Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control
In this paper, a nonlinear fractional order epidemic model for HIV transmission is proposed and analyzed by including extra compartment namely exposed class to the basic SIR epidemic model. Also, the infected class of female sex workers is divided into unaware infectives and the aware infectives. Th...
- Autores:
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Universidad de Bogotá Jorge Tadeo Lozano
- Repositorio:
- Expeditio: repositorio UTadeo
- Idioma:
- eng
- OAI Identifier:
- oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/12091
- Acceso en línea:
- https://doi.org/10.1016/j.chaos.2020.109826
http://hdl.handle.net/20.500.12010/12091
- Palabra clave:
- SEIR epidemic model
Caputo fractional derivative
Adams-Bashforth-Moulton method
Female sex workers
Stability analysis
Reproduction number R0
Fractional optimal control problem
Síndrome respiratorio agudo grave
COVID-19
SARS-CoV-2
Coronavirus
- Rights
- License
- Acceso restringido
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oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/12091 |
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Expeditio: repositorio UTadeo |
repository_id_str |
|
dc.title.spa.fl_str_mv |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control |
title |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control |
spellingShingle |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control SEIR epidemic model Caputo fractional derivative Adams-Bashforth-Moulton method Female sex workers Stability analysis Reproduction number R0 Fractional optimal control problem Síndrome respiratorio agudo grave COVID-19 SARS-CoV-2 Coronavirus |
title_short |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control |
title_full |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control |
title_fullStr |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control |
title_full_unstemmed |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control |
title_sort |
Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control |
dc.subject.spa.fl_str_mv |
SEIR epidemic model Caputo fractional derivative Adams-Bashforth-Moulton method Female sex workers Stability analysis Reproduction number R0 Fractional optimal control problem |
topic |
SEIR epidemic model Caputo fractional derivative Adams-Bashforth-Moulton method Female sex workers Stability analysis Reproduction number R0 Fractional optimal control problem Síndrome respiratorio agudo grave COVID-19 SARS-CoV-2 Coronavirus |
dc.subject.lemb.spa.fl_str_mv |
Síndrome respiratorio agudo grave COVID-19 SARS-CoV-2 Coronavirus |
description |
In this paper, a nonlinear fractional order epidemic model for HIV transmission is proposed and analyzed by including extra compartment namely exposed class to the basic SIR epidemic model. Also, the infected class of female sex workers is divided into unaware infectives and the aware infectives. The focus is on the spread of HIV by female sex workers through prostitution, because in the present world sexual transmission is the major cause of the HIV transmission. The exposed class contains those susceptible males in the population who have sexual contact with the female sex workers and are exposed to the infection directly or indirectly. The Caputo type fractional derivative is involved and generalized Adams-BashforthMoulton method is employed to numerically solve the proposed model. Model equilibria are determined and their stability analysis is considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle invariant principle. Analysis of the model demonstrates that the population is free from the disease if R0 < 1 and disease spreads in the population if R0 > 1. Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed. Furthermore, for the fractional optimal control problem associated with the control strategies such as condom use for exposed class, treatment for aware infectives, awareness about disease among unaware infectives and behavioral change for susceptibles, we formulated a fractional optimality condition for the proposed model. The existence of fractional optimal control is analyzed and the Euler-Lagrange necessary conditions for the optimality of fractional optimal control are obtained. The effectiveness of control strategies is shown through numerical simulations and it can be seen through simulation, that the control measures effectively increase the quality of life and age limit of the HIV patients. It significantly reduces the number of HIV/AIDS patients during the whole epidemic. |
publishDate |
2020 |
dc.date.accessioned.none.fl_str_mv |
2020-08-21T16:35:11Z |
dc.date.available.none.fl_str_mv |
2020-08-21T16:35:11Z |
dc.date.created.none.fl_str_mv |
2020 |
dc.type.local.spa.fl_str_mv |
Artículo |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
format |
http://purl.org/coar/resource_type/c_6501 |
dc.identifier.issn.spa.fl_str_mv |
0960-0779 |
dc.identifier.other.spa.fl_str_mv |
https://doi.org/10.1016/j.chaos.2020.109826 |
dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/20.500.12010/12091 |
dc.identifier.doi.spa.fl_str_mv |
https://doi.org/10.1016/j.chaos.2020.109826 |
identifier_str_mv |
0960-0779 |
url |
https://doi.org/10.1016/j.chaos.2020.109826 http://hdl.handle.net/20.500.12010/12091 |
dc.language.iso.spa.fl_str_mv |
eng |
language |
eng |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_f1cf |
dc.rights.local.spa.fl_str_mv |
Acceso restringido |
rights_invalid_str_mv |
Acceso restringido http://purl.org/coar/access_right/c_f1cf |
dc.format.extent.spa.fl_str_mv |
24 páginas |
dc.format.mimetype.spa.fl_str_mv |
image/jepg |
dc.publisher.spa.fl_str_mv |
Chaos, Solitons and Fractals |
dc.source.spa.fl_str_mv |
reponame:Expeditio Repositorio Institucional UJTL instname:Universidad de Bogotá Jorge Tadeo Lozano |
instname_str |
Universidad de Bogotá Jorge Tadeo Lozano |
institution |
Universidad de Bogotá Jorge Tadeo Lozano |
reponame_str |
Expeditio Repositorio Institucional UJTL |
collection |
Expeditio Repositorio Institucional UJTL |
bitstream.url.fl_str_mv |
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2020-08-21T16:35:11Z2020-08-21T16:35:11Z20200960-0779https://doi.org/10.1016/j.chaos.2020.109826http://hdl.handle.net/20.500.12010/12091https://doi.org/10.1016/j.chaos.2020.109826In this paper, a nonlinear fractional order epidemic model for HIV transmission is proposed and analyzed by including extra compartment namely exposed class to the basic SIR epidemic model. Also, the infected class of female sex workers is divided into unaware infectives and the aware infectives. The focus is on the spread of HIV by female sex workers through prostitution, because in the present world sexual transmission is the major cause of the HIV transmission. The exposed class contains those susceptible males in the population who have sexual contact with the female sex workers and are exposed to the infection directly or indirectly. The Caputo type fractional derivative is involved and generalized Adams-BashforthMoulton method is employed to numerically solve the proposed model. Model equilibria are determined and their stability analysis is considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle invariant principle. Analysis of the model demonstrates that the population is free from the disease if R0 < 1 and disease spreads in the population if R0 > 1. Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed. Furthermore, for the fractional optimal control problem associated with the control strategies such as condom use for exposed class, treatment for aware infectives, awareness about disease among unaware infectives and behavioral change for susceptibles, we formulated a fractional optimality condition for the proposed model. The existence of fractional optimal control is analyzed and the Euler-Lagrange necessary conditions for the optimality of fractional optimal control are obtained. The effectiveness of control strategies is shown through numerical simulations and it can be seen through simulation, that the control measures effectively increase the quality of life and age limit of the HIV patients. It significantly reduces the number of HIV/AIDS patients during the whole epidemic.24 páginasimage/jepgengChaos, Solitons and Fractalsreponame:Expeditio Repositorio Institucional UJTLinstname:Universidad de Bogotá Jorge Tadeo LozanoSEIR epidemic modelCaputo fractional derivativeAdams-Bashforth-Moulton methodFemale sex workersStability analysisReproduction number R0Fractional optimal control problemSíndrome respiratorio agudo graveCOVID-19SARS-CoV-2CoronavirusGlobal dynamics of a fractional order model for the transmission of HIV epidemic with optimal controlArtículohttp://purl.org/coar/resource_type/c_6501Acceso restringidohttp://purl.org/coar/access_right/c_f1cfAhmad Naik, ParvaizZu, JianOwolabi, Kolade M.THUMBNAILCaptura.PNGCaptura.PNGPortadaimage/png201078https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/12091/4/Captura.PNGeded0000b9fd4ff64a59fb44fa42f623MD54open accessGlobal-dynamics-of-a-fractional-order-model-for-the-tran_2020_Chaos--Soliton.pdf.jpgGlobal-dynamics-of-a-fractional-order-model-for-the-tran_2020_Chaos--Soliton.pdf.jpgIM Thumbnailimage/jpeg15549https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/12091/5/Global-dynamics-of-a-fractional-order-model-for-the-tran_2020_Chaos--Soliton.pdf.jpg377061479275f15fd117ef0a20534c9eMD55open accessORIGINALCaptura.PNGCaptura.PNGVer portadaimage/png201078https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/12091/1/Captura.PNGeded0000b9fd4ff64a59fb44fa42f623MD51open accessGlobal-dynamics-of-a-fractional-order-model-for-the-tran_2020_Chaos--Soliton.pdfGlobal-dynamics-of-a-fractional-order-model-for-the-tran_2020_Chaos--Soliton.pdfArtículo reservadoapplication/pdf4912685https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/12091/3/Global-dynamics-of-a-fractional-order-model-for-the-tran_2020_Chaos--Soliton.pdfcb7176e339dd822ac30a05ac14115c4aMD53embargoed access|||2200-08-21LICENSElicense.txtlicense.txttext/plain; charset=utf-82938https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/12091/2/license.txtabceeb1c943c50d3343516f9dbfc110fMD52open access20.500.12010/12091oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/120912020-08-21 11:35:11.714open accessRepositorio Institucional - Universidad Jorge Tadeo Lozanoexpeditio@utadeo.edu.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 |