Modeling mathematical and analysis of an alcohol drinking with n complications

Abstract

In this article, we propose a new continuous mathematical approach to model and analyze the dynamics of the population of heavy drinkers and their health complications. The model has several compartments, including a new one that represents the number of heavy drinkers with different complications associated with excessive alcohol consumption. We study the stability of the model using mathematical theories such as the Routh-Hurwitz criteria for local stability, in order to study the equilibrium without and with excessive alcohol consumption, and the construction of Lyapunov functions makes it possible to study global stability. A sensitivity analysis is performed to determine which parameters have the most significant impact on the number of reproductions R0. The results were validated using numerical simulations carried out under MATLAB. This model may be useful in guiding public health policies aimed at reducing the number of drinkers and the complications associated with alcohol consumption.