scholarly journals Mathematical analysis of an HIV model with latent reservoir, delayed CTL immune response and immune impairment

2021 ◽  
Vol 18 (2) ◽  
pp. 1689-1707
Author(s):  
Ning Bai ◽  
◽  
Rui Xu
Keyword(s):  
Immune Response ◽  
Mathematical Analysis ◽  
Latent Reservoir ◽  
Hiv Model ◽  
Immune Impairment ◽  
Ctl Immune Response

scholarly journals Analysis of an HIV model with post-treatment control

2018 ◽  
Author(s):  
Shaoli Wang ◽  
Fei Xu
Keyword(s):  
Hiv Infection ◽  
Mathematical Analysis ◽  
Post Treatment ◽  
Proliferation Rate ◽  
Latent Reservoir ◽  
Immune Control ◽  
Treatment Control ◽  
Hiv Model ◽  
Control Threshold ◽  
Immune Impairment

AbstractRecent 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 R0 to characterize the viral dynamics. We prove that when R0 < 1, the uninfected equilibrium of the proposed model is globally asymptotically stable. When R0 > 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 summaryIn 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 R0 > 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.

scholarly journals Analysis and Optimal Control of an Intracellular Delayed HIV Model with CTL Immune Response

2018 ◽  
Vol 12 (2) ◽  
pp. 111-127 ◽  
Author(s):  
Karam Allali ◽  
Sanaa Harroudi ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Immune Response ◽  
Hiv Model ◽  
Ctl Immune Response

scholarly journals Mathematical Analysis and Clinical Implications of an HIV Model with Adaptive Immunity

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Jaouad Danane ◽  
Karam Allali
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Steady State ◽  
Adaptive Immunity ◽  
Reproduction Number ◽  
Adaptive Immune Response ◽  
Hiv Model ◽  
Adaptive Immune ◽  
The Impact ◽  
Ctl Immune Response

In this paper, a mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with adaptive immune response is presented and studied. The mathematical model includes six nonlinear differential equations describing the interaction between the uninfected cells, the exposed cells, the actively infected cells, the free viruses, and the adaptive immune response. The considered adaptive immunity will be represented by cytotoxic T-lymphocytes cells (CTLs) and antibodies. First, the global stability of the disease-free steady state and the endemic steady states is established depending on the basic reproduction number R0, the CTL immune response reproduction number R1z, the antibody immune response reproduction number R1w, the antibody immune competition reproduction number R2w, and the CTL immune response competition reproduction number R3z. On the other hand, different numerical simulations are performed in order to confirm numerically the stability for each steady state. Moreover, a comparison with some clinical data is conducted and analyzed. Finally, a sensitivity analysis for R0 is performed in order to check the impact of different input parameters.

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