A discrete mathematical modeling for drinking alcohol model resulting in road accidents and violence: an optimal control approach

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 that practice violence (V), the individuals that practice accidents(A) and recovred and quitters of drinking (Q). We also focus on the importance of awareness programs, media and education of drinkers to aiming to find the optimal strategies to minimize the number of drinkers practice violence and accidents and maximize the number of the individuals who recovred and quitters of drinking. We use three controls which represent awareness programs and traitment through media and education for the heavy drinkers, awareness programs and security campaigns for heavy drinkers that practice violence and heavy drinkers that practice accidents and follow-up and the psychological support for temporary quitters of drinking. 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.