Optimal control and mathematical models in epidemiology

Bibliographic Details
Main Author: Paião, Ana Pedro Lemos
Publication Date: 2019
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/29401
Summary: In this PhD thesis, we prove sufficient optimality conditions for delayed optimal control problems, by transforming them into equivalent non-delayed problems. Such transformation is done by considering a technique proposed by Guinn in 1976 and later promoted by Maurer and his collaborators. In this way, we are able to use well-known sufficient optimality conditions for non-delayed optimal control problems and to return to the delayed ones. We propose and study several models that can translate the spread of cholera and that consider different types of treatment or prevention measures. Corresponding optimal control problems are formulated and studied. Such theoretical analysis are then applied to real cholera outbreaks that occured in Haiti and Yemen.
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spelling Optimal control and mathematical models in epidemiologyTime delaysOptimal controlSufficient optimality conditionsMathematical models for cholera transmissionLocal asymptotic stabilityIn this PhD thesis, we prove sufficient optimality conditions for delayed optimal control problems, by transforming them into equivalent non-delayed problems. Such transformation is done by considering a technique proposed by Guinn in 1976 and later promoted by Maurer and his collaborators. In this way, we are able to use well-known sufficient optimality conditions for non-delayed optimal control problems and to return to the delayed ones. We propose and study several models that can translate the spread of cholera and that consider different types of treatment or prevention measures. Corresponding optimal control problems are formulated and studied. Such theoretical analysis are then applied to real cholera outbreaks that occured in Haiti and Yemen.Nesta tese de doutoramento, provamos condições suficientes de otimalidade para problemas de controlo ótimo com tempos de atraso, transformando-os em problemas equivalentes sem tempos de atraso. Tal transformação é feita considerando uma técnica proposta por Guinn em 1976 e mais tarde promovida por Maurer e seus colaboradores. Deste modo, somos capazes de usar condições suficientes de otimalidade conhecidas para problemas de controlo ótimo sem tempos de atraso e voltar aos que consideram tempos de atraso. Propomos e estudamos vários modelos que traduzem a propagação da cólera e que consideram diferentes tipos de tratamento ou de medidas de prevenção. Problemas de controlo ótimo correspondentes são formulados e estudados. Tais análises teóricas são depois aplicadas a epidemias de cólera reais que ocorreram no Haiti e no Iémen.2019-122019-12-01T00:00:00Zdoctoral thesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10773/29401TID:101586604engPaião, Ana Pedro Lemosinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:27:45Zoai:ria.ua.pt:10773/29401Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:09:13.357853Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Optimal control and mathematical models in epidemiology
title Optimal control and mathematical models in epidemiology
spellingShingle Optimal control and mathematical models in epidemiology
Paião, Ana Pedro Lemos
Time delays
Optimal control
Sufficient optimality conditions
Mathematical models for cholera transmission
Local asymptotic stability
title_short Optimal control and mathematical models in epidemiology
title_full Optimal control and mathematical models in epidemiology
title_fullStr Optimal control and mathematical models in epidemiology
title_full_unstemmed Optimal control and mathematical models in epidemiology
title_sort Optimal control and mathematical models in epidemiology
author Paião, Ana Pedro Lemos
author_facet Paião, Ana Pedro Lemos
author_role author
dc.contributor.author.fl_str_mv Paião, Ana Pedro Lemos
dc.subject.por.fl_str_mv Time delays
Optimal control
Sufficient optimality conditions
Mathematical models for cholera transmission
Local asymptotic stability
topic Time delays
Optimal control
Sufficient optimality conditions
Mathematical models for cholera transmission
Local asymptotic stability
description In this PhD thesis, we prove sufficient optimality conditions for delayed optimal control problems, by transforming them into equivalent non-delayed problems. Such transformation is done by considering a technique proposed by Guinn in 1976 and later promoted by Maurer and his collaborators. In this way, we are able to use well-known sufficient optimality conditions for non-delayed optimal control problems and to return to the delayed ones. We propose and study several models that can translate the spread of cholera and that consider different types of treatment or prevention measures. Corresponding optimal control problems are formulated and studied. Such theoretical analysis are then applied to real cholera outbreaks that occured in Haiti and Yemen.
publishDate 2019
dc.date.none.fl_str_mv 2019-12
2019-12-01T00:00:00Z
dc.type.driver.fl_str_mv doctoral thesis
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/29401
TID:101586604
url http://hdl.handle.net/10773/29401
identifier_str_mv TID:101586604
dc.language.iso.fl_str_mv eng
language eng
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.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833594337813856256

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