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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.
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Unified model of short- and long-term HIV viral rebound for clinical trial planning
Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. Typically suspension of therapy is rapidly followed by rebound of viral loads to high, pre-therapy levels. Indeed, a recent study showed that approximately 90% of treatment interruption study participants show viral rebound within at most a few months of therapy suspension, but the remaining 10%, showed viral rebound some months, or years, after ART suspension. Some may even never rebound. We investigate and compare branching process models aimed at gaining insight into these viral dynamics. Specifically, we provide a theory that explains both short- and long-term viral rebounds, and post-treatment control, via a multitype branching process with time-inhomogeneous rates, validated with data from Li et al. (Li et al. 2016 AIDS 30 , 343–353. ( doi:10.1097/QAD.0000000000000953 )). We discuss the associated biological interpretation and implications of our best-fit model. To test the effectiveness of an experimental intervention in delaying or preventing rebound, the standard practice is to suspend therapy and monitor the study participants for rebound. We close with a discussion of an important application of our modelling in the design of such clinical trials.
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- Award ID(s):
- 1714654
- PAR ID:
- 10302317
- Date Published:
- Journal Name:
- Journal of The Royal Society Interface
- Volume:
- 18
- Issue:
- 177
- ISSN:
- 1742-5662
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rsif.2020.1015
