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Optimal Control Strategies in an Alcoholism Model

Author

Listed:
  • Xun-Yang Wang
  • Hai-Feng Huo
  • Qing-Kai Kong
  • Wei-Xuan Shi

Abstract

This paper presents a deterministic SATQ‐type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results.

Suggested Citation

  • Xun-Yang Wang & Hai-Feng Huo & Qing-Kai Kong & Wei-Xuan Shi, 2014. "Optimal Control Strategies in an Alcoholism Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:954069
    DOI: 10.1155/2014/954069
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    References listed on IDEAS

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    1. 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.
    2. Hai-Feng Huo & Cheng-Cheng Zhu, 2013. "Influence of Relapse in a Giving Up Smoking Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Mubayi, Anuj & Greenwood, Priscilla E. & Castillo-Chávez, Carlos & Gruenewald, Paul J. & Gorman, Dennis M., 2010. "The impact of relative residence times on the distribution of heavy drinkers in highly distinct environments," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 45-56, March.
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    Cited by:

    1. Maranya M. Mayengo, 2022. "Optimal Control Model for Alcohol–Related Risk Behaviors and Beliefs in Tanzania," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Bouchaib Khajji & Abderrahim Labzai & Abdelfatah Kouidere & Omar Balatif & Mostafa Rachik, 2020. "A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).

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