Modeling the Non-monotonic Homeostatic Proliferation of T Cells in HIV Infection

In this paper, we propose an HIV infection model to simulate the homeostatic proliferation of T cells in the presence of a large number of viruses. By using Sturm’s theorem, we find that the system has a unique uninfected equilibrium and at most two infected equilibria (smaller and larger ones). Then, we perform the stability and bifurcation analysis. The model shows rich dynamics such as forward and backward bifurcation, saddle-node bifurcation and Hopf bifurcation. And we find the bistability of uninfected equilibrium and larger infected equilibrium. Besides, our results show that Hopf bifurcation can occur near larger infected equilibrium and induce stable periodic orbits. This indicates that T cells and HIV can coexist in the form of periodic oscillation for a long time, and lead to an increase of the robustness of HIV persistence.