Analysis of an HIV model with post-treatment control

Recent investigation indicated that latent reservoir and immune impairment are responsible for the post-treatment control of HIV infection. In this paper, we simplify the disease model with latent reservoir and immune impairment and perform a series of mathematical analysis. We obtain the basic infection reproductive number R 0 to characterize the viral dynamics. We prove that when R 0 1, we obtain two thresholds, the post-treatment immune control threshold and the elite control threshold. The model has bistable behaviors in the interval between the two thresholds. If the proliferation rate of CTLs is less than the post-treatment immune control threshold, the model does not have positive equilibria. In this case, the immune free equilibrium is stable and the system will have virus rebound. On the other hand, when the proliferation rate of CTLs is greater than the elite control threshold, the system has stable positive immune equilibrium and unstable immune free equilibrium. Thus, the system is under elite control. Author summary In this article, we use mathematical model to investigate the combined effect of latent reservoir and immune impairment on the post-treatment control of HIV infection. By simplifying an HIV model with latent reservoir and immune impairment, and performing mathematical analysis, we obtain the post-treatment immune control threshold and the elite control threshold for the HIV dynamics when R 0 > 1. The HIV model displays bistable behaviors in the interval between the two thresholds. We illustrate our results using both mathematical analysis and numerical simulation. Our result is consistent with recent medical experiment. We show that patient with low proliferation rate of CTLs may undergo virus rebound, and patient with high proliferation rate of CTLs may obtain elite control of HIV infection. We perform bifurcation analysis to illustrate the infection status of patient with the variation of proliferation rate of CTLs, which potentially explain the reason behind different outcomes among HIV patients.