# American Institute of Mathematical Sciences

September  2009, 12(2): 511-524. doi: 10.3934/dcdsb.2009.12.511

## Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay

 1 School of Mathematics and Physics, Nanhua University, Hengyang, Hunan 421001, China 2 Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7

Received  October 2008 Revised  January 2009 Published  July 2009

In this paper, we consider a mathematical model for HIV-1 infection with intracellular delay and cell-mediated immune response. A novel feature is that both cytotoxic T lymphocytes (CTLs) and the intracellular delay are incorporated into the model. We 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. We also perform some numerical simulations which support the obtained theoretical results. These results show that larger intracellular delay may help eradicate the virus, while the activation of CTLs can only help reduce the virus load and increase the healthy CD$_4^+$ cells population in the long term sense.
Citation: Huiyan Zhu, Xingfu Zou. Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 511-524. doi: 10.3934/dcdsb.2009.12.511
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