Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase
A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First,...
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| Format: | Article |
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MDPI AG
2017-08-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/7/8/861 |
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| author | Karam Allali Jaouad Danane Yang Kuang |
| author_facet | Karam Allali Jaouad Danane Yang Kuang |
| author_sort | Karam Allali |
| collection | DOAJ |
| description | A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R 0 and the CTL immune response reproduction number R C T L . Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection. |
| first_indexed | 2024-12-18T10:14:04Z |
| format | Article |
| id | doaj.art-6557617225044445bb748b6859e6522c |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-18T10:14:04Z |
| publishDate | 2017-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-6557617225044445bb748b6859e6522c2022-12-21T21:11:21ZengMDPI AGApplied Sciences2076-34172017-08-017886110.3390/app7080861app7080861Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse PhaseKaram Allali0Jaouad Danane1Yang Kuang2Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, Mohammedia 20650, MoroccoLaboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, Mohammedia 20650, MoroccoSchool of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USAA modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R 0 and the CTL immune response reproduction number R C T L . Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.https://www.mdpi.com/2076-3417/7/8/861CTL immune responseglobal stabilityHIV infection modelviral dynamics |
| spellingShingle | Karam Allali Jaouad Danane Yang Kuang Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase Applied Sciences CTL immune response global stability HIV infection model viral dynamics |
| title | Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase |
| title_full | Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase |
| title_fullStr | Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase |
| title_full_unstemmed | Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase |
| title_short | Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase |
| title_sort | global analysis for an hiv infection model with ctl immune response and infected cells in eclipse phase |
| topic | CTL immune response global stability HIV infection model viral dynamics |
| url | https://www.mdpi.com/2076-3417/7/8/861 |
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