Once a pathogen is introduced in a population, key factors governing rate of spread include contact structure, supply of susceptible individuals and pathogen life-history. We examined the interplay of these factors on emergence dynamics and efficacy of disease prevention and response. We contrasted transmission dynamics of livestock viruses with different life-histories in hypothetical populations of feral swine with different contact structures (homogenous, metapopulation, spatial and network). Persistence probability was near 0 for the FMDV-like case under a wide range of parameter values and contact structures, while persistence was probable for the CSFV-like case. There were no sets of conditions where the FMDV-like pathogen persisted in every stochastic simulation. Even when population growth rates were up to 300% annually, the FMDV-like pathogen persisted in <25% of simulations regardless of transmission probabilities and contact structure. For networks and spatial contact structure, persistence probability of the FMDV-like pathogen was always <10%. Because of its low persistence probability, even very early response to the FMDV-like pathogen in feral swine was unwarranted while response to the CSFV-like pathogen was generally effective. When pre-emergence culling of feral swine caused population declines, it was effective at decreasing outbreak size of both diseases by ≥80%.