Stability Analysis of Fractional-Order Nonlinear Alcohol Consumption Model and Numerical Simulation

This study explores the motivational factors behind alcohol consumption and its societal impacts. It identifies key reasons for drinking, such as improving sociability, boosting confidence, coping with challenges, participating in rituals, and seeking detoxification. The study highlights the substantial societal harm caused by the use of alcohol and drugs, with a particular emphasis on the increase in sexual violence, both within and outside families, as a result of impaired behavior. In this work, we present a newly developed mathematical model within the Caputo fractional framework, designed to reflect the lifestyle and behaviors of individuals in the alcohol model. We analyze the existence and uniqueness of solutions using the Lipschitz growth condition and fixed point theory. In addition, we explore equilibrium points, compute basic reproduction numbers, and explore the Hyers-Ulam stability of the alcohol model. Finally, we develop a numerical scheme for computational analysis of the proposed fractional model.