Smoking model with cravings to smoke

Abstract

Among smokers, often the desire to quit smoking arise. A large number of smokers attempt to quit, but only a fraction of them are successful. While the health and monetary benefits are inarguable. The huge amount of stress associated with smoking, a combination of powerful cravings, sleep and mood disturbances and cognitive changes often stymie even the most motivated of individuals. In this paper, a mathematical model is proposed and analyzed in which the temporary quitters turn back to smoking by powerful cravings for smoking. We have discussed the qualitative behavior of the model and numerical simulations are carried out to support the analytical results.

Analysis of a mathematical model of smoking

“…Most smokers who know the dangers of tobacco wish to quit and, in theory, after taking up smoking it is possible to stop voluntarily and permanently [6,1], but counseling and medication can double the likelihood that a smoker who wants to quit will do so. The process of giving up smoking occurs in five phases: pre-contemplation, contemplation, preparation, action and maintenance [6].…”

“…Mathematical models are used to interpret the increase in smoking and anticipate the impact of smokers on society [1]. This is how some studies related to the subject have appeared in the literature.…”

“…In [7,4] a model of four nonlinear differential equations is constructed where groups of people are: potential smokers; smokers; and temporary or permanent ex-smokers. While in [1] a model of five nonlinear differential equations is formulated, distinguishing between to classes of smokers according the the frequency of consumption, high or low. Similar to [1], Sintayehu Matintu [9] studies a non-constant population but holding the other characteristics constant that make a great difference to the model when varied as proposed in this article.…”

Stability Analysis of Chain, Mild and Passive Smoking Model

“…The equilibria of smoking-free equilibrium point in system (1a)-(1b), are given in [10] as ( ) 1 1,0 0 2,0 2 , , ,0,0 , P E I E v µ   ∆ = =   +   (2) and the basic reproduction number 0  is defined as 0 β µ θ = + +   .…”

“…Our paper is divided into: section (2), evaluating the global stability of the model in [10]. The modification of the model was stated in section (3) to include two classes of smokers: chain smokers 1 S and mild smokers 2 S , with the full study of stability analysis and effect of each group on the population behavior (qualitative behavior).…”