IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i22p2863-d676856.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/22/2863/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/22/2863/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ghanbari, Behzad, 2020. "On forecasting the spread of the COVID-19 in Iran: The second wave," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. 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.
    3. 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.
    4. Samanta, G.P., 2014. "Analysis of a delayed epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 74-85.
    5. 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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    3. Elise Blandenier & Zahra Habibi & Timokleia Kousi & Paolo Sestito & Antoine Flahault & Liudmila Rozanova, 2020. "Initial COVID-19 Outbreak: An Epidemiological and Socioeconomic Case Review of Iran," IJERPH, MDPI, vol. 17(24), pages 1-13, December.
    4. Ghanbari, Behzad, 2020. "On forecasting the spread of the COVID-19 in Iran: The second wave," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Zhu, Ligang & Li, Xiang & Xu, Fei & Yin, Zhiyong & Jin, Jun & Liu, Zhilong & Qi, Hong & Shuai, Jianwei, 2022. "Network modeling-based identification of the switching targets between pyroptosis and secondary pyroptosis," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. Faik Bilgili & Emrah Koçak & Sevda Kuşkaya, 2023. "Dynamics and Co-movements Between the COVID-19 Outbreak and the Stock Market in Latin American Countries: An Evaluation Based on the Wavelet-Partial Wavelet Coherence Model," Evaluation Review, , vol. 47(4), pages 630-652, August.
    7. John D. Ditekemena & Hypolite M. Mavoko & Michael Obimpeh & Stijn Van Hees & Joseph Nelson Siewe Fodjo & Dalau M. Nkamba & Antoinette Tshefu & Wim Van Damme & Jean Jacques Muyembe & Robert Colebunders, 2021. "Adherence to COVID-19 Prevention Measures in the Democratic Republic of the Congo, Results of Two Consecutive Online Surveys," IJERPH, MDPI, vol. 18(5), pages 1-12, March.
    8. Şuayip Yüzbaşı & Gamze Yıldırım, 2023. "A Pell–Lucas Collocation Approach for an SIR Model on the Spread of the Novel Coronavirus (SARS CoV-2) Pandemic: The Case of Turkey," Mathematics, MDPI, vol. 11(3), pages 1-22, January.
    9. Qiang Wang & Min Su & Min Zhang & Rongrong Li, 2021. "Integrating Digital Technologies and Public Health to Fight Covid-19 Pandemic: Key Technologies, Applications, Challenges and Outlook of Digital Healthcare," IJERPH, MDPI, vol. 18(11), pages 1-50, June.
    10. Huo, Liang’an & Gu, Jiafeng, 2023. "The influence of individual emotions on the coupled model of unconfirmed information propagation and epidemic spreading in multilayer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    11. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    12. Panwar, Harsh & Gupta, P.K. & Siddiqui, Mohammad Khubeb & Morales-Menendez, Ruben & Bhardwaj, Prakhar & Singh, Vaishnavi, 2020. "A deep learning and grad-CAM based color visualization approach for fast detection of COVID-19 cases using chest X-ray and CT-Scan images," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    13. Miraj Ahmed Bhuiyan & Tiziana Crovella & Annarita Paiano & Helena Alves, 2021. "A Review of Research on Tourism Industry, Economic Crisis and Mitigation Process of the Loss: Analysis on Pre, During and Post Pandemic Situation," Sustainability, MDPI, vol. 13(18), pages 1-27, September.
    14. Kalantari, Mahdi, 2021. "Forecasting COVID-19 pandemic using optimal singular spectrum analysis," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    15. Haghighat, Fatemeh, 2021. "Predicting the trend of indicators related to Covid-19 using the combined MLP-MC model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2863-:d:676856. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.