Modeling environmental crime in protected areas using the level set method

D. J. Arnold, D. Fernandez, R. Jia, Christian Parkinson, D. Tonne, Y. Yaniv, Andrea Bertozzi, Stanley Osher

Research output: Contribution to journalArticle

2 Citations (Scopus)


National parks often serve as hotspots for environmental crime such as illegal deforestation and animal poaching. Previous attempts to model environmental crime either were 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.
Original languageEnglish
Pages (from-to)802-821
Number of pages20
JournalSIAM Journal on Applied Mathematics
Issue number3
Publication statusPublished - 2019
Externally publishedYes


  • level set method
  • Hamilton-Jacobi equation
  • environmental crime

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