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...

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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
id UTADEO2_2948c896efc9d41cf6d5359f8811d1b2
oai_identifier_str oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/12091
network_acronym_str UTADEO2
network_name_str 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
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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
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dc.rights.local.spa.fl_str_mv Acceso restringido
rights_invalid_str_mv Acceso restringido
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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
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collection Expeditio Repositorio Institucional UJTL
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spelling 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; 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