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November  2006, 6(6): 1417-1430. doi: 10.3934/dcdsb.2006.6.1417

HIV infection and CD4+ T cell dynamics

Liancheng Wang 1, and  Sean Ellermeyer 2,

1. 

Department of Mathematics & Statistics, Kennesaw State University, Kennesaw, GA 30144, United States
2. 

Department of Mathematics and Statistics, Kennesaw State University, 1000 Chastain Road, Kennesaw, GA 30144, United States

Received  September 2004 Revised  February 2006 Published  August 2006

We study a mathematical model for the interaction of HIV infection and CD4$^+$ T cells. Local and global analysis is carried out. Let $N$ be the number of HIV virus produced per actively infected T cell. After identifying a critical number $N_{crit}$, we show that if $N\le N_{crit},$ then the uninfected steady state $P_{0}$ is the only equilibrium in the feasible region, and $P_{0}$ is globally asymptotically stable. Therefore, no HIV infection persists. If $N>N_{crit},$ then the infected steady state $P^$* emerges as the unique equilibrium in the interior of the feasible region, $P_{0}$ becomes unstable and the system is uniformly persistent. Therefore, HIV infection persists. In this case, $P^$* can be either stable or unstable. We show that $P^$* is stable only for $r$ (the proliferation rate of T cells) small or large and unstable for some intermediate values of $r.$ In the latter case, numerical simulations indicate a stable periodic solution exists.
Keywords: local and global stability, HIV infection, dynamics, Oscillations..
Mathematics Subject Classification: 34D23, 34A3.
Citation: Liancheng Wang, Sean Ellermeyer. HIV infection and CD4+ T cell dynamics. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1417-1430. doi: 10.3934/dcdsb.2006.6.1417
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