The circulation of zoonotic influenza A viruses including pH1N1 2009 and H5N1 continue to present a constant threat to animal and human populations. Recently, an H3N2 variant spread from pigs to humans and between humans in limited numbers. Accordingly, this research investigated a range of scenarios of the transmission dynamics of pH1N1 2009 virus at the swine–human interface while accounting for different percentages of swine workers initially immune. Furthermore, the feasibility of using NAADSM (North American Animal Disease Spread Model) applied as a one-health simulation model was assessed. The study population included 488 swine herds and 29, 707 households of people within a county in Ontario, Canada. Households were categorized as follows: (i) rural households with swine workers, (ii) rural households without swine workers, and (iii) urban households without swine workers. Forty-eight scenarios were investigated, based on the combination of six scenarios around the transmissibility of the virus at the interface and four vaccination coverage levels of swine workers (0–60%), all under two settings of either swine or human origin of the virus. Outcomes were assessed in terms of stochastic ‘die-out’ fraction, size and time to peak epidemic day, overall size and duration of the outbreaks. The modelled outcomes indicated that minimizing influenza transmissibility at the interface and targeted vaccination of swine workers had significant beneficial effects. Our results indicate that NAADSM can be used as a framework to model the spread and control of contagious zoonotic diseases among animal and human populations, under certain simplifying assumptions. Further evaluation of the model is required. In addition to these specific findings, this study serves as a benchmark that can provide useful input to a future one-health influenza modelling studies. Some pertinent information gaps were also identified. Enhanced surveillance and the collection of high-quality information for more accurate parameterization of such models are encouraged.