The ratio of hidden HIV infection in Cuba
In this work we propose the definition of the ratio of hidden infection of HIV/AIDS epidemics, as the division of the unknown infected population by the known one. The merit of the definition lies in allowing for an indirect estimation of the whole of the infected population. A dynamical model for t...
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| Language: | English |
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AIMS Press
2013-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.959 |
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| author | Miguel Atencia Esther García-Garaluz Gonzalo Joya |
| author_facet | Miguel Atencia Esther García-Garaluz Gonzalo Joya |
| author_sort | Miguel Atencia |
| collection | DOAJ |
| description | In this work we propose the definition of the ratio of hidden infection of HIV/AIDS epidemics, as the division of the unknown infected population by the known one. The merit of the definition lies in allowing for an indirect estimation of the whole of the infected population. A dynamical model for the ratio is derived from a previous HIV/AIDS model, which was proposed for the Cuban case, where active search for infected individuals is carried out through a contact tracing program. The stability analysis proves that the model for the ratio possesses a single positive equilibrium, which turns out to be globally asymptotically stable. The sensitivity analysis provides an insight into the relative performance of various methods for detection of infected individuals. An exponential regression has been performed to fit the known infected population, owing to actual epidemiological data of HIV/AIDS epidemics in Cuba. The goodness of the obtained fit provides additional support to the proposed model. |
| format | Article |
| id | doaj-art-e4f7273d674a4249a68e4eadf7a5498c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e4f7273d674a4249a68e4eadf7a5498c2025-01-24T02:26:20ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-05-0110495997710.3934/mbe.2013.10.959The ratio of hidden HIV infection in CubaMiguel Atencia0Esther García-Garaluz1Gonzalo Joya2Dept. of Applied Mathematics, University of Málaga, 29071 MálagaDept. of Applied Mathematics, University of Málaga, 29071 MálagaDept. of Applied Mathematics, University of Málaga, 29071 MálagaIn this work we propose the definition of the ratio of hidden infection of HIV/AIDS epidemics, as the division of the unknown infected population by the known one. The merit of the definition lies in allowing for an indirect estimation of the whole of the infected population. A dynamical model for the ratio is derived from a previous HIV/AIDS model, which was proposed for the Cuban case, where active search for infected individuals is carried out through a contact tracing program. The stability analysis proves that the model for the ratio possesses a single positive equilibrium, which turns out to be globally asymptotically stable. The sensitivity analysis provides an insight into the relative performance of various methods for detection of infected individuals. An exponential regression has been performed to fit the known infected population, owing to actual epidemiological data of HIV/AIDS epidemics in Cuba. The goodness of the obtained fit provides additional support to the proposed model.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.959dynamical systemssystem identification.hiv/aids epidemiologypopulation dynamicslyapunov stability |
| spellingShingle | Miguel Atencia Esther García-Garaluz Gonzalo Joya The ratio of hidden HIV infection in Cuba Mathematical Biosciences and Engineering dynamical systems system identification. hiv/aids epidemiology population dynamics lyapunov stability |
| title | The ratio of hidden HIV infection in Cuba |
| title_full | The ratio of hidden HIV infection in Cuba |
| title_fullStr | The ratio of hidden HIV infection in Cuba |
| title_full_unstemmed | The ratio of hidden HIV infection in Cuba |
| title_short | The ratio of hidden HIV infection in Cuba |
| title_sort | ratio of hidden hiv infection in cuba |
| topic | dynamical systems system identification. hiv/aids epidemiology population dynamics lyapunov stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.959 |
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