An official website of the United States government
This study examines the interactions between healthy target cells, infected target cells, virus particles, and immune cells within an HIV model. The model exhibits two equilibrium points: an infection-free equilibrium and an infection equilibrium. Stability analysis shows that the infection-free equilibrium is locally asymptotically stable when R0<1. Further, it is unstable when R0>1. The infection equilibrium is locally asymptotically stable when R0>1. The structural and practical identifiabilities of the within-host model for HIV infection dynamics were investigated using differential algebra techniques and Monte Carlo simulations. The HIV model was structurally identifiable by observing the total uninfected and infected target cells, immune cells, and viral load. Monte Carlo simulations assessed the practical identifiability of parameters. The production rate of target cells (λ), the death rate of healthy target cells (d), the death rate of infected target cells (δ), and the viral production rate by infected cells (π) were practically identifiable. The rate of infection of target cells by the virus (β), the death rate of infected cells by immune cells (Ψ), and antigen-driven proliferation rate of immune cells (b) were not practically identifiable. Practical identifiability was constrained by the noise and sparsity of the data. Analysis shows that increasing the frequency of data collection can significantly improve the identifiability of all parameters. This highlights the importance of optimal data sampling in HIV clinical studies, as it determines the best time points, frequency, and the number of sample points required to accurately capture the dynamics of the HIV infection within a host.
more »
« less
Dynamic analysis of a latent HIV infection model with CTL immune and antibody responses
This paper develops a mathematical model to investigate the Human Immunodeficiency Virus (HIV) infection dynamics. The model includes two transmission modes (cell-to-cell and cell-free), two adaptive immune responses (cytotoxic T-lymphocyte (CTL) and antibody), a saturated CTL immune response, and latent HIV infection. The existence and local stability of equilibria are fully characterized by four reproduction numbers. Through sensitivity analyses, we assess the partial rank correlation coefficients of these reproduction numbers and identify that the infection rate via cell-to-cell transmission, the number of new viruses produced by each infected cell during its life cycle, the clearance rate of free virions, and immune parameters have the greatest impact on the reproduction numbers. Additionally, we compare the effects of immune stimulation and cell-to-cell spread on the model’s dynamics. The findings highlight the significance of adaptive immune responses in increasing the population of uninfected cells and reducing the numbers of latent cells, infected cells, and viruses. Furthermore, cell-to-cell transmission is identified as a facilitator of HIV transmission. The analytical and numerical results presented in this study contribute to a better understanding of HIV dynamics and can potentially aid in improving HIV management strategies.
more »
« less
- PAR ID:
- 10533158
- Publisher / Repository:
- World Scientific
- Date Published:
- Journal Name:
- International Journal of Biomathematics
- Volume:
- 17
- Issue:
- 03
- ISSN:
- 1793-5245
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Abstract Recombination has been shown to contribute to human immunodeficiency virus-1 (HIV-1) evolution in vivo, but the underlying dynamics are extremely complex, depending on the nature of the fitness landscapes and of epistatic interactions. A less well-studied determinant of recombinant evolution is the mode of virus transmission in the cell population. HIV-1 can spread by free virus transmission, resulting largely in singly infected cells, and also by direct cell-to-cell transmission, resulting in the simultaneous infection of cells with multiple viruses. We investigate the contribution of these two transmission pathways to recombinant evolution, by applying mathematical models to in vitro experimental data on the growth of fluorescent reporter viruses under static conditions (where both transmission pathways operate), and under gentle shaking conditions, where cell-to-cell transmission is largely inhibited. The parameterized mathematical models are then used to extrapolate the viral evolutionary dynamics beyond the experimental settings. Assuming a fixed basic reproductive ratio of the virus (independent of transmission pathway), we find that recombinant evolution is fastest if virus spread is driven only by cell-to-cell transmission and slows down if both transmission pathways operate. Recombinant evolution is slowest if all virus spread occurs through free virus transmission. This is due to cell-to-cell transmission 1, increasing infection multiplicity; 2, promoting the co-transmission of different virus strains from cell to cell; and 3, increasing the rate at which point mutations are generated as a result of more reverse transcription events. This study further resulted in the estimation of various parameters that characterize these evolutionary processes. For example, we estimate that during cell-to-cell transmission, an average of three viruses successfully integrated into the target cell, which can significantly raise the infection multiplicity compared to free virus transmission. In general, our study points towards the importance of infection multiplicity and cell-to-cell transmission for HIV evolution.more » « less
-
Recent studies have demonstrated the superiority of cell-to-cell transmission over cell-free virus infection, and highlighted the role of inflammatory cytokines in enhancing viral infection. To investigate their impacts on viral infection dynamics, we have proposed an HIV infection model incorporating general incidence rates, these infection modes, and two time delays. We derived the basic reproduction number and showed that it governs the existence and local stability of steady states. Through the construction of appropriate Lyapunov functionals and application of the LaSalle invariance principle, we established the global asymptotic stability of both the infection-free and infected steady states.more » « less
-
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
-
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
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S1793524523500791
