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Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand

Author

Listed:
  • Napasool Wongvanich

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

  • I-Ming Tang

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

  • Marc-Antoine Dubois

    (CREATE 132 Route du Havre de la Vanlee, 50270 Bricqueville-sur-Mer, France)

  • Puntani Pongsumpun

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

Abstract

Hand, foot and mouth disease (HFMD) is a virulent disease most commonly found in East and Southeast Asia. Symptoms include ulcers or sores, inside or around the mouth. In this research, we formulate the dynamic model of HFMD by using the SEIQR model. We separated the infection episodes where there is a higher outbreak and a lower outbreak of the disease associated with regional residency, with the higher level of outbreak occurring in the urban region, and a lower outbreak level occurring in the rural region. We developed two different optimal control programs for the types of outbreaks. Optimal Control Policy 1 (OPC1) is limited to the use of treatment only, whereas Optimal Control Policy 2 (OPC2) includes vaccination along with the treatment. The Pontryagin’s maximum principle is used to establish the necessary and optimal conditions for the two policies. Numerical solutions are presented along with numerical sensitivity analyses of the required control efforts needed as the control parameters are changed. Results show that the time t m a x required for the optimal control effort to stay at the maximum amount u m a x exhibits an intrinsic logarithmic relationship with respect to the control parameters.

Suggested Citation

  • Napasool Wongvanich & I-Ming Tang & Marc-Antoine Dubois & Puntani Pongsumpun, 2021. "Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand," Mathematics, MDPI, vol. 9(22), pages 1-30, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2863-:d:676856
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    References listed on IDEAS

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    1. Ghanbari, Behzad, 2020. "On forecasting the spread of the COVID-19 in Iran: The second wave," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    3. Djilali, Salih & Ghanbari, Behzad, 2020. "Coronavirus pandemic: A predictive analysis of the peak outbreak epidemic in South Africa, Turkey, and Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Yeting Zhu & Boyang Xu & Xinze Lian & Wang Lin & Zumu Zhou & Weiming Wang, 2014. "A Hand-Foot-and-Mouth Disease Model with Periodic Transmission Rate in Wenzhou, China," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, March.
    5. Eric Okyere & Johnson De-Graft Ankamah & Anthony Kodzo Hunkpe & Dorcas Mensah, 2020. "Deterministic Epidemic Models for Ebola Infection with Time-Dependent Controls," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-12, July.
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    Cited by:

    1. Bing Li & Ziye Xiang, 2023. "Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes," Mathematics, MDPI, vol. 11(12), pages 1-26, June.

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