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Mathematical analysis of giving up smoking model via harmonic mean type incidence rate

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  • ur Rahman, Ghaus
  • Agarwal, Ravi P.
  • Din, Qamar

Abstract

This article deals with qualitative analysis of a smoking model and provides parametric conditions for controlling diseases under the influence of smoking. The model is obtained by taking into account a novel uptake function, which relates the incidence of potential smoker with occasional smoker, of harmonic mean type for the potential and occasional smokers. Introducing a new type of incidence rate, the local as well as global stabilities for the proposed model are discussed at its steady–states. Minimizing the number of individuals involved in a substance abuse in any community is very difficult task, therefore we have introduced four control variables in the controlled system. Pontrygin’s maximum principal is used to derive optimality system. Finally, the obtained results are illustrated numerically and graphically.

Suggested Citation

  • ur Rahman, Ghaus & Agarwal, Ravi P. & Din, Qamar, 2019. "Mathematical analysis of giving up smoking model via harmonic mean type incidence rate," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 128-148.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:128-148
    DOI: 10.1016/j.amc.2019.01.053
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    References listed on IDEAS

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    1. Pang, Liuyong & Zhao, Zhong & Liu, Sanhong & Zhang, Xinan, 2015. "A mathematical model approach for tobacco control in China," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 497-509.
    2. Liqiang Ge & Gaodi Xie & Caixia Zhang & Shimei Li & Yue Qi & Shuyan Cao & Tingting He, 2011. "An Evaluation of China’s Water Footprint," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(10), pages 2633-2647, August.
    3. Flynn, B.S. & Worden, J.K. & Secker-Walker, R.H. & Pirie, P.L. & Badger, G.J. & Carpenter, J.H. & Geller, B.M., 1994. "Mass media and school interventions for cigarette smoking prevention: Effects 2 years after completion," American Journal of Public Health, American Public Health Association, vol. 84(7), pages 1148-1150.
    4. Hai-Feng Huo & Cheng-Cheng Zhu, 2013. "Influence of Relapse in a Giving Up Smoking Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, February.
    5. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
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    Cited by:

    1. Li, Xuhui & Agarwal, Ravi P. & Gómez-Aguilar, J.F. & Badshah, Qaisar & Rahman, Ghaus ur, 2022. "Threshold dynamics: Formulation, stability & sensitivity analysis of co-abuse model of heroin and smoking," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Hu Zhang & Anwar Zeb & Aying Wan & Zizhen Zhang, 2022. "Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    3. Tingting Li & Youming Guo, 2022. "Optimal Control Strategy of an Online Game Addiction Model with Incomplete Recovery," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 780-807, December.
    4. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.

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