A new simple discrete-time model for the description of excessive alcohol consumption with n complications

Abstract

In this paper, we developed a new discrete-time mathematical model as a promising approach to understand and analyze the progression of disease complications related to excessive alcohol consumption, namely potential drinkers (P_i), moderate drinkers (M_i), heavy drinkers (H_i), and heavy drinkers (C_i,j) with different disease complications and quitters of drinking (Q_i) . First, we study the local stability using mathematical theories such as the Routh-Hurwitz criteria and propose three control measures. The Pontryagin maximum principle is employed to characterize the optimality of the controls. This new model makes it possible to optimize strategies aimed at reducing alcohol abuse with complications, prevention and treatment, taking into account the many factors that contribute to these complications. this model offers new perspectives for a better understanding of these disease complications and the development of more effective treatments to improve public health. Numerical simulations of the model are performed using MATLAB.