Modeling illegal logging in Brazil

May 1, 2021·
Bohan Chen
,
Kaiyan Peng
,
Christian Parkinson
,
Andrea L. Bertozzi
,
Tara Lyn Slough
,
Johannes Urpelainen
· 1 min read
Abstract
Deforestation is a major threat to global environmental wellness, with illegal logging as one of the major causes. Recently, there has been increased effort to model environmental crime, with the goal of assisting law enforcement agencies in deterring these activities. We present a continuous model for illegal logging applicable to arbitrary domains. We model the practice of criminals under influence of law enforcement agencies using tools from multiobjective optimal control theory and consider non-instantaneous logging events and load-dependent travel velocity. We calibrate our model using real deforestation data from the Brazilian rainforest and demonstrate the importance of geographically targeted patrol strategies.
Type
Publication
Research in the Mathematical Sciences

This paper builds a continuous optimal-control model of illegal logging on general geographic domains. Loggers choose routes and harvesting behavior in response to resource value, travel cost, and law-enforcement pressure, while the model accounts for finite-time logging events and slower travel under heavier loads.

The competing objectives are expressed through Hamilton–Jacobi–Bellman and level-set methods, producing spatial predictions of attractive logging locations and transport paths. Calibrating the model with observed deforestation in the Brazilian rainforest makes it possible to compare patrol strategies under realistic terrain and economic conditions.

The numerical results show that enforcement is most effective when it is geographically targeted rather than distributed uniformly. The framework provides a quantitative way to study how patrol placement changes the incentives and routes of environmental offenders.

Environmental Crime Hamilton–Jacobi–Bellman Equations Level Set Methods Multiobjective Optimization Optimal Control Rainforest Conservation