Stability analysis for HIV infection delay model with protease inhibitor

In this article, we considered a model of HIV-1 infection with a protease inhibitor therapy and three delays. The frequency of the bifurcating periodic solution as well as the threshold value is approximated numerically using realistic parameter. The estimated threshold value is realistic and the frequency of the oscillations is consistent with that of the observed viral blips.     

The amplitudes of viral blips in HIV-1 infected patients treated with antiretroviral therapy are power-law distributed

We previously reported that in patients treated with highly active antiretroviral therapy (HAART) who achieve viral load (VL) suppression, low fluctuations of viral load over the threshold of detection (viral blips) more than 4 weeks apart occur at random, with a frequency that does not change with longer times of observation. The etiology of viral blips is currently unknown, but viral blip frequency inversely correlates with the decay of the latent reservoir, whose stability has been proposed as the major hurdle to HIV eradication. We show here that the distribution of viral blip amplitudes observed in a group of 272 patients successfully treated with highly active antiretroviral therapy appears to be power-law distributed. Such a distribution can be theoretically generated by randomly sampling the arrival of asynchronous and overlapping elementary pulses of viremia, with asymptotic exponential decay of kinetics, thus suggesting that the low fluctuations of viremia observed in patients during HAART treatment is, in part, a discrete phenomenon consistent with random activation of latently infected cells or release of virus and infected cells into the blood compartment from unknown sites of active viral replication.     

Viral blip dynamics during highly active antiretroviral therapy

Although intermittent episodes of low-level viremia are often observed in well-suppressed highly active antiretroviral therapy (HAART)-treated patients, the timing and amplitude of viral blips have never been examined in detail. We analyze here the dynamics of viral blips, i.e., plasma VL measurements of >50 copies/ml, in 123 HAART-treated patients monitored for a mean of 2.6 years (range, 5 months to 5.3 years). The mean (+/- the standard deviation) blip frequency was 0.09 +/- 0.11/sample, with about one-third of patients showing no viral blips. The mean viral blip amplitude was 158 +/- 132 human immunodeficiency virus type 1 (HIV-1) RNA copies/ml. Analysis of the blip frequency and amplitude distributions suggest that two blips less than 22 days apart have a significant chance of being part of the same episode of viremia. The data are consistent with a hypothetical model in which each episode of viremia consists of a phase of VL rise, followed by two-phase exponential decay. Thus, the term "viral blip" may be a misnomer, since viral replication appears to be occurring over an extended period. Neither the frequency nor the amplitude of viral blips increases with longer periods of observation, but the frequency is inversely correlated with the CD4(+)-T-cell count at the start of therapy, suggesting that host-specific factors but not treatment fatigue are determinants of blip frequency.     

Modeling HIV persistence, the latent reservoir, and viral blips

HIV-1 eradication from infected individuals has not been achieved with the prolonged use of highly active antiretroviral therapy (HAART). The cellular reservoir for HIV-1 in resting memory CD4⁺ T cells remains a major obstacle to viral elimination. The reservoir does not decay significantly over long periods of time but is able to release replication-competent HIV-1 upon cell activation. Residual ongoing viral replication may likely occur in many patients because low levels of virus can be detected in plasma by sensitive assays and transient episodes of viremia, or HIV-1 blips, are often observed in patients even with successful viral suppression for many years. Here we review our current knowledge of the factors contributing to viral persistence, the latent reservoir, and blips, and mathematical models developed to explore them and their relationships. We show how mathematical modeling has helped improve our understanding of HIV-1 dynamics in patients on HAART and of the quantitative events underlying HIV-1 latency, reservoir stability, low-level viremic persistence, and emergence of intermittent viral blips. We also discuss treatment implications related to these studies.     

Dynamics of intermittent viremia during highly active antiretroviral therapy in patients who initiate therapy during chronic versus acute and early human immunodeficiency virus type 1 infection

The meaning of viral blips in human immunodeficiency virus type 1 (HIV-1)-infected patients treated with seemingly effective highly active antiretroviral therapy (HAART) is still controversial and under investigation. Blips might represent low-level ongoing viral replication in the presence of drug or simply release of virions from the latent reservoir. Patients treated early during HIV-1 infection are more likely to have a lower total body viral burden, a homogenous viral population, and preserved HIV-1-specific immune responses. Consequently, viral blips may be less frequent in them than in patients treated during chronic infection. To test this hypothesis, we compared the occurrence of viral blips in 76 acutely infected patients (primary HIV infection [PHI] group) who started therapy within 6 months of the onset of symptoms with that in 47 patients who started HAART therapy during chronic infection (chronic HIV infection [CHI] group). Viral blip frequency was approximately twofold higher in CHI patients (0.122 +/- 0.12/viral load [VL] sample, mean +/- standard deviation) than in PHI patients (0.066 +/- 0.09/VL sample). However, in both groups, viral blip frequency did not increase with longer periods of observation. Also, no difference in viral blip frequency was observed between treatment subgroups, and the occurrence of a blip was not associated with a recent change in CD4(+) T-cell count. Finally, in PHI patients the VL set point was a significant predictor of blip frequency during treatment.     

Duration of an intermittent episode of viremia

HIV-1 infected patients after being treated with potent combinations of antiretroviral drugs for 2–6 months typically reach a state in which virus can no longer be detected within their blood. These patients with undetectable virus occasionally have viral load measurements that are above the limit of detection of current assays. Such measurements are called blips. Here we examine the possibility that such blips represent infrequent measurements taken during a period of time in which there is a transient elevation of virus in the patient’s blood, i.e., a so-called transient episode of viremia. By analyzing time series of blips from a large number of patients, we conclude that transient episodes of viremia exist and that on average they extend for a period of about 3 weeks.