Rehabilitation and Law Enforcement as Optimal Controls in a Mathematical Model of Social Behavior
DOI:
https://doi.org/10.36456/jstat.vol18.no1.a10579Keywords:
law enforcement, rehabilitation, social behaviorAbstract
Social behavior is the result of interactions between individuals, which can lead to tendencies toward either positive or deviant behavior. From this perspective, a mathematical model of social behavior is developed, dividing the population into criminal and non-criminal groups. Previous studies generally considered only law enforcement strategies—such as arrest and imprisonment—as responses to deviant behavior, without incorporating the aspect of rehabilitation. This study examines the application of optimal control in a mathematical model of social behavior to minimize the number of individuals in the criminal group, using rehabilitation and law enforcement as control variables. The optimal control problem is solved using Pontryagin’s Minimum Principle, and numerical simulations are performed using the Forward-Backward Sweep Method. The simulation results show that a combination of rehabilitation and law enforcement strategies can significantly reduce the criminal population in the model.
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