Environmental degradation and global warming are intensifying due to the heavy dependence of transportation sector on non-renewable energy sources like fossil fuels. Despite the implementation of various incentive policies aimed at encouraging the transition from internal combustion engine vehicles to electric vehicles (EVs), market growth for EVs remains stagnant in many regions. This study examines the impact of media advertisements and incentive policies, through employing Holling type II saturated contact rates, on the adoption of EVs through a nonlinear dynamical model. Stability analysis, along with considerations for time delays that reflect the lag in planning and execution of media advertisements, is incorporated to capture realistic dynamics. Numerical simulations are performed to validate the analytical findings of the proposed dynamical system.