Purpose

The purpose of this paper is to investigate the effects of irregular unsettling on the smoking model in form of the stochastic model as in the deterministic model these effects are neglected for simplicity.

Design/methodology/approach

In this research, the authors investigate a stochastic smoking system in which the contact rate is perturbed by Lévy noise to control the trend of smoking. First, present the formulation of the stochastic model and study the dynamics of the deterministic model. Then the global positive solution of the stochastic system is discussed. Further, extinction and the persistence of the proposed system are presented on the base of the reproductive number.

Findings

The authors discuss the dynamics of the deterministic smoking model form and further present the existence and uniqueness of non-negative global solutions for the stochastic system. Some previous study’s mentioned in the Introduction can be improved with the help of obtaining results, graphically present in this manuscript. In this regard, the authors present the sufficient conditions for the extinction of smoking for reproductive number is less than 1.

Research limitations/implications

In this work, the authors investigated the dynamic stochastic smoking model with non-Gaussian noise. The authors discussed the dynamics of the deterministic smoking model form and further showed for the stochastic system the existence and uniqueness of the non-negative global solution. Some previous study’s mentioned in the Introduction can be improved with the help of obtained results, clearly shown graphically in this manuscript. In this regard, the authors presented the sufficient conditions for the extinction of smoking, if <1, which can help in the control of smoking. Motivated from this research soon, the authors will extent the results to propose new mathematical models for the smoking epidemic in the form of fractional stochastic modeling. Especially, will investigate the effective strategies for control smoking throughout the world.

Originality/value

This study is helpful in the control of smoking throughout the world.

中文翻译：

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具有随机扰动的吸烟模型的稳定性分析

目的

本文的目的是以随机模型的形式研究不规则不稳定对吸烟模型的影响，因为在确定性模型中，为简单起见，这些影响被忽略了。

设计/方法/方法

在这项研究中，作者调查了一个随机吸烟系统，其中接触率受到 Lévy 噪声的干扰，以控制吸烟趋势。首先，提出随机模型的公式，研究确定模型的动力学。然后讨论了随机系统的全局正解。此外，所提出的系统的灭绝和持久性是根据再生数提出的。

发现

作者讨论了确定性吸烟模型形式的动力学，并进一步展示了随机系统非负全局解的存在性和唯一性。引言中提到的一些以前的研究可以在获得结果的帮助下得到改进，在本手稿中以图形方式呈现。对此，作者提出了生殖数小于1的吸烟灭绝的充分条件。

研究限制/影响

在这项工作中，作者研究了具有非高斯噪声的动态随机吸烟模型。作者讨论了确定性吸烟模型形式的动力学，并进一步为随机系统展示了非负全局解的存在性和唯一性。引言中提到的一些以前的研究可以在获得的结果的帮助下改进，在本手稿中以图形方式清楚地显示。对此，作者提出了戒烟的充分条件，如果<1，有助于控制吸烟。受这项研究的启发，作者将扩展结果，以分数随机模型的形式提出新的吸烟流行数学模型。特别是，将调查在世界范围内控制吸烟的有效策略。

原创性/价值

这项研究有助于控制全世界的吸烟。