The term “Landscape of Fear” broadly refers to the impact of predators (real or perceived) on the spatial distribution of and resource utilization by foraging prey animals. However, many classical optimal foraging models have primarily considered simple, discrete environments that do not capture the richness of this spatial structure. In this talk, we present a spatially explicit optimal foraging model that seeks to capture the impact of predation, imperfect planning, and the distribution and depletion of food on the behavior of the prey animal. We represent the resulting system as a piecewise-deterministic Markov process over a finite time horizon with value functions governed by a system of coupled Hamilton-Jacobi-Bellman PDEs. We close by highlighting some of the behavior of the model using a series of numerical experiments. Joint work with Alex Vladimirsky and REU students (Nicolas Gonzalez-Granda, Sunay Joshi, Nagaprasad Rudrapatna, and Anne Somalwar).