Fuzzy-Fractional Modeling and Analysis of Tobacco Smoking Dynamics via He–Laplace–Carson Framework

Mubashir Qayyum, Aneeqa Bilal, Abdou Al Zubaidi, Syed Tauseef Saeed and Gilbert Chambashi

Journal of Mathematics, 2026, vol. 2026, 1-20

Abstract: This study develops a fuzzy-fractional nonlinear tobacco smoking model by incorporating triangular fuzzy numbers and Caputo fractional derivative. The He–Laplace–Carson algorithm is used to solve and analyze the uncertainties and memory dependent effects involved in potential smokers, mild smokers, regular smokers, and quit smokers. The precision of obtained fuzzy solution is investigated by calculating residual errors at the upper and lower bounds. A detailed graphical analysis of the system is done by observing the impact of smoking recovery rate, transmission rate, smoking relapse rate, and death rate of people associated with smoking disease. In addition, contour plots are also presented to analyze the smoking trends. The results indicate that tobacco smoking dynamics through the proposed scheme preserve realistic epidemiological trends. This can be helpful for authorities in the process of policy making related to smoking and can assist in preventive strategies for smoking.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9336693

DOI: 10.1155/jom/9336693

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