skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, June 13 until 2:00 AM ET on Friday, June 14 due to maintenance. We apologize for the inconvenience.


Title: Stochastic investigation of HIV infection and the emergence of drug resistance

Drug-resistant HIV-1 has caused a growing concern in clinic and public health. Although combination antiretroviral therapy can contribute massively to the suppression of viral loads in patients with HIV-1, it cannot lead to viral eradication. Continuing viral replication during sub-optimal therapy (due to poor adherence or other reasons) may lead to the accumulation of drug resistance mutations, resulting in an increased risk of disease progression. Many studies also suggest that events occurring during the early stage of HIV-1 infection (i.e., the first few hours to days following HIV exposure) may determine whether the infection can be successfully established. However, the numbers of infected cells and viruses during the early stage are extremely low and stochasticity may play a critical role in dictating the fate of infection. In this paper, we use stochastic models to investigate viral infection and the emergence of drug resistance of HIV-1. The stochastic model is formulated by a continuous-time Markov chain (CTMC), which is derived based on an ordinary differential equation model proposed by Kitayimbwa et al. that includes both forward and backward mutations. An analytic estimate of the probability of the clearance of HIV infection of the CTMC model near the infection-free equilibrium is obtained by a multitype branching process approximation. The analytical predictions are validated by numerical simulations. Unlike the deterministic dynamics where the basic reproduction number $ \mathcal{R}_0 $ serves as a sharp threshold parameter (i.e., the disease dies out if $ \mathcal{R}_0 < 1 $ and persists if $ \mathcal{R}_0 > 1 $), the stochastic models indicate that there is always a positive probability for HIV infection to be eradicated in patients. In the presence of antiretroviral therapy, our results show that the chance of clearance of the infection tends to increase although drug resistance is likely to emerge.

 
more » « less
Award ID(s):
1950254
NSF-PAR ID:
10350818
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Mathematical Biosciences and Engineering
Volume:
19
Issue:
2
ISSN:
1551-0018
Page Range / eLocation ID:
1174 to 1194
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Individuals infected by human immunodeficiency virus (HIV) are under oxidative stress due to the imbalance between reactive oxygen species (ROS) production and elimination. This paper presents a mathematical model with the cytotoxic T lymphocytes (CTL) immune response to examine the role of ROS in the dynamics of HIV infection. We classify the equilibria of the model and study the stability of these equilibria. Numerical simulations show that incorporating ROS and CTL immune response into the model leads to very rich dynamics, including bistable phenomena and periodic solutions. Although the current antiretroviral therapy can suppress viral load to the undetectable level, it cannot eradicate the virus. A high level of ROS may be a factor for HIV persistence in patients despite suppressive therapy. These results suggest that oxidative damage and anti-oxidant therapy should be considered in the study of HIV infection and treatment. 
    more » « less
  2. Regoes, Roland R. (Ed.)
    While highly active antiretroviral therapy (HAART) is successful in controlling the replication of Human Immunodeficiency Virus (HIV-1) in many patients, currently there is no cure for HIV-1, presumably due to the presence of reservoirs of the virus. One of the least studied viral reservoirs is the brain, which the virus enters by crossing the blood-brain barrier (BBB) via macrophages, which are considered as conduits between the blood and the brain. The presence of HIV-1 in the brain often leads to HIV associated neurocognitive disorders (HAND), such as encephalitis and early-onset dementia. In this study we develop a novel mathematical model that describes HIV-1 infection in the brain and in the plasma coupled via the BBB. The model predictions are consistent with data from macaques infected with a mixture of simian immunodeficiency virus (SIV) and simian-human immunodeficiency virus (SHIV). Using our model, we estimate the rate of virus transport across the BBB as well as viral replication inside the brain, and we compute the basic reproduction number. We also carry out thorough sensitivity analysis to define the robustness of the model predictions on virus dynamics inside the brain. Our model provides useful insight into virus replication within the brain and suggests that the brain can be an important reservoir causing long-term viral persistence. 
    more » « less
  3. null (Ed.)
    Multidrug resistance continues to be a barrier to the effectiveness of highly active antiretroviral therapy in the treatment of human immunodeficiency virus 1 (HIV-1) infection. Darunavir (DRV) is a highly potent protease inhibitor (PI) that is oftentimes effective when drug resistance has emerged against first-generation inhibitors. Resistance to darunavir does evolve and requires 10–20 amino acid substitutions. The conformational landscapes of six highly characterized HIV-1 protease (PR) constructs that harbor up to 19 DRV-associated mutations were characterized by distance measurements with pulsed electron double resonance (PELDOR) paramagnetic resonance spectroscopy, namely double electron–electron resonance (DEER). The results show that the accumulated substitutions alter the conformational landscape compared to PI-naïve protease where the semi-open conformation is destabilized as the dominant population with open-like states becoming prevalent in many cases. A linear correlation is found between values of the DRV inhibition parameter Ki and the open-like to closed-state population ratio determined from DEER. The nearly 50% decrease in occupancy of the semi-open conformation is associated with reduced enzymatic activity, characterized previously in the literature. 
    more » « less
  4. AIDS is a syndrome caused by the HIV. During the progression of AIDS, a patient's immune system is weakened, which increases the patient's susceptibility to infections and diseases. Although antiretroviral drugs can effectively suppress HIV, the virus mutates very quickly and can become resistant to treatment. In addition, the virus can also become resistant to other treatments not currently being used through mutations, which is known in the clinical research community as cross-resistance. Since a single HIV strain can be resistant to multiple drugs, this problem is naturally represented as a multilabel classification problem. Given this multilabel relationship, traditional single-label classification methods often fail to effectively identify the drug resistances that may develop after a particular virus mutation. In this work, we propose a novel multilabel Robust Sample Specific Distance (RSSD) method to identify multiclass HIV drug resistance. Our method is novel in that it can illustrate the relative strength of the drug resistance of a reverse transcriptase (RT) sequence against a given drug nucleoside analog and learn the distance metrics for all the drug resistances. To learn the proposed RSSDs, we formulate a learning objective that maximizes the ratio of the summations of a number of ℓ1-norm distances, which is difficult to solve in general. To solve this optimization problem, we derive an efficient, nongreedy iterative algorithm with rigorously proved convergence. Our new method has been verified on a public HIV type 1 drug resistance data set with over 600 RT sequences and five nucleoside analogs. We compared our method against several state-of-the-art multilabel classification methods, and the experimental results have demonstrated the effectiveness of our proposed method. 
    more » « less
  5. Acquired immunodeficiency syndrome (AIDS) is a syndrome caused by the human immunodeficiency virus (HIV). During the progression of AIDS, a patient’s the immune system is weakened, which increases the patient’s susceptibility to infections and diseases. Although antiretroviral drugs can effectively suppress HIV, the virus mutates very quickly and can become resistant to treatment. In addition, the virus can also become resistant to other treatments not currently being used through mutations, which is known in the clinical research community as cross-resistance. Since a single HIV strain can be resistant to multiple drugs, this problem is naturally represented as a multi-label classification problem. Given this multi-class relationship, traditional single-label classification methods usually fail to effectively identify the drug resistances that may develop after a particular virus mutation. In this paper, we propose a novel multi-label Robust Sample Specific Distance (RSSD) method to identify multi-class HIV drug resistance. Our method is novel in that it can illustrate the relative strength of the drug resistance of a reverse transcriptase sequence against a given drug nucleoside analogue and learn the distance metrics for all the drug resistances. To learn the proposed RSSDs, we formulate a learning objective that maximizes the ratio of the summations of a number of ℓ1-norm distances, which is difficult to solve in general. To solve this optimization problem, we derive an efficient, non-greedy, iterative algorithm with rigorously proved convergence. Our new method has been verified on a public HIV-1 drug resistance data set with over 600 RT sequences and five nucleoside analogues. We compared our method against other state-of-the-art multi-label classification methods and the experimental results have demonstrated the effectiveness of our proposed method. 
    more » « less