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**Qualitative behavior of giving up smoking models.**
*(English)*
Zbl 1221.92067

Summary: 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 analyse 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.

### MSC:

92D25 | Population dynamics (general) |

92D99 | Genetics and population dynamics |

49N90 | Applications of optimal control and differential games |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

93C95 | Application models in control theory |