Immune impairment thresholds in HIV infection

Abstract

Longitudinal studies of patients infected with HIV-1 reveal a long and variable length of asymptomatic phase between infection and development of AIDS. Some HIV infected patients are still asymptomatic after 15 or more years of infection but some patients develop AIDS within 2 years. The mechanistic basis of the disease progression has remained obscure but many researchers have been trying to explain it. For example, the possible importance of viral diversity for the disease progression and the development of AIDS has been very well worked out in the early-1990s, especially by some important works of Martin A. Nowak. These studies can give an elegant explanation for a variability of asymptomatic phase. Here, a simple mathematical model was used to propose a new explanation for a variable length of asymptomatic phase. The main idea is that the immune impairment rate increases over the HIV infection. Our model suggested the existence of so-called "Risky threshold" and "Immunodeficiency threshold" on the impairment rate. The former implies that immune system may collapse when the impairment rate of HIV exceeds the threshold value. The latter implies that immune system always collapses when the impairment rate exceeds the value. We found that the length of asymptomatic phase is determined stochastically between these threshold values depending on the virological and immunological states. Furthermore, we investigated a distribution of the length of asymptomatic phase and a survival rate of the immune responses in one HIV patient.

Dynamics analysis of a delayed viral infection model with immune impairment

“…In order to check our results and find the effect of immune impairment on the stability of DDE system, we firstly choose a set of parameters as shown in Table 1 based on the data of [20,21,25,26].…”

“…It contributes to viral evasion from immunity because the dysfunction of dendritic cells engenders some impairment effects for CTL inducement [19], and Regoes et al provided some models with immune impairment. Iwasa et al [20,21] discovered the existence of so-called Risky threshold and Immunodeficiency threshold on the impairment rate. The former implies that immune system may collapse when the impairment rate of HIV exceeds the threshold value.…”

Apoptosis in virus infection dynamics models

“…Since the early 1990s numerous epidemic models have been used to describe the dynamics between viral infections and the immune response [6,8,25,26,36,39,44,46,51,53,55], particularly in the context of HIV infection [4,9,10,12,13,23,24,27,28,30,34,35,40–43,45,49,52,54,58]. The basic model for viral dynamics is given by the following simple three-dimensional system, Here x ( t ) represents the concentration of uninfected or healthy cells at time t, y ( t ) represents the concentration of infected cells that produce virion at time t and v ( t ) represents the concentration of viruses at time t .…”

“…The equality holds in the quasi-equilibrium state and hence . This assumption is referred to as ‘separation of time scales’ and is in common use in the virus dynamics [24,27,28,44]. We have to stress that this assumption does not imply that the virus concentration v ( t ) remains constant; on the contrary, it is assumed to be proportional to the varying concentration of infected cells y ( t ).…”

Analysis of a viral infection model with immune impairment and cure rate

“…It contributes to viral evasion from immunity because the dysfunction of dendritic cells engenders some impairment effects for CTL inducement [12], and Regoes et al provided some models with immune impairment. Iwasa et al [8] discovered the existence of so-called Risky threshold and Immunodeficiency threshold on the impairment rate. The former implies that immune system may collapse when the impairment rate of HIV exceeds the threshold value.…”