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

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

Content Provider	MDPI
Author	Wongvanich, Napasool Tang, I-Ming Dubois, Marc-Antoine Pongsumpun, Puntani
Copyright Year	2021
Description	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 $t\max$ required for the optimal control effort to stay at the maximum amount $u\max$ exhibits an intrinsic logarithmic relationship with respect to the control parameters.
Starting Page	2863
e-ISSN	22277390
DOI	10.3390/math9222863
Journal	Mathematics
Issue Number	22
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-11-11
Access Restriction	Open
Subject Keyword	Mathematics Biology Hand Foot Mouth Disease Optimal Control Epidemiological Control Regional Residency
Content Type	Text
Resource Type	Article

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