Recent modelling and empirical work on influenza A virus (IAV) suggests that piglets play an important role as an endemic reservoir. The objective of this study is to test intervention strategies aimed at reducing the incidence of IAV in piglets and ideally, preventing piglets from becoming exposed in the first place. These interventions include biosecurity measures, vaccination, and management options that swine producers may employ individually or jointly to control IAV in their herds. We have developed a stochastic Susceptible-Exposed-Infectious-Recovered-Vaccinated (SEIRV) model that reflects the spatial organization of a standard breeding herd and accounts for the different production classes of pigs therein. Notably, this model allows for loss of immunity for vaccinated and recovered animals, and for vaccinated animals to have different latency and infectious periods from unvaccinated animals as suggested by the literature. The interventions tested include: (1) varied timing of gilt introductions to the breeding herd, (2) gilt separation (no indirect transmission to or from the gilt development unit), (3) gilt vaccination upon arrival to the farm, (4) early weaning, and (5) vaccination strategies of sows with different timing (mass and pre-farrow) and efficacy (homologous vs. heterologous). We conducted a Latin Hypercube Sampling and Partial Rank Correlation Coefficient (LHS-PRCC) analysis combined with a random forest analysis to assess the relative importance of each epidemiological parameter in determining epidemic outcomes. In concert, mass vaccination, early weaning of piglets (removal 0-7days after birth), gilt separation, gilt vaccination, and longer periods between introductions of gilts (6 months) were the most effective at reducing prevalence. Endemic prevalence overall was reduced by 51% relative to the null case; endemic prevalence in piglets was reduced by 74%; and IAV was eliminated completely from the herd in 23% of all simulations. Importantly, elimination of IAV was most likely to occur within the first few days of an epidemic. The latency period, infectious period, duration of immunity, and transmission rate for piglets with maternal immunity had the highest correlation with three separate measures of IAV prevalence; therefore, these are parameters that warrant increased attention for obtaining empirical estimates. Our findings support other studies suggesting that piglets play a key role in maintaining IAV in breeding herds. We recommend biosecurity measures in combination with targeted homologous vaccination or vaccines that provide wider cross-protective immunity to prevent incursions of virus to the farm and subsequent establishment of an infected piglet reservoir.