Optimal Control of a Delayed Alcoholism Model with Saturated Treatment View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2021-05-18

AUTHORS

Rachid Bouajaji, Abdelhadi Abta, Hassan Laarabi, Mostafa Rachik

ABSTRACT

In the present work, we have proposed a new mathematical model of alcohol abuse with delay, saturated incidence function and logistic recruitment. The model is made up of the following four population classes: occasional drinkers, heavy drinkers, drinkers during treatment and drinkers who are temporarily recovered. In particular, we incorporate time delay because the non consumer population will take a period of time to become an alcohol consumer. We have studied the optimal control problem by considering a saturated control function and an objective function of type L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{1}$$\end{document}. The delay is incorporated in our model to make it more realistic and to describe the latency period. The existence of the optimal control is also proved. Pontryagin’s maximum principle with delay is used to characterize these optimal controls. The optimality system is derived and then solved numerically using an algorithm based on the forward and backward difference approximation. More... »

PAGES

1-16

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12591-021-00570-y

DOI

http://dx.doi.org/10.1007/s12591-021-00570-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1138151661


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