Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity
We formulate a (2n+2)-dimensional viral infection model with humoral immunity, n classes of uninfected target cells and n classes of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/654507 |
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| author | Xinxin Tian Jinliang Wang |
| author_facet | Xinxin Tian Jinliang Wang |
| author_sort | Xinxin Tian |
| collection | DOAJ |
| description | We formulate a (2n+2)-dimensional viral infection model with humoral immunity, n classes of uninfected target cells and n classes of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters: R0 and R1. Namely, a typical two-threshold scenario is shown. If R0≤1, the infection-free equilibrium P0 is globally asymptotically stable, and the viruses are cleared. If R1≤1<R0, the immune-free equilibrium P1 is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. If R1>1, the endemic equilibrium P2 is globally asymptotically stable, and the infection is chronic with persistent antibody immune response. |
| format | Article |
| id | doaj-art-55be297f037c477a9c9572f91bd9c585 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-55be297f037c477a9c9572f91bd9c5852025-02-03T05:50:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/654507654507Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral ImmunityXinxin Tian0Jinliang Wang1School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaWe formulate a (2n+2)-dimensional viral infection model with humoral immunity, n classes of uninfected target cells and n classes of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters: R0 and R1. Namely, a typical two-threshold scenario is shown. If R0≤1, the infection-free equilibrium P0 is globally asymptotically stable, and the viruses are cleared. If R1≤1<R0, the immune-free equilibrium P1 is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. If R1>1, the endemic equilibrium P2 is globally asymptotically stable, and the infection is chronic with persistent antibody immune response.http://dx.doi.org/10.1155/2015/654507 |
| spellingShingle | Xinxin Tian Jinliang Wang Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity Discrete Dynamics in Nature and Society |
| title | Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity |
| title_full | Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity |
| title_fullStr | Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity |
| title_full_unstemmed | Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity |
| title_short | Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity |
| title_sort | stability analysis for viral infection model with multitarget cells beddington deangelis functional response and humoral immunity |
| url | http://dx.doi.org/10.1155/2015/654507 |
| work_keys_str_mv | AT xinxintian stabilityanalysisforviralinfectionmodelwithmultitargetcellsbeddingtondeangelisfunctionalresponseandhumoralimmunity AT jinliangwang stabilityanalysisforviralinfectionmodelwithmultitargetcellsbeddingtondeangelisfunctionalresponseandhumoralimmunity |