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

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 i...

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Autores principales:	Napasool Wongvanich, I-Ming Tang, Marc-Antoine Dubois, Puntani Pongsumpun
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	hand foot mouth disease optimal control epidemiological control regional residency Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b8218bf7e390430ea447b9d01c85cf3c
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spelling	oai:doaj.org-article:b8218bf7e390430ea447b9d01c85cf3c2021-11-25T18:16:41ZMathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand10.3390/math92228632227-7390https://doaj.org/article/b8218bf7e390430ea447b9d01c85cf3c2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2863https://doaj.org/toc/2227-7390Hand, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> required for the optimal control effort to stay at the maximum amount <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> exhibits an intrinsic logarithmic relationship with respect to the control parameters.Napasool WongvanichI-Ming TangMarc-Antoine DuboisPuntani PongsumpunMDPI AGarticlehand foot mouth diseaseoptimal controlepidemiological controlregional residencyMathematicsQA1-939ENMathematics, Vol 9, Iss 2863, p 2863 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	hand foot mouth disease optimal control epidemiological control regional residency Mathematics QA1-939
spellingShingle	hand foot mouth disease optimal control epidemiological control regional residency Mathematics QA1-939 Napasool Wongvanich I-Ming Tang Marc-Antoine Dubois Puntani Pongsumpun Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> required for the optimal control effort to stay at the maximum amount <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> exhibits an intrinsic logarithmic relationship with respect to the control parameters.
format	article
author	Napasool Wongvanich I-Ming Tang Marc-Antoine Dubois Puntani Pongsumpun
author_facet	Napasool Wongvanich I-Ming Tang Marc-Antoine Dubois Puntani Pongsumpun
author_sort	Napasool Wongvanich
title	Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand
title_short	Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand
title_full	Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand
title_fullStr	Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand
title_full_unstemmed	Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand
title_sort	mathematical modeling and optimal control of the hand foot mouth disease affected by regional residency in thailand
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b8218bf7e390430ea447b9d01c85cf3c
work_keys_str_mv	AT napasoolwongvanich mathematicalmodelingandoptimalcontrolofthehandfootmouthdiseaseaffectedbyregionalresidencyinthailand AT imingtang mathematicalmodelingandoptimalcontrolofthehandfootmouthdiseaseaffectedbyregionalresidencyinthailand AT marcantoinedubois mathematicalmodelingandoptimalcontrolofthehandfootmouthdiseaseaffectedbyregionalresidencyinthailand AT puntanipongsumpun mathematicalmodelingandoptimalcontrolofthehandfootmouthdiseaseaffectedbyregionalresidencyinthailand
_version_	1718411403477385216

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

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