Stability of Virus Infection Models with Antibodies and Chronically Infected Cells
Two virus infection models with antibody immune response and chronically infected cells are proposed and analyzed. Bilinear incidence rate is considered in the first model, while the incidence rate is given by a saturated functional response in the second one. One main feature of these models is tha...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/650371 |
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| _version_ | 1832559132154003456 |
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| author | Mustafa A. Obaid A. M. Elaiw |
| author_facet | Mustafa A. Obaid A. M. Elaiw |
| author_sort | Mustafa A. Obaid |
| collection | DOAJ |
| description | Two virus infection models with antibody immune response and chronically infected cells are proposed and analyzed. Bilinear incidence rate is considered in the first model, while the incidence rate is given by a saturated functional response in the second one. One main feature of these models is that it includes both short-lived infected cells and chronically infected cells. The chronically infected cells produce much smaller amounts of virus than the short-lived infected cells and die at a much slower rate. Our mathematical analysis establishes that the global dynamics of the two models are determined by two threshold parameters R0 and R1. By constructing Lyapunov functions and using LaSalle's invariance principle, we have established the global asymptotic stability of all steady states of the models. We have proven that, the uninfected steady state is globally asymptotically
stable (GAS) if R0<1, the infected steady state without antibody immune response exists and it
is GAS if R1<1<R0, and the infected steady state with antibody immune response exists and it is GAS if R1>1. We check our theorems with numerical simulation in the end. |
| format | Article |
| id | doaj-art-3f932bfe0fcc4cb393ec54af261b660c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3f932bfe0fcc4cb393ec54af261b660c2025-02-03T01:30:40ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/650371650371Stability of Virus Infection Models with Antibodies and Chronically Infected CellsMustafa A. Obaid0A. M. Elaiw1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaTwo virus infection models with antibody immune response and chronically infected cells are proposed and analyzed. Bilinear incidence rate is considered in the first model, while the incidence rate is given by a saturated functional response in the second one. One main feature of these models is that it includes both short-lived infected cells and chronically infected cells. The chronically infected cells produce much smaller amounts of virus than the short-lived infected cells and die at a much slower rate. Our mathematical analysis establishes that the global dynamics of the two models are determined by two threshold parameters R0 and R1. By constructing Lyapunov functions and using LaSalle's invariance principle, we have established the global asymptotic stability of all steady states of the models. We have proven that, the uninfected steady state is globally asymptotically stable (GAS) if R0<1, the infected steady state without antibody immune response exists and it is GAS if R1<1<R0, and the infected steady state with antibody immune response exists and it is GAS if R1>1. We check our theorems with numerical simulation in the end.http://dx.doi.org/10.1155/2014/650371 |
| spellingShingle | Mustafa A. Obaid A. M. Elaiw Stability of Virus Infection Models with Antibodies and Chronically Infected Cells Abstract and Applied Analysis |
| title | Stability of Virus Infection Models with Antibodies and Chronically Infected Cells |
| title_full | Stability of Virus Infection Models with Antibodies and Chronically Infected Cells |
| title_fullStr | Stability of Virus Infection Models with Antibodies and Chronically Infected Cells |
| title_full_unstemmed | Stability of Virus Infection Models with Antibodies and Chronically Infected Cells |
| title_short | Stability of Virus Infection Models with Antibodies and Chronically Infected Cells |
| title_sort | stability of virus infection models with antibodies and chronically infected cells |
| url | http://dx.doi.org/10.1155/2014/650371 |
| work_keys_str_mv | AT mustafaaobaid stabilityofvirusinfectionmodelswithantibodiesandchronicallyinfectedcells AT amelaiw stabilityofvirusinfectionmodelswithantibodiesandchronicallyinfectedcells |