Whistler waves are electromagnetic waves in the very-low-frequency range which propagate in the near-earth space plasma environment, specifically within a region called the Van Allen Radiation Belts. This region contains many highly energetic particles which pose a significant threat to spacecraft in Earth orbit, including the International Space Station. Whistler waves are particularly interesting because they can interact with the energetic particles and precipitate them out of the Van Allen Radiation Belts. One important characteristic of whistlers is that they can become trapped inside enhancements or depletions of the ambient plasma density. We compare wave and particle observations from the Van Allen Probes spacecraft to results from a numerical simulation developed to model the wave propagation physics. By using the observed conditions as inputs to the simulation, we can reproduce the ducted waves with good, quantitative agreement. The results from this study will be important for future experiments of launching whistler waves into the Van Allen Radiation Belts from ground antennae or space vehicles.