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Optimal Control Strategies in an Alcoholism Model

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  • 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, Hindawi, vol. 2014, pages 1-18, March.
    • Handle: RePEc:hin:jnlaaa:954069
    DOI: 10.1155/2014/954069
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    Cited by:

    1. Crokidakis, Nuno & Sigaud, Lucas, 2021. "Modeling the evolution of drinking behavior: A Statistical Physics perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    2. Şengül, Taylan & Yıldız, Esmanur, 2021. "A dynamical systems approach to the interplay between tobacco smokers, electronic-cigarette smokers and smoking quitters," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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