Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB
Autor(a) principal: | |
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Data de Publicação: | 2023 |
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/10773/36753 |
Resumo: | In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa's fde12 solver and two simple methods coded here in Octave/MATLAB: the fractional forward {Euler's} method and the predict-evaluate-correct-evaluate (PECE) method of Adams--Bashforth--Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with MATLAB. The developed Octave/Matlab code is available at [https://github.com/SilverioRosa/numres-focp] |
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Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLABNumerical algorithmsFractional optimal controlOctave and MatlabRespiratory syncytial virus infectionOpen source code for fractional optimal controlIn this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa's fde12 solver and two simple methods coded here in Octave/MATLAB: the fractional forward {Euler's} method and the predict-evaluate-correct-evaluate (PECE) method of Adams--Bashforth--Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with MATLAB. The developed Octave/Matlab code is available at [https://github.com/SilverioRosa/numres-focp]MDPI2023-03-30T15:12:55Z2023-03-20T00:00:00Z2023-03-20info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/36753eng10.3390/math11061511Rosa, SilvérioTorres, 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:RCAAP2024-02-22T12:10:38Zoai:ria.ua.pt:10773/36753Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:07:22.487280Repositório 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 |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB |
title |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB |
spellingShingle |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB Rosa, Silvério Numerical algorithms Fractional optimal control Octave and Matlab Respiratory syncytial virus infection Open source code for fractional optimal control |
title_short |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB |
title_full |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB |
title_fullStr |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB |
title_full_unstemmed |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB |
title_sort |
Numerical fractional optimal control of respiratory syncytial virus infection in Octave/MATLAB |
author |
Rosa, Silvério |
author_facet |
Rosa, Silvério Torres, Delfim F. M. |
author_role |
author |
author2 |
Torres, Delfim F. M. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Rosa, Silvério Torres, Delfim F. M. |
dc.subject.por.fl_str_mv |
Numerical algorithms Fractional optimal control Octave and Matlab Respiratory syncytial virus infection Open source code for fractional optimal control |
topic |
Numerical algorithms Fractional optimal control Octave and Matlab Respiratory syncytial virus infection Open source code for fractional optimal control |
description |
In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa's fde12 solver and two simple methods coded here in Octave/MATLAB: the fractional forward {Euler's} method and the predict-evaluate-correct-evaluate (PECE) method of Adams--Bashforth--Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with MATLAB. The developed Octave/Matlab code is available at [https://github.com/SilverioRosa/numres-focp] |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-03-30T15:12:55Z 2023-03-20T00:00:00Z 2023-03-20 |
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/10773/36753 |
url |
http://hdl.handle.net/10773/36753 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.3390/math11061511 |
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 |
MDPI |
publisher.none.fl_str_mv |
MDPI |
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) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137729209958400 |