# American Institute of Mathematical Sciences

January  2012, 17(1): 297-302. doi: 10.3934/dcdsb.2012.17.297

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

 1 School of Mathematical Science, Heilongjiang University, Harbin, Heilongjiang 150080, China 2 Department of Mathematics, Arts and Science College, Harbin Normal University, Harbin, Heilongjiang 150025, China

Received  April 2011 Revised  August 2011 Published  October 2011

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.
Citation: Jinliang Wang, Lijuan Guan. Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 297-302. doi: 10.3934/dcdsb.2012.17.297
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##### References:
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