Mathematical modeling of alcoholism as a social contagion: dynamics, bifurcation, and control
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Alcoholism modeling;, Social contagion, Basic reproduction number;, Optimal control, Bifurcation analysis##article.abstract##
Alcoholism remains a critical social and public health problem worldwide, characterized by behavioral transmission through peer influence and social reinforcement. In this study, we develop and analyze a deterministic compartmental model describing alcoholism dynamics as a social contagion process. We derive the basic reproduction number, examine local and global stability, and investigate bifurcation behavior. Sensitivity analysis identifies key parameters driving the persistence of alcohol abuse. Finally, we introduce optimal control interventions to guide public health policies. Numerical simulations reveal that combined interventions—awareness, rehabilitation, and relapse prevention—are the most effective in reducing alcohol dependence. The study provides qualitative insights into alcoholism dynamics rather than quantitative prediction.
