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Optimal Control of Dengue Transmission with Vaccination

Author

Listed:
  • Anusit Chamnan

    (Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

  • Puntani Pongsumpun

    (Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

  • I-Ming Tang

    (Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand)

  • Napasool Wongvanich

    (Department of Instrumentation and Control Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand)

Abstract

Dengue disease is caused by four serotypes of the dengue virus: DEN-1, DEN-2, DEN-3, and DEN-4. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV) is a vaccine currently used in Thailand. This research investigates what the optimal control is when only individuals having documented past dengue infection history are vaccinated. This is the present practice in Thailand and is the latest recommendation of the WHO. The model used is the Susceptible-Infected-Recovered (SIR) model in series configuration for the human population and the Susceptible-Infected (SI) model for the vector population. Both dynamical models for the two populations were recast as optimal control problems with two optimal control parameters. The analysis showed that the equilibrium states were locally asymptotically stable. The numerical solution of the control systems and conclusions are presented.

Suggested Citation

  • Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2021. "Optimal Control of Dengue Transmission with Vaccination," Mathematics, MDPI, vol. 9(15), pages 1-33, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1833-:d:607747
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    References listed on IDEAS

    as
    1. Hengki Tasman & Asep K. Supriatna & Nuning Nuraini & Edy Soewono, 2012. "A Dengue Vaccination Model for Immigrants in a Two-Age-Class Population," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-15, May.
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    Cited by:

    1. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2022. "Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    2. Li, Yazhi & Wang, Yan & Liu, Lili, 2023. "Optimal control of dengue vector based on a reaction–diffusion model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 250-270.

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