2009-07-023_R1 - Qualitative behavior of giving up smoking...

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Unformatted text preview: Qualitative behavior of giving up smoking model Gul Zaman Centre for Advanced Mathematics and Physics, National University, of Sciences and Technology, Peshawar Road, Rawalpindi 46000, Pakistan October 29, 2009 Abstract Smoking is a large problem in the entire world. Despite overwhelming facts about the risks, smoking is still a bad habit widely spread and socially accepted. Many people start smoking during their gymnasium period. The main purpose of this paper is to determine the asymptotic behavior of a mathematical model using for giving up smoking. Our interest here is to derive and analysis the model taking into account the occasional smokers compartment in the giving up smoking model. Analysis of this model reveals that there are four equilibria, one of them is the smoking-free and the other three correspond to presence of smoking. We also present the global stability and parameter estimates that characterize the natural history of this disease with numerical simulations. Key words : Population dynamics; Mathematical model; Stability analysis; Numeri- cal simulation Subject classification : 92D25, 49J15, 93D20 † Corresponding author. Tel.: +92 51 927 8590; Fax: +92 51 547 3989. E-mail addresses: [email protected], 1 Introduction The smoking subject is an interesting area to study. There is strong medical evidence that smoking tobacco is related to more than two dozen diseases and conditions. It has negative effects on nearly every organ of the body and reduces overall health. Smoking tobacco remains the leading cause of preventable death and has negative health impacts on people of all ages in the world. The effects of smoking bring big problems both in personal and public matters. The gymnasium age, between 16 and 20 years old, is a time where many of our attitudes change; this includes the attitude towards smoking. 1 In order to understand the dynamics of this disease we use the concept of mathematical modeling. There is a lot of mathematical theory on the concept of diseases and epidemics see, for example [1, 3, 6, 7, 14, 17, 18, 19]. The basic ideas in these theories are that all people in a community start as healthy. Healthy people may become infected by diseases. But infected people may become healthy again in a community. Epidemic models with both linear and nonlinear incidence have been studied by many authors and related literature of SIR disease transmission model is quite large, where S denotes the number of individuals that are susceptible to infection, I denotes the number of individuals that are infectious and R denotes the number of individuals that have been recovered. The chronic disease model (CDM) is a model that describes the effects of risk factors, including smoking and overweight, on the incidence and mortality of chronic diseases in the population [10]. In 2000, Castillo-Garsow et al. [5] proposed a simple mathematical model for giving up smoking. They consider a system with a total constant population which is divided into three classes: potential smokers, i.e.with a total constant population which is divided into three classes: potential smokers, i....
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2009-07-023_R1 - Qualitative behavior of giving up smoking...

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