pig population following a simulated incursion. The study area (300 000 km2) was in northern Australia. Published data on wild pig ecology from Australia, and international Classical Swine Fever data was used to parameterise the model. Sensitivity analyses revealed that herd density (best estimate 1-3 pigs km-2), daily herd movement distances (best estimate approximately 1 km), probability of infection transmission between herds (best estimate 0.75) and disease related herd mortality (best estimate 42%) were highly influential on epidemic size but that extraordinary movements of pigs and the yearly home range size of a pig herd were not. CSF generally established (98% of simulations) following a single point introduction. CSF spread at approximately 9 km2 per day with low incidence rates (< 2 herds per day) in an epidemic wave along contiguous habitat for several years, before dying out (when the epidemic arrived at the end of a contiguous sub-population or at a low density wild pig area). The low incidence rate indicates that surveillance for wildlife disease epidemics caused by short lived infections will be most efficient when surveillance is based on detection and investigation of clinical events, although this may not always be practical. Epidemics could be contained and eradicated with culling (aerial shooting) or vaccination when these were adequately implemented. It was apparent that the spatial structure, ecology and behaviour of wild populations must be accounted for during disease management in wildlife. An important finding was that it may only be necessary to cull or vaccinate relatively small proportions of a population to successfully contain and eradicate some wildlife disease epidemics.