  National parks often serve as hotspots for environmental crime such as
illegal deforestation and animal poaching. Previous attempts to model
environmental crime were either discrete and network-based or required very
restrictive assumptions on the geometry of the protected region and made heavy
use of radial symmetry. We formulate a level set method to track criminals
inside a protected region which uses real elevation data to determine speed of
travel, does not require any assumptions of symmetry, and can be applied to
regions of arbitrary shape. In doing so, we design a Hamilton-Jacobi equation
to describe movement of criminals while also incorporating the effects of
patrollers who attempt to deter the crime. We discuss the numerical schemes
that we use to solve this Hamilton-Jacobi equation. Finally, we apply our
method to Yosemite National Park and Kangaroo Island, Australia and design
practical patrol strategies with the goal of minimizing the area that is
affected by criminal activity.
