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Optimal strategy of vaccination & treatment in an SIR epidemic model

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  • Zaman, Gul
  • Kang, Yong Han
  • Cho, Giphil
  • Jung, Il Hyo

Abstract

In this work, we propose a susceptible–infected–recovered (SIR) epidemic model which describes the interaction between susceptible and infected individuals in a community and analyze the SIR epidemic model through the optimal control theory and mathematical analysis. In addition, we present some possible strategies to prevent the spread of some infection causing epidemic in the society. In order to do this, we introduce an optimal control problem with an objective functional, where two control functions, vaccination and treatment have been used as control measures for susceptible and infected individuals. We show the existence of an optimal control pair for the optimal control problem and derive the optimality condition. Finally we consider a smoking epidemic model to illustrate our theoretical results with some numerical simulations, which use real data collected in April and May 2004 from 300 male students at three vocational technical high schools in Korean metropolitan areas. Our analysis suggests that two control strategies are more effective than only one control strategy in controlling the increase of male student smokers in Korean metropolitan areas.

Suggested Citation

  • Zaman, Gul & Kang, Yong Han & Cho, Giphil & Jung, Il Hyo, 2017. "Optimal strategy of vaccination & treatment in an SIR epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 63-77.
    • Handle: RePEc:eee:matcom:v:136:y:2017:i:c:p:63-77
    DOI: 10.1016/j.matcom.2016.11.010
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    References listed on IDEAS

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    1. Satsuma, J & Willox, R & Ramani, A & Grammaticos, B & Carstea, A.S, 2004. "Extending the SIR epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 369-375.
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    Cited by:

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    2. Tingqiang Chen & Lei Wang & Jining Wang & Qi Yang, 2017. "A Network Diffusion Model of Food Safety Scare Behavior considering Information Transparency," Complexity, Hindawi, vol. 2017, pages 1-16, December.
    3. Chen, Ya & Zhang, Juping & Jin, Zhen, 2023. "Optimal control of an influenza model with mixed cross-infection by age group," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 410-436.
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    5. Kumar, Arjun & Dubey, Uma S. & Dubey, Balram, 2024. "The impact of social media advertisements and treatments on the dynamics of infectious diseases with optimal control strategies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 50-86.
    6. Xie, Yingkang & Wang, Zhen, 2022. "A ratio-dependent impulsive control of an SIQS epidemic model with non-linear incidence," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    7. Yusheng Zhang & Liang Li & Yuewen Jiang & Biqing Huang, 2020. "Analysis of COVID-19 Prevention and Control Effects Based on the SEITRD Dynamic Model and Wuhan Epidemic Statistics," IJERPH, MDPI, vol. 17(24), pages 1-16, December.

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