Bobcats (Lynx rufus) were extirpated from many midwestern states in the mid‐1800s owing to habitat loss and overharvesting. Recently, bobcats have recolonized Ohio, USA, and neighboring states and given their furbearer status elsewhere, there is interest in opening a harvest season; however, demographic factors and viability of this population are currently unknown. We developed a spatial population simulation model to assess the long‐term viability of the bobcat population in Ohio in the face of 2 human‐induced factors limiting population growth: potential harvest and road mortality. We combined habitat suitability and road mortality risk data with vital rates for bobcats from Ohio and other populations to simulate possible scenarios for Ohio's population. Our baseline scenario simulations showed no risk of extinction for Ohio's bobcat population in the next 40 years, but population trajectories were lower and exhibited greater uncertainty when we modeled the population with a lower maximum density of animals per cell. At low harvest intensity (αh = 0.05), the bobcat population also exhibits low risk of extinction. When harvest intensity increases (αh = 0.1, 0.15) or when adults (≥2 yr) are targeted by harvest, simulations show declining populations, greater uncertainty in projections, and possible risk of extirpation. Our models indicated that if harvest and road mortality are additive, then the bobcat population could withstand marginal increases in road mortality (αr = 0.1) at low harvest intensity (αh = 0.05). Future increases in road mortality with higher harvest intensity (αh = 0.1, 0.15) were unsustainable. Our results can be used by wildlife managers to assist with decisions on population‐level management. This simulation model can easily be adapted for other large mammals and can be modified to assess a variety of ecological and anthropogenic influences to wildlife populations.