Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays
We propose a class of virus dynamics models with multitarget cells and multiple intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations (DDEs) that describes the interaction of the virus with two classes of target ce...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/201274 |
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| author | A. M. Elaiw M. A. Alghamdi |
| author_facet | A. M. Elaiw M. A. Alghamdi |
| author_sort | A. M. Elaiw |
| collection | DOAJ |
| description | We propose a class of virus dynamics models with multitarget cells and multiple
intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations (DDEs) that describes the interaction of the virus with two classes of target cells.
The second model is a (2𝑛+1)-dimensional system of nonlinear DDEs that describes the dynamics of the virus, 𝑛 classes of uninfected target cells, and 𝑛 classes of infected target cells. The third model generalizes the
second one by assuming that the incidence rate of infection is given by saturation functional response.
Two types of discrete time delays are incorporated into these models to describe (i) the latent period
between the time the target cell is contacted by the virus particle and the time the virus enters the cell,
(ii) the latent period between the time the virus has penetrated into a cell and the time of the emission of
infectious (mature) virus particles. Lyapunov functionals are constructed to establish the global asymptotic stability of the
uninfected and infected steady states of these models. We have proven that if the basic reproduction
number 𝑅0 is less than unity, then the uninfected steady state is globally asymptotically stable, and if
𝑅0>1 (or if the infected steady state exists), then the infected steady state is globally asymptotically stable. |
| format | Article |
| id | doaj-art-4d7d135660bd44ba9c2048eababfe79d |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4d7d135660bd44ba9c2048eababfe79d2025-08-20T02:38:43ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/201274201274Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time DelaysA. M. Elaiw0M. A. Alghamdi1Department 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 ArabiaWe propose a class of virus dynamics models with multitarget cells and multiple intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations (DDEs) that describes the interaction of the virus with two classes of target cells. The second model is a (2𝑛+1)-dimensional system of nonlinear DDEs that describes the dynamics of the virus, 𝑛 classes of uninfected target cells, and 𝑛 classes of infected target cells. The third model generalizes the second one by assuming that the incidence rate of infection is given by saturation functional response. Two types of discrete time delays are incorporated into these models to describe (i) the latent period between the time the target cell is contacted by the virus particle and the time the virus enters the cell, (ii) the latent period between the time the virus has penetrated into a cell and the time of the emission of infectious (mature) virus particles. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of these models. We have proven that if the basic reproduction number 𝑅0 is less than unity, then the uninfected steady state is globally asymptotically stable, and if 𝑅0>1 (or if the infected steady state exists), then the infected steady state is globally asymptotically stable.http://dx.doi.org/10.1155/2011/201274 |
| spellingShingle | A. M. Elaiw M. A. Alghamdi Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays Discrete Dynamics in Nature and Society |
| title | Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays |
| title_full | Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays |
| title_fullStr | Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays |
| title_full_unstemmed | Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays |
| title_short | Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays |
| title_sort | global properties of virus dynamics models with multitarget cells and discrete time delays |
| url | http://dx.doi.org/10.1155/2011/201274 |
| work_keys_str_mv | AT amelaiw globalpropertiesofvirusdynamicsmodelswithmultitargetcellsanddiscretetimedelays AT maalghamdi globalpropertiesofvirusdynamicsmodelswithmultitargetcellsanddiscretetimedelays |