IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v354y2019icp128-148.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319300682
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.01.053?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gao, Fei & Li, Xiling & Li, Wenqin & Zhou, Xianjin, 2021. "Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Abdel-Gawad, Hamdy I. & Baleanu, Dumitru & Abdel-Gawad, Ahmed H., 2021. "Unification of the different fractional time derivatives: An application to the epidemic-antivirus dynamical system in computer networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    4. Dwivedi, Kushal Dhar & Singh, Jagdev, 2021. "Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 38-50.
    5. Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a time fractional advection-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Shamima Akter & Md. Mizanur Rahman & Thomas Rouyard & Sarmin Aktar & Raïssa Shiyghan Nsashiyi & Ryota Nakamura, 2024. "A systematic review and network meta-analysis of population-level interventions to tackle smoking behaviour," Nature Human Behaviour, Nature, vol. 8(12), pages 2367-2391, December.
    7. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    9. Shah, Kamal & Arfan, Muhammad & Ullah, Aman & Al-Mdallal, Qasem & Ansari, Khursheed J. & Abdeljawad, Thabet, 2022. "Computational study on the dynamics of fractional order differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    11. Odibat, Zaid & Baleanu, Dumitru, 2023. "A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 224-233.
    12. Ghalib, M. Mansha & Zafar, Azhar A. & Riaz, M. Bilal & Hammouch, Z. & Shabbir, Khurram, 2020. "Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    13. Gao, Wei & Veeresha, P. & Prakasha, D.G. & Baskonus, Haci Mehmet & Yel, Gulnur, 2020. "New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    14. Yuanhong Tian & Matthias Ruth & Dajian Zhu, 2017. "Using the IPAT identity and decoupling analysis to estimate water footprint variations for five major food crops in China from 1978 to 2010," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 19(6), pages 2355-2375, December.
    15. Feten Maddouri, 2025. "Stability and Convergence Analysis of a Numerical Method for Solving a $$\zeta$$ ζ -Caputo Time Fractional Black–Scholes Model via European Options," Computational Economics, Springer;Society for Computational Economics, vol. 65(6), pages 3419-3446, June.
    16. Ameen, Ismail Gad & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2022. "Different strategies to confront maize streak disease based on fractional optimal control formulation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    17. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    18. Sharma, Anupama, 2020. "Quantifying the effect of demographic stochasticity on the smoking epidemic in the presence of economic stimulus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    19. Owolabi, Kolade M., 2018. "Numerical patterns in reaction–diffusion system with the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 160-169.
    20. Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:128-148. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.