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 (...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022054?viewType=HTML |
| _version_ | 1819284410699087872 |
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| author | Damilola Olabode Libin Rong Xueying Wang |
| author_facet | Damilola Olabode Libin Rong Xueying Wang |
| author_sort | Damilola Olabode |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-24T01:46:56Z |
| format | Article |
| id | doaj.art-c6d7e81b5f3645dfb502ab5b7c4112ee |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-24T01:46:56Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-c6d7e81b5f3645dfb502ab5b7c4112ee2022-12-21T17:21:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-01-011921174119410.3934/mbe.2022054Stochastic investigation of HIV infection and the emergence of drug resistanceDamilola Olabode0Libin Rong 1Xueying Wang 21. Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA2. Department of Mathematics, University of Florida, Gainesville, FL 32611, USA1. Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USADrug-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.https://www.aimspress.com/article/doi/10.3934/mbe.2022054?viewType=HTMLhiv-1stochastic modelsbranching processescontinuous-time markov chainsbasic reproduction number |
| spellingShingle | Damilola Olabode Libin Rong Xueying Wang Stochastic investigation of HIV infection and the emergence of drug resistance Mathematical Biosciences and Engineering hiv-1 stochastic models branching processes continuous-time markov chains basic reproduction number |
| title | Stochastic investigation of HIV infection and the emergence of drug resistance |
| title_full | Stochastic investigation of HIV infection and the emergence of drug resistance |
| title_fullStr | Stochastic investigation of HIV infection and the emergence of drug resistance |
| title_full_unstemmed | Stochastic investigation of HIV infection and the emergence of drug resistance |
| title_short | Stochastic investigation of HIV infection and the emergence of drug resistance |
| title_sort | stochastic investigation of hiv infection and the emergence of drug resistance |
| topic | hiv-1 stochastic models branching processes continuous-time markov chains basic reproduction number |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022054?viewType=HTML |
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