Fractional Optimal Control Model for Studying Illicit Drug Usage
Bashir Abdullahi Baba, Abdulrashid Sabo and Nuruddeen Tijjani Wurno
Keywords:Optimal control; fractional order model; illicit drug usage; mathematical model
Abstract
A global issue of significant concern involves the rise in illicit drug use, primarily attributed to inadequate maintenance and/or the absence of effective principles governing the situation. This paper introduces a fractional optimal control problem designed to address illicit drug usage, utilizing a mathematical model with a fractionalorder derivative in the Caputo sense. The paper presents state and co-state equations, and it identifies the most effective strategy for substantially curbing the escalation of illicit drug use. This is achieved by employing two timedependent control measures, �”(�) , which encompasses awareness campaigns against illicit drugs, proper monitoring and guidance, stringent punishments for offenders both from governmental and parental perspectives, assuming responsibility for minors, and implementing comprehensive measures to minimize the recruitment of new illicit drug users from vulnerable populations. Additionally, �&(�) involves apprehending illicit drug users, imposing penalties, and employing rehabilitation centers for the monitoring and treatment of individuals with mild illicit drug use