##### Title: Stability and Convergence Analysis of Smoking Impact in Society with Algorithm Aspects

##### Pages: 503-516

##### Cite as:

Aqeel Ahmad, Maryam Shahid, Muhammad Farman, M.O. Ahmad, Stability and Convergence Analysis of Smoking Impact in Society with Algorithm Aspects, Int. J. Anal. Appl., 17 (4) (2019), 503-516.#### Abstract

In this manuscript, an epidemic model employed the dynamics of drugs usage among adults. Among smokers, often the desire to quit smoking arises. A large number of smokers attempt to quit, but only a few of them are successful. A non-linear mathematical model is employed to study and assess the dynamics of smoking and its impact on public health in a community. We prove the essential properties, bounded, positivity and well-posed, also local and global stability analysis has been made for the epidemic model. The sensitivity analysis of the model is provided by threshold or reproductive number as well as analyzed qualitatively. We develop an unconditionally convergent nonstandard finite difference scheme by applying Mickens approach φ(h) = h + O(h2) instead of h to control the spread of bad impact in society. Finally numerical simulations are also established to investigate the influence of the system parameters on the spread of the smoking impact in society.

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