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. 1. Introduction Tobacco epidemic is one of the biggest public health threats the world has ever faced. It kills up to half of its users. Nearly, each year six million people die from smoking of whom more than 5 million are users and ex-users and more than 600,000 are nonsmokers exposed to second-hand smoke. Tobacco users who die prematurely deprive their families of income, raise the cost of health care, and hinder economic development. In smoking death statistics, there is a death caused by tobacco every 8 seconds; 10% of the adult population who smoke die of tobacco related diseases. The World Health Organization predicts that, by 2030, 10 million people will die every year due to tobacco related illnesses. This makes smoking the biggest killer globally. In Saudi Arabia, the prevalence of current smoking ranges from 2.4 to 52.3% (median = 17.5%) depending on the age group. The results of a Saudi modern study predicted an increase of smokers number in the country to 10 million smokers by 2020. The current number of smokers in Saudi Arabia is approximately 6 million, and they spend around 21 billion Saudi Riyal on smoking annually. Clearly smoking is a prevalent problem among Saudis that requires intervention for eradication. Persistent education of the health hazards related to smoking is recommended particularly at early ages in order to prevent initiation of smoking [1, 2]. In 1997, Castillo-Garsow et al. [3] proposed a simple mathematical model for giving up smoking. They considered a system described by the simplified model with a total constant population which is divided into three classes: potential smokers, that is, people who do not smoke yet but might become smokers in the future ( ), smokers ( ), and people (former smokers) who have quit smoking permanently ( ). Later, this mathematical model was developed by Sharomi and Gumel (2008) [4]; they introduced a new class of smokers who temporarily quit smoking and they described the dynamics of smoking by the following four nonlinear differential equations: They concluded that the smoking-free
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