A Mathematical Model for Controlling the Alcohol Addiction: Stability and Numerical Analysis

The aim of this work is to develop a model of alcohol that takes drug features into account. We assess the model feasibility and explain its formulation in terms of a nonlinear differential equation. Using the subsequent matrix generation technique, we ascertain the reproductive number in order to assess the dynamics of the model. We also examine the system equilibrium points, namely the positive and free alcohol equilibrium points. To gain insights into the stability properties of the model, we utilize the Lyapunov function and the Routh–Hurwitz criterion. Through these methods, we investigate both the local stability and global stability of the considered model. Furthermore, we employ numerical simulations to complement and illustrate the theoretical results obtained. These simulations provide visual representations that enhance the understanding of the model dynamics and behavior.