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National parks often serve as hotspots for environmental crime such asillegal deforestation and animal poaching. Previous attempts to modelenvironmental crime were either discrete and network-based or required veryrestrictive assumptions on the geometry of the protected region and made heavyuse of radial symmetry. We formulate a level set method to track criminalsinside a protected region which uses real elevation data to determine speed oftravel, does not require any assumptions of symmetry, and can be applied toregions of arbitrary shape. In doing so, we design a Hamilton-Jacobi equationto describe movement of criminals while also incorporating the effects ofpatrollers who attempt to deter the crime. We discuss the numerical schemesthat we use to solve this Hamilton-Jacobi equation. Finally, we apply ourmethod to Yosemite National Park and Kangaroo Island, Australia and designpractical patrol strategies with the goal of minimizing the area that isaffected by criminal activity.

National parks often serve as hotspots for environmental crime such asillegal deforestation and animal poaching. Previous attempts to modelenvironmental crime were either discrete and network-based or required veryrestrictive assumptions on the geometry of the protected region and made heavyuse of radial symmetry. We formulate a level set method to track criminalsinside a protected region which uses real elevation data to determine speed oftravel, does not require any assumptions of symmetry, and can be applied toregions of arbitrary shape. In doing so, we design a Hamilton-Jacobi equationto describe movement of criminals while also incorporating the effects ofpatrollers who attempt to deter the crime. We discuss the numerical schemesthat we use to solve this Hamilton-Jacobi equation. Finally, we apply ourmethod to Yosemite National Park and Kangaroo Island, Australia and designpractical patrol strategies with the goal of minimizing the area that isaffected by criminal activity.