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Journal of Applied Nonlinear Dynamics 15(2) (2026) 291--302 | DOI:10.5890/JAND.2026.06.002

Swapnil Talele$^1$, Ravi Gor$^2$

$^1$ Department of Applied Mathematical Science, Actuarial Science & Analytics, Gujarat University, India

$^2$ Department of Mathematics, Gujarat University, India

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Abstract

Smoking is a leading cause of death due to its detrimental effects on various organs, leading to strokes, heart diseases, and other respiratory issues. This paper presents a mathematical model to examine the dynamics of smoking and the recovery rate within a community. The model employs a compartmental approach, consisting of five non-linear differential equations, to analyze these dynamics. Both the local and global stability of the model are investigated. Additionally, the next-generation matrix technique is utilized to perform an in-depth analysis based on the reproduction number $R_0$, which is calculated using Python. Several numerical simulations are conducted to illustrate the findings, highlighting the impact of various parameters on smoking dynamics and the effectiveness of intervention strategies.

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