具有饱和发生率的Filippov戒烟模型及全局动力学分析

doi:10.12677/aam.2026.158364

期刊菜单

具有饱和发生率的Filippov戒烟模型及全局动力学分析
Global Dynamics Analysis of a Filippov Smoking Cessation Model with Saturated Incidence Rate

DOI: 10.12677/aam.2026.158364, PDF,
作者: 张红艳：长沙理工大学数学与统计学院，湖南长沙
关键词: Filippov系统；饱和发生率；全局稳定性；Filippov System； Saturated Incidence Rate； Global Stability

摘要: 本文在经典传染病模型的基础上，考虑了饱和发生率，同时结合政府对吸烟的不连续干预策略，建立了具有饱和发生率的Filippov戒烟模型。利用Filippov理论方法，分析了该模型的滑模动力学行为，探究了系统的全局动力学特性，得到了系统无病平衡点、地方病平衡点或伪平衡点的全局渐近稳定性条件。结果表明，一定的干预措施能够降低吸烟人数并将吸烟人数控制在阈值范围之内。

Abstract: Based on a classical epidemic model, this study develops a Filippov smoking cessation model incorporating a saturated incidence rate and government’s discontinuous intervention strategies. By employing the approach of Filippov theory, we analyze the sliding mode dynamics and investigate the global dynamical behaviors of the system. Sufficient conditions are derived for the global asymptotical stability of a disease-free equilibrium, an endemic equilibrium, or a pseudo equilibrium. The results indicate that appropriate intervention measures can reduce the number of smokers and keep them within a predetermined threshold level.

文章引用：张红艳. 具有饱和发生率的Filippov戒烟模型及全局动力学分析[J]. 应用数学进展, 2026, 15(8): 414-426. https://doi.org/10.12677/aam.2026.158364

参考文献

[1]	赵保路. 吸烟, 自由基与健康[J]. 生物物理学报, 2012, 28(4): 332-340.
[2]	Elders, M.J., Perry, C.L., Eriksen, M.P. and Giovino, G.A. (1994) The Report of the Surgeon General: Preventing Tobacco Use among Young People. American Journal of Public Health, 84, 543-547. https://doi.org/10.2105/ajph.84.4.543
[3]	Khan, Z.A., Rahman, M.U. and Shah, K. (2021) Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate. Journal of Function Spaces, 2021, 1-11. https://doi.org/10.1155/2021/6344079
[4]	Alzahrani, E. and Zeb, A. (2020) Stability Analysis and Prevention Strategies of Tobacco Smoking Model. Boundary Value Problems, 2020, Article No. 3. https://doi.org/10.1186/s13661-019-01315-1
[5]	van Voorn, G.A.K. and Kooi, B.W. (2013) Smoking Epidemic Eradication in a Eco-Epidemiological Dynamical Model. Ecological Complexity, 14, 180-189. https://doi.org/10.1016/j.ecocom.2013.01.008
[6]	Acevedo-Estephania, C.A., Gonzalez, C., Riossoto, K.R., et al. (2000) A Mathematical Model for Lung Cancer: The Effects of Second-Hand Smoke and Education. Biometrics Unit Technical Reports No. BU-1525-M, Department of Biometrics, Cornell University. https://www.researchgate.net/publication/221711448_A_Mathematical_Model_for_Lung_Cancer_The_Effects_of_Second-Hand_Smoke_and_Education
[7]	Bhunu, C.P. and Mushayabasa, S. (2012) A Theoretical Analysis of Smoking and Alcoholism. Journal of Mathematical Modelling and Algorithms, 11, 387-408. https://doi.org/10.1007/s10852-012-9195-3
[8]	Guerrero, F., Santonja, F.J. and Villanueva, R.J. (2013) Solving a Model for the Evolution of Smoking Habit in Spain with Homotopy Analysis Method. Nonlinear Analysis: Real World Applications, 14, 549-558. https://doi.org/10.1016/j.nonrwa.2012.07.015
[9]	Rowe, D.C., Chassin, L., Presson, C.C., Edwards, D. and Sherman, S.J. (1992) An “Epidemic” Model of Adolescent Cigarette Smoking. Journal of Applied Social Psychology, 22, 261-285. https://doi.org/10.1111/j.1559-1816.1992.tb01539.x
[10]	Castillo-Garsow, C., Jordán-Salivia, G. and Rodriguez-Herrera, A. (1997) Mathematical Models for the Dynamics of Tobacco Use, Recovery, and Relapse. Technical Reports No. BU-1505-M, Cornell University. https://api.semanticscholar.org/CorpusID:89440950
[11]	Sharomi, O. and Gumel, A.B. (2008) Curtailing Smoking Dynamics: A Mathematical Modeling Approach. Applied Mathematics and Computation, 195, 475-499. https://doi.org/10.1016/j.amc.2007.05.012
[12]	Zeb, A., Zaman, G. and Momani, S. (2013) Square-Root Dynamics of a Giving up Smoking Model. Applied Mathematical Modelling, 37, 5326-5334. https://doi.org/10.1016/j.apm.2012.10.005
[13]	Pang, L., Zhao, Z., Liu, S. and Zhang, X. (2015) A Mathematical Model Approach for Tobacco Control in China. Applied Mathematics and Computation, 259, 497-509. https://doi.org/10.1016/j.amc.2015.02.078
[14]	王霞, 李保林, 葛情. 一类具有非线性接触率的戒烟模型[J]. 信阳师范学院学报(自然科学版), 2019, 32(3): 362-366.
[15]	Sharma, A. and Misra, A.K. (2015) Backward Bifurcation in a Smoking Cessation Model with Media Campaigns. Applied Mathematical Modelling, 39, 1087-1098. https://doi.org/10.1016/j.apm.2014.07.022
[16]	Yadav, A., Srivastava, P.K. and Kumar, A. (2015) Mathematical Model for Smoking: Effect of Determination and Education. International Journal of Biomathematics, 8, Article 1550001. https://doi.org/10.1142/s1793524515500011
[17]	Maurya, J., Kumari, M. and Misra, A.K. (2025) Modeling the Effect of Fear-Inducing Awareness Programs on Smoking Cessation. Journal of Computational Science, 87, Article 102584. https://doi.org/10.1016/j.jocs.2025.102584
[18]	Syata, I., Toaha, S. and Firman, F. (2025) Stability Analysis and Optimal Control as Strategies Reducing Smokers in Model of Addicted Smoking with Incident Rate Holling Type Function. Nonlinear Dynamics, Psychology, and Life Sciences, 29, 313-331.
[19]	马慧丽, 黄立宏, 王佳伏. 有干预措施的Filippov戒烟模型的全局动力学[J]. 经济数学, 2020, 37(3): 208-213.
[20]	Filippov, A.F. (1988) Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic Publishers.

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