期刊
MATHEMATICS
卷 9, 期 22, 页码 -出版社
MDPI
DOI: 10.3390/math9222863
关键词
hand foot mouth disease; optimal control; epidemiological control; regional residency
类别
资金
- School of Science, King Mongkut's Institute of Technology Ladkrabang, Thailand
This study formulated a dynamic model of hand, foot and mouth disease (HFMD) using the SEIQR model, identifying higher and lower outbreak periods associated with regional residency. Two optimal control programs were developed, with one focusing on treatment and the other on vaccination in addition to treatment. Numerical solutions and sensitivity analyses revealed a logarithmic relationship between optimal control effort and control parameters.
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 tmax required for the optimal control effort to stay at the maximum amount umax exhibits an intrinsic logarithmic relationship with respect to the control parameters.
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