# Optimal Control in a Mathematical Model of Smoking

## Authors

• Nur Ilmayasinta Department of Mathematic Education, Faculty of Teacher Training and Education, Universitas Islam Lamongan, 62211, Indonesia
• Heri Purnawan Department of Electrical Engineering, Faculty of Engineering, Universitas Islam Lamongan, 62211, Indonesia

## Keywords:

fourth-order Runge-Kutta, mathematical model, numerical solutions, optimal control, Pontryagin maximum principle (PMP)

## Abstract

This paper presents a dynamic model of smoking with optimal control. The mathematical model is divided into 5 sub-classes, namely, non-smokers, occasional smokers, active smokers, individuals who have temporarily stopped smoking, and individuals who have stopped smoking permanently. Four optimal controls, i.e., anti-smoking education campaign, anti-smoking gum, anti-nicotine drug, and government prohibition of smoking in public spaces are considered in the model. The existence of the controls is also presented. The Pontryagin maximum principle (PMP) was used to solve the optimal control problem. The fourth-order Runge-Kutta was employed to gain the numerical solutions.

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2021-12-03

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