Optimal Control Model for Alcohol–Related Risk Behaviors and Beliefs in Tanzania

Maranya M Mayengo,Wei-Chiang Hong

doi:10.1155/2022/9094494

Abstract

An optimal control theory is applied to a system of ordinary differential equations representing the dynamics of health-related risks associated with alcoholism in the community with active religious beliefs. Two nonautonomous control variables are proposed to reduce the health risks associated with alcoholism in the community. Consequently, three control strategies are presented using Pontryagin’s maximum principle (PMP), and the necessary conditions for the existence of the optimal controls are obtained. The simulation results revealed that the health risks associated with alcoholism behaviors may be effectively eradicated when both controls, u 1 t and u 2 t , are applied in a combination. On the other hand, the cost–effective analysis of the three different strategies confirmed that the desired cost–effective results may be attained when both controls, u 1 t and u 2 t , are applied together. Based on these results, this study concludes that, health risks associated with alcoholism behaviors may be efficiently and cost–effectively eradicated from the community when both controls, u 1 t and u 2 t , are applied together. Whereas application of control option u 1 t implies increasing the level of protection to the susceptible population by implementing public health education campaign; the control option u 2 t implies increasing the removal rate of the moderate risky individuals into recovered population. The control strategy in which the two options are featured in a combination is presented in this study as Strategy C exhibiting the least ICER value and more cost–effective than the rest of strategies presented.

Highlights

Alcohol drinking behaviors have long been identified as a risk factor for several diseases [1, 2]
We introduce the following control functions as follows: u1ðtÞ, and u2ðtÞ to extend the crisp model for alcoholrelated health risk presented by Mayengo et al [21] and Mayengo et al [22], whereby the time dependent variable u1ðtÞ is introduced as a control variable describing public health education campaigns aiming at increasing public awareness on health risks in connection to alcoholism
For effective reduction of health risks associated with alcoholism in the community, we investigate the impacts of individual control strategies or in combination and simulate it in a period of fifteen years

Summary

Introduction

Alcohol drinking behaviors have long been identified as a risk factor for several diseases [1, 2]. According to Griswold et al [1], alcohol drinking may be harmful to human health regardless of the volume and frequency in which it is taken. Based on this context, alcohol consumption at any drinking level subjects drinkers’ health at stake. Studies consistently reveal the negative association between religiosity and alcoholism behaviors [10,11,12] This makes religious belief an important change agent for promoting the health and molding behaviors of its members [13, 14]

Objectives

Methods

Conclusion