HIV infection and CD4+ T cell dynamics

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 <= 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.