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.
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