Thresholds and bistability in virus-immune dynamics

In this paper, we investigate an impaired or immunosuppressive HIV infection model. By analyzing the model, we obtain two thresholds R0 and Rc. It is shown that R0 determines whether the virus dies out. We also obtain the post-treatment control threshold and the elite control threshold. There exists a bistable interval between these two thresholds. When R0>Rc, immune intensity is in the bistable interval, which implies that the system has bistable behavior and as such the virus is under post-treatment control. On the other hand, when the immune intensity is greater than the elite immune control threshold, virus will be under elite control. Our investigation shows that when antiviral therapy cannot completely clear the virus, introducing immunotherapy is an optimal choice.