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 be the number of HIV virus produced per actively infected T cell. After identifying a critical number , we show that if then the uninfected steady state is the only equilibrium in the feasible region, and is globally asymptotically stable. Therefore, no HIV infection persists. If then the infected steady state * emerges as the unique equilibrium in the interior of the feasible region, becomes unstable and the system is uniformly persistent. Therefore, HIV infection persists. In this case, * can be either stable or unstable. We show that * is stable only for (the proliferation rate of T cells) small or large and unstable for some intermediate values of In the latter case, numerical simulations indicate a stable periodic solution exists.
Wang, L., & Sellermeyer, S. (2006). HIV infection and CD4+ T cell dynamics. Discrete and Continuous Dynamical Systems - Series B, 6(6), 1417-1430.