In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal-fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal-fractional alcohol addiction model are shown using the Picard-Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam-Hyers coupled with the Ulam-Hyers-Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community.

Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon

Department of Mathematics Abdul Wali Khan University Mardan Mardan Khyber Pakhtunkhwa Pakistan

Department of Mathematics College of Natural and Computational Scieces Debre Berhan University 445 Debre Berhan Ethiopia

Department of Mathematics University of Peshawar Peshawar Khyber Pakhtunkhwa Pakistan

Department of Quantitative analysis College of Business Administration King Saud University P O Box 71115 Riyadh 11587 Saudi Arabia

IT4Innovations VSB Technical University of Ostrava Ostrava Czech Republic

School of Mathematics and Data Sciences Changji University Changji 831100 Xinjiang People's Republic of China

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