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Optimal Control Strategy of an Online Game Addiction Model with Incomplete Recovery

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  • Tingting Li

    (Guilin University of Technology)

  • Youming Guo

    (Guilin University of Technology)

Abstract

Since the global COVID-19 pandemic in 2020, some people who have dropped out of online game have become re-addicted to it due to the order of stay-at-home, making the phenomenon of online game addiction even worse. Controlling the prevalence of online game addiction is of great significance to protect people’s healthy life. For this purpose, a mathematical model of online game addiction with incomplete recovery and relapse is established. First, we analyze the basic properties of the model and obtain the expression of the basic reproduction number and all equilibria. By constructing suitable Lyapunov functions, the global asymptotical stability of the equilibria are proved. Then in the numerical simulation, we use the least squares estimation method to fit the real data of e-sports users in China from 2010 to 2020, and obtain the estimated value of all parameters. The approximation value of the basic reproduction number is obtained as $$R_{0}\approx 5.05$$ R 0 ≈ 5.05 . The result reflects that the spread of game addiction in China is very serious. The stability of the equilibria are proved by using the estimated parameter values. Finally, the simulation results between with control and without control during 2020 to 2050 are compared, and the optimal control strategy is found by comparing the total infectious people. The results of optimal control suggest that if we increase our continuous attention to incompletely recovered people, we can prevent more people from becoming addicted to games. The findings in this paper reveal new mechanisms of game addiction transmission and demonstrate a more detailed and reliable control strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:3:d:10.1007_s10957-022-02123-x
    DOI: 10.1007/s10957-022-02123-x
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    References listed on IDEAS

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    1. 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.
    2. Ullah, Saif & Khan, Muhammad Altaf, 2020. "Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Li, Tingting & Guo, Youming, 2022. "Modeling and optimal control of mutated COVID-19 (Delta strain) with imperfect vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Tian, Yong & Ding, Xuejun, 2019. "Rumor spreading model with considering debunking behavior in emergencies," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    5. Bonyah, Ebenezer & Gómez-Aguilar, J.F. & Adu, Augustina, 2018. "Stability analysis and optimal control of a fractional human African trypanosomiasis model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 150-160.
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