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- Title
Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response.
- Authors
Haibin Wang; Rui Xu
- Abstract
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 equilibriumis globally asymptotically stable. If the basic reproduction ratio for CTL immune response R1 > 1, the global stability of the CTL-activated infection equilibriumis also derived when the time delay τ= 0. Numerical simulations are carried out to illustrate the main results.
- Subjects
HOPF bifurcations; STABILITY theory; HIV infections; MATHEMATICAL models; EXISTENCE theorems; IMMUNE response; COMPUTER simulation
- Publication
Discrete Dynamics in Nature & Society, 2013, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2013/169427