Abstract
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 $, the uninfected equilibrium of the proposed model is globally asymptotically stable. 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.
Highlights
Author summaryWe use mathematical model to investigate the combined effect of latent 1 reservoir and immune impairment on the post-treatment control of HIV infection
In 2010, an HIV-infected mother gave birth to a baby prematurely in a Mississippi clinic
We perform bifurcation analysis to illustrate the 10 infection status of patient with the variation of proliferation rate of CTLs, which potentially explain the reason behind different outcomes among HIV patients
Summary
We use mathematical model to investigate the combined effect of latent 1 reservoir and immune impairment on the post-treatment control of HIV infection. By 2 simplifying an HIV model with latent reservoir and immune impairment, and performing 3 mathematical analysis, we obtain the post-treatment immune control threshold and the 4 elite control threshold for the HIV dynamics when R0 > 1. We illustrate our results 6 using both mathematical analysis and numerical simulation. We show that patient with low proliferation rate of CTLs may undergo virus rebound, and patient with high proliferation rate of CTLs may 9 obtain elite control of HIV infection. We perform bifurcation analysis to illustrate the 10 infection status of patient with the variation of proliferation rate of CTLs, which potentially explain the reason behind different outcomes among HIV patients. The copyright holder for this preprint It is made available under
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