Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response
An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibr...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/169427 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849691220580761600 |
|---|---|
| author | Haibin Wang Rui Xu |
| author_facet | Haibin Wang Rui Xu |
| author_sort | Haibin Wang |
| collection | DOAJ |
| description | An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection R0≤1; if the basic reproduction ratio for viral infection R0>1 and the basic reproduction ratio for CTL immune response R1≤1, the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune response R1>1, the global stability of the CTL-activated infection equilibrium is also derived when the time delay τ=0. Numerical simulations are carried out to illustrate the main results. |
| format | Article |
| id | doaj-art-e2d2d303b9b44b1fb188ee7c39e841d7 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e2d2d303b9b44b1fb188ee7c39e841d72025-08-20T03:21:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/169427169427Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune ResponseHaibin Wang0Rui Xu1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang, Hebei 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang, Hebei 050003, ChinaAn HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection R0≤1; if the basic reproduction ratio for viral infection R0>1 and the basic reproduction ratio for CTL immune response R1≤1, the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune response R1>1, the global stability of the CTL-activated infection equilibrium is also derived when the time delay τ=0. Numerical simulations are carried out to illustrate the main results.http://dx.doi.org/10.1155/2013/169427 |
| spellingShingle | Haibin Wang Rui Xu Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response Discrete Dynamics in Nature and Society |
| title | Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response |
| title_full | Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response |
| title_fullStr | Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response |
| title_full_unstemmed | Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response |
| title_short | Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response |
| title_sort | stability and hopf bifurcation in an hiv 1 infection model with latently infected cells and delayed immune response |
| url | http://dx.doi.org/10.1155/2013/169427 |
| work_keys_str_mv | AT haibinwang stabilityandhopfbifurcationinanhiv1infectionmodelwithlatentlyinfectedcellsanddelayedimmuneresponse AT ruixu stabilityandhopfbifurcationinanhiv1infectionmodelwithlatentlyinfectedcellsanddelayedimmuneresponse |