Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay

Pages: 297 - 302, Volume 17, Issue 1, January 2012

doi:10.3934/dcdsb.2012.17.297       Abstract        References        Full Text (281.0K)       Related Articles

Jinliang Wang - School of Mathematical Science, Heilongjiang University, Harbin, Heilongjiang 150080, China (email)
Lijuan Guan - Department of Mathematics, Arts and Science College, Harbin Normal University, Harbin, Heilongjiang 150025, China (email)

Abstract: A recent paper [H. Zhu and X. Zou, Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay, Discrete and Continuous Dynamical Systems - Series B, 12(2009), 511--524] presented a mathematical model for HIV-1 infection with intracellular delay and cell-mediated immune response. By combining the analysis of the characteristic equation and the Lyapunov-LaSalle method, they obtain a necessary and sufficient condition for the global stability of the infection-free equilibrium and give sufficient conditions for the local stability of the two infection equilibria: one without CTLs being activated and the other with. In the present paper, we show that the global dynamics are fully determined for $\Re_1<1<\Re_0$ and $\Re_1>1$ (Theorem 4.2 and Theorem 4.3) without other additional conditions. The approach used here, is to use a direct Lyapunov functional and Lyapunov-LaSalle invariance principle.

Keywords:  Intracellular delay, Immune response, Global stability, Lyapunov functional.
Mathematics Subject Classification:  Primary: 92B05, 92C50; Secondary: 92D25.

Received: April 2011;      Revised: August 2011;      Published: October 2011.

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