Optimal control and discrete-time modelling of alcohol model with physical and psychological complications

Abstract

In this paper, we propose a discrete mathematical model that describes the interaction between the classes of drinkers, namely, potential drinkers (P), moderate drinkers (M), heavy drinkers(H), heavy drinkers with physical complications(C1), the individuals with psychological complications(C2) and recovered and quitters of drinking (Q). We also focus on the importance of treatment of heavy drinkers with and without complications to aiming to find the optimal strategies to minimize the number of drinkers and maximize the number of the individuals who recovered and quitters of drinking. We use three controls which represent awareness programs through media and education for the potential drinkers, efforts treatment for the heavy drinkers and treatment for the heavy drinkers with physical complications. We use Pontryagin’s maximum principle in discrete time to characterize these optimal controls. The resulting optimality system is solved numerically by Matlab. Consequently, the obtained results confirm the performance of the optimization strategy.