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<p>A novel non-linear fractional alcohol consumption model using the Atangana–Baleanu Caputo (ABC) fractional derivative has been developed in this study. Using sophisticated mathematical methods and the finite difference method, the model is developed to reflect the intricate dynamics of alcohol consumption. Several fundamental theorems connected to the ABC fractional derivative have been thoroughly demonstrated, ensuring the validity and dependability of the model when examining complex systems. The fundamental reproduction number, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2307_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Re _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℜ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, is calculated, and a comprehensive sensitivity analysis is conducted to evaluate the impact of different parameters on alcohol consumption. This study shows that when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2307_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Re _0&lt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ℜ</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the alcohol-free steady-state solutions are asymptotically locally and globally stable. Numerical simulations validate the theoretical findings, confirming the model’s high accuracy and convergence. The findings emphasize that increasing the rate of people taking treatment cause decreasing the interaction rates between heavy and non-heavy alcohol drinkers. This framework provides useful information to develop successful strategies for intervention for alcohol dynamics.</p>

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An advanced ABC finite difference approach for modified mathematical modeling of alcohol consumption dynamics

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Syeda Alishwa Zanib,
  • Tamour Zubair,
  • Nadeem Abbas,
  • Wasfi Shatanawi

摘要

A novel non-linear fractional alcohol consumption model using the Atangana–Baleanu Caputo (ABC) fractional derivative has been developed in this study. Using sophisticated mathematical methods and the finite difference method, the model is developed to reflect the intricate dynamics of alcohol consumption. Several fundamental theorems connected to the ABC fractional derivative have been thoroughly demonstrated, ensuring the validity and dependability of the model when examining complex systems. The fundamental reproduction number, \(\Re _0\) ℜ 0 , is calculated, and a comprehensive sensitivity analysis is conducted to evaluate the impact of different parameters on alcohol consumption. This study shows that when \(\Re _0<1\) ℜ 0 < 1 , the alcohol-free steady-state solutions are asymptotically locally and globally stable. Numerical simulations validate the theoretical findings, confirming the model’s high accuracy and convergence. The findings emphasize that increasing the rate of people taking treatment cause decreasing the interaction rates between heavy and non-heavy alcohol drinkers. This framework provides useful information to develop successful strategies for intervention for alcohol dynamics.