Global Dynamics of a Mathematical Model on Smoking

Abstract

We derive and analyze a mathematical model of smoking in which the population is divided into four classes: potential smokers, smokers, temporary quitters, and permanent quitters. In this model we study the effect of smokers on temporary quitters. Two equilibria of the model are found: one of them is the smoking-free equilibrium and the other corresponds to the presence of smoking. We examine the local and global stability of both equilibria and we support our results by using numerical simulations.

Smoking as Epidemic: Modeling and Simulation Study

“…Therefore, as it has been shown in [14], the solution of equation ( We denote the boundary and the interior of H by IH and H * , respectively.…”

“…One of an interesting area in epidemiology to study is smoking subject. There are a lot of studies that has been done on the epidemics of smoking [3][4][5][6][7][8][9][10][11][12]. In order to understand the dynamics of this disease, like many infectious diseases, mathematical models can be used.…”

“…Zaman [5] derived and analyzed a smoking model taking into account the occasional smokers compartment in the basic model. In [6], Z. Alkhudhari, S. Al-Sheikh and S. Al-Tuwairqi adopted the model developed and studied in [6] and considered the effect of peer pressure on temporary quitters. In 2014 [7], Z. Alkhudhari, S. Al-Sheikh and S. AlTuwairqi introduced a new model by dividing the smokers into two subclasses: occasional smokers and heavy smokers, and the impact of these two subclasses on the existence and stability of equilibrium points.…”

Stability analysis of a giving up smoking model

“…Van Voorn and Kooi [10] presented a three compartment smoking model which was studied using brute force simulations for the short term dynamics and bifurcation analysis for the long-term dynamics. In 2013 [11], we adopted the model developed and studied in [4,5] and considered the effect of peer pressure on temporarily quitters. By this we mean the effect of smokers on temporarily quitters which is considered one of the main causes of their relapse.…”

“…In this paper, we introduce a new model based on the model in [11] by considering the possibility of temporarily quitters becoming permanent quitters and the impact of this transformation on the existence and stability of equilibrium points. The aim of this work, is to analyze the model by using stability theory of non-linear differential equations and supporting the results with numerical simulation.…”