Necessary Optimality Conditions For a Delayed Alcoholism Model with Saturated Treatment |
Rachid Bouajaji, Abdelhadi Abta, Hassan Laarabi, Mostafa Rachik, Youssef El foutayeni
Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
January 31, 2021 |
February 15, 2021 |
March 15, 2021 |
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. The delay is ...