Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse

Nita Anggriani; Syamsuddin  Toaha; Kasbawati Kasbawati

doi:10.20956/j.v17i3.12467

Authors

Nita Anggriani Hasanuddin University
Syamsuddin Toaha
Kasbawati Kasbawati

DOI:

https://doi.org/10.20956/j.v17i3.12467

Keywords:

The Dynamics of Drug Abuse Spread, Mathematical Model, Pontryagin Minimum Principles, Forward-Backward Sweep Method, Optimal Control

Abstract

This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.

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