A SIQRB delayed model for cholera and optimal control treatment
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/35008 |
Resumo: | We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non-delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication. |
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A SIQRB delayed model for cholera and optimal control treatmentSIQRB cholera delayed modelTime-delayDisease-free and endemic equilibriaStabilityOptimal controlCase study in HaitiWe improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non-delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.EDP Sciences2022-10-26T14:53:50Z2022-01-01T00:00:00Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/35008eng0973-534810.1051/mmnp/2022027Lemos-Paião, Ana P.Maurer, HelmutSilva, Cristiana J.Torres, Delfim F. M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:06:34Zoai:ria.ua.pt:10773/35008Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:05:47.344319Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A SIQRB delayed model for cholera and optimal control treatment |
title |
A SIQRB delayed model for cholera and optimal control treatment |
spellingShingle |
A SIQRB delayed model for cholera and optimal control treatment Lemos-Paião, Ana P. SIQRB cholera delayed model Time-delay Disease-free and endemic equilibria Stability Optimal control Case study in Haiti |
title_short |
A SIQRB delayed model for cholera and optimal control treatment |
title_full |
A SIQRB delayed model for cholera and optimal control treatment |
title_fullStr |
A SIQRB delayed model for cholera and optimal control treatment |
title_full_unstemmed |
A SIQRB delayed model for cholera and optimal control treatment |
title_sort |
A SIQRB delayed model for cholera and optimal control treatment |
author |
Lemos-Paião, Ana P. |
author_facet |
Lemos-Paião, Ana P. Maurer, Helmut Silva, Cristiana J. Torres, Delfim F. M. |
author_role |
author |
author2 |
Maurer, Helmut Silva, Cristiana J. Torres, Delfim F. M. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Lemos-Paião, Ana P. Maurer, Helmut Silva, Cristiana J. Torres, Delfim F. M. |
dc.subject.por.fl_str_mv |
SIQRB cholera delayed model Time-delay Disease-free and endemic equilibria Stability Optimal control Case study in Haiti |
topic |
SIQRB cholera delayed model Time-delay Disease-free and endemic equilibria Stability Optimal control Case study in Haiti |
description |
We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non-delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-10-26T14:53:50Z 2022-01-01T00:00:00Z 2022 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/35008 |
url |
http://hdl.handle.net/10773/35008 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0973-5348 10.1051/mmnp/2022027 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
EDP Sciences |
publisher.none.fl_str_mv |
EDP Sciences |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137712646651904 |