GLOBAL STABILITY OF HYBRID SMOKING MODEL WITH NONLOCAL DIFFUSION

Salih Djilali, Soufiane Bentout, Anwar Zeb and Tareq Saeed
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Salih Djilali: ��Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria¶Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef 02000, Algeria
Soufiane Bentout: Department of Mathematics and Informatics, Ain Temouchent University, Belhadj Bouchaib, Ain Temouchent 46000, Algeria†Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria
Anwar Zeb: �Department of Mathematics, COMSATS University Islamabad, Abbottabad, 22060, Khyber Pakhtunkhwa, Pakistan
Tareq Saeed: ��Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-13

Abstract: Smoking has many harmful effects due to its toxic chemicals, which cause serious diseases. Our major interest in this research is to formulate a spatiotemporal mathematical model that predicts the evolution of smoking in society using a mathematical model that includes the large mobility of individuals. Indeed, we are concerned to study the global asymptotic stability of the unique positive steady state related to this model. The principal objective of this paper is to show that the smoking has no threshold dynamics as it has been shown for a large sample of epidemic models, and the consumption of cigarettes is always persistent, and based on the assumption of the parameters that verify the Lipschitz condition. We proved that the investigated model is always persistent and the unique positive equilibrium state is always globally stable. The mathematical finding is supported numerically using numerical simulations.

Keywords: Smoking Model; Hybrid System; Global Stability; Nonlocal Diffusion; Lyapunov Function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402241

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