On bifurcation analysis and numerical investigation of alcohol consumption dynamics

Abstract

This research article investigates the dynamics of alcohol consumption and the impact of addiction treatment using the continuous mathematical model [Formula: see text]. The study is significant as it incorporates the Atangana–Baleanu Caputo fractional derivatives, offering a novel approach to establishing the existence and uniqueness of solutions within this context. Our model formulation captures various stages of alcohol consumption and treatment, providing a comprehensive framework for analysis. We employ the next-generation matrix approach to explore the disease-free and endemic equilibria to calculate the basic reproduction number, [Formula: see text]. Sensitivity analysis is conducted to identify the parameters that most significantly influence [Formula: see text], which helps in understanding the dynamics of alcohol use and the effectiveness of intervention strategies. The local and global stability of both the alcohol-free and alcohol-present equilibria are rigorously examined to provide insights into potential long-term outcomes of alcohol consumption in the presence of treatment facilities. Furthermore, we utilize Lagrange interpolation polynomial in a numerical framework implemented in Python to perform detailed simulations and validate our theoretical results. This numerical analysis helps visualize the model's predictions and understand the temporal evolution of alcohol consumption within the population.