Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali

Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali

The dynamics of many epidemiological models for infectious diseases that spread in the sexually active population presents a crucial period: the period of the influx or recruitment of susceptible. In this paper, we assume that the recruitment of susceptible is done among the juvenile group. We propo...

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Main Authors: Ouaténi Diallo, Yaya Koné, Jérôme Pousin
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2010/638021
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spelling doaj-d4fb42f4f8e147619bd108e82f45f0012020-11-24T22:57:47ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/638021638021Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in MaliOuaténi Diallo0Yaya Koné1Jérôme Pousin2Département de Mathématiques et D'Informatique, Faculté des Sciences et Techniques, B.P.E 3206, Bamako, MaliDépartement de Mathématiques et D'Informatique, Faculté des Sciences et Techniques, B.P.E 3206, Bamako, MaliUniversité de Lyon, INSA, ICJ UMR CNRS 5208, 69100 Lyon, FranceThe dynamics of many epidemiological models for infectious diseases that spread in the sexually active population presents a crucial period: the period of the influx or recruitment of susceptible. In this paper, we assume that the recruitment of susceptible is done among the juvenile group. We propose a dynamical system to modelize the disease spread, and we study the dynamical behavior of this system. Then, the controllability of the system is studied. We prove that the survival rate allows to control the dynamic of the system. Numerical simulations are given to illustrate the results.http://dx.doi.org/10.1155/2010/638021
collection DOAJ
language English
format Article
sources DOAJ
author Ouaténi Diallo
Yaya Koné
Jérôme Pousin
spellingShingle Ouaténi Diallo
Yaya Koné
Jérôme Pousin
Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali
International Journal of Mathematics and Mathematical Sciences
author_facet Ouaténi Diallo
Yaya Koné
Jérôme Pousin
author_sort Ouaténi Diallo
title Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali
title_short Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali
title_full Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali
title_fullStr Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali
title_full_unstemmed Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali
title_sort dynamics and thresholds of a simple epidemiological model: example of hiv/aids in mali
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2010-01-01
description The dynamics of many epidemiological models for infectious diseases that spread in the sexually active population presents a crucial period: the period of the influx or recruitment of susceptible. In this paper, we assume that the recruitment of susceptible is done among the juvenile group. We propose a dynamical system to modelize the disease spread, and we study the dynamical behavior of this system. Then, the controllability of the system is studied. We prove that the survival rate allows to control the dynamic of the system. Numerical simulations are given to illustrate the results.
url http://dx.doi.org/10.1155/2010/638021
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AT yayakone dynamicsandthresholdsofasimpleepidemiologicalmodelexampleofhivaidsinmali
AT jeromepousin dynamicsandthresholdsofasimpleepidemiologicalmodelexampleofhivaidsinmali
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