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Deterministic and stochastic stability of a mathematical model of smoking

Author

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  • Lahrouz, A.
  • Omari, L.
  • Kiouach, D.
  • Belmaâti, A.

Abstract

Our aim in this paper, is first constructing a Lyapunov function to prove the global stability of the unique smoking-present equilibrium state of a mathematical model of smoking. Next we incorporate random noise into the deterministic model. We show that the stochastic model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. Then a stochastic Lyapunov method is performed to obtain the sufficient conditions for mean square and asymptotic stability in probability of the stochastic model. Our analysis reveals that the stochastic stability of the smoking-present equilibrium state, depends on the magnitude of the intensities of noise as well as the parameters involved within the model system.

Suggested Citation

  • Lahrouz, A. & Omari, L. & Kiouach, D. & Belmaâti, A., 2011. "Deterministic and stochastic stability of a mathematical model of smoking," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1276-1284, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1276-1284
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    Cited by:

    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. Lu, Chun, 2022. "Dynamical analysis and numerical simulations on a crowley-Martin predator-prey model in stochastic environment," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    3. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    4. Lu, Chun & Liu, Honghui & Zhang, De, 2021. "Dynamics and simulations of a second order stochastically perturbed SEIQV epidemic model with saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Nisar, Kottakkaran Sooppy & Farman, Muhammad & Hincal, Evren & Shehzad, Aamir, 2023. "Modelling and analysis of bad impact of smoking in society with Constant Proportional-Caputo Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.

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