Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays

Hui Miao, Zhidong Teng, Chengjun Kang, Shigui Ruan

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

In this paper, the dynamical behaviors of a viral infection model with cytotoxic T-lymphocyte (CTL) immune response, immune response delay and production delay are investigated. The threshold values for virus infection and immune response are established. By means of Lyapunov functionals methods and LaSalle's invariance principle, sufficient conditions for the global stability of the infection-free and CTL-absent equilibria are established. Global stability of the CTL-present infection equilibrium is also studied when there is no immune delay in the model. Furthermore, to deal with the local stability of the CTL-present infection equilibrium in a general case with two delays being positive, we extend an existing geometric method to treat the associated characteristic equation. When the two delays are positive, we show some conditions for Hopf bifurcation at the CTL-present infection equilibrium by using the immune delay as a bifurcation parameter. Numerical simulations are performed in order to illustrate the dynamical behaviors of the model.

Original languageEnglish (US)
Pages (from-to)2365-2387
Number of pages23
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume22
Issue number6
DOIs
StatePublished - Aug 1 2017

Keywords

  • CTL immune response
  • Delay
  • Hopf bifurcation
  • Lyapunov functional
  • Stability
  • Viral infection model

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays'. Together they form a unique fingerprint.

  • Cite this