Rich dynamics induced by homeostatic proliferation of both CD4+ T cells and macrophages in HIV infection and persistence

In this paper, we investigate an HIV infection model with the homeostatic proliferation of both CD4+ T cells and macrophages. The model exhibits at most five equilibria, including a unique infection-free equilibrium and up to four infected equilibria. The inclusion of homeostatic proliferation induces very rich dynamics, such as saddle-node bifurcations, supercritical and subcritical Hopf bifurcations, and Bogdanov–Takens (BT) bifurcations. Notably, our new findings identify several bistable and tristable phenomena, including bistability of an infection-free equilibrium and an infected equilibrium, bistability of two distinct infected equilibria, tristability of an infection-free equilibrium and two infected equilibria, and the coexistence of a stable infection-free equilibrium and a stable periodic solution. The newly discovered dynamics reveal the dual-edged effect of homeostatic proliferation in HIV infection and persistence, which highlights the challenges posed by immune system regulation. On the one hand, the homeostatic proliferation makes the model have more steady states, thus making HIV clearance highly sensitive to initial cell counts. On the other hand, an increase in the maximum homeostatic proliferation rate of macrophages shrinks the region where the infection-free equilibrium remains globally asymptotically stable, eventually eliminating this region entirely. This requires a more integrated collaborative control strategy for HIV eradication.