Dynamics of HIV infection of CD4+ T cells

Perelson, Alan S.; Kirschner, Denise E.; Boer, Rob J. de

doi:10.1016/0025-5564(93)90043-a

Cited by 835 publications

(580 citation statements)

References 49 publications

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“…This is, in part, because the definition of viral fitness we derive is independent of how T cells are regulated. Another plausible scenario is that l changes with V or T Ã as in models that account for thymic infection by reducing the source of new T cells (Perelson et al, 1993). We leave the formal exploration of this possibility for future studies.…”

Section: Discussionmentioning

confidence: 99%

Optimizing within-host viral fitness: infected cell lifespan and virion production rate

Gilchrist

Coombs

Perelson

2004

Journal of Theoretical Biology

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We explore how an infected cell's virion production rate can affect the relative fitness of a virus within a host. We perform an invasion analysis, based on an age-structured model of viral dynamics, to derive the within-host relative viral fitness. We find that for chronic infections, in the absence of trade-offs between viral life history stages, natural selection favors viral strains whose virion production rate maximizes viral burst size. We then show how various life history trade-offs such as that between virion production and immune system recognition and clearance of virally infected cells can lead to natural selection favoring production rates lower than the one that maximizes burst size. Our findings suggest that HIV replication rates should vary between cells with different life spans, as has been suggested by recent observation. Published by Elsevier Ltd.

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Section: Discussionmentioning

confidence: 99%

Optimizing within-host viral fitness: infected cell lifespan and virion production rate

Gilchrist

Coombs

Perelson

2004

Journal of Theoretical Biology

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“…In [29,30], a simple model is given which simulates the interaction of the immune system with HIV. We use this model and recommend that the reader see those papers for a more complete background and analysis of the model.…”

Section: Presentation Of a Working Modelmentioning

confidence: 99%

“…See [30] for the analysis leading to parameter restrictions and stability results. Even after the thymus involutes (a normal process is adulthood by where the thymus retrogresses), the thymus still remains functional.…”

Section: Presentation Of a Working Modelmentioning

confidence: 99%

“…The second, the endemically infected steady state, has each of the cell populations at positive values. Perelson et al [30] showed that if the parameter N was below a critical value, N , the uninfected steady state is stable and the infected steady state is unstable. At N"N , the stability is exchanged through a transcritical bifurcation and the infected steady state becomes locally stable.…”

Section: Presentation Of a Working Modelmentioning

confidence: 99%

“…For example, stability can be lost for the infected steady state, giving rise to stable limit cycles. Perelson et al [30] believe that this occurs for parameter values that lie outside of the biologically possible ranges.…”

Section: Presentation Of a Working Modelmentioning

confidence: 99%

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Optimal control of the chemotherapy of HIV

Kirschner¹,

Lenhart²,

Serbin³

1997

Journal of Mathematical Biology

427

324

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Abstract. Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system composed of four ordinary differential equations and four adjoint ordinary differential equations.

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A Bayesian approach for mixed effects state‐space models under skewness and heavy tails

Hernandez‐Velasco,

Abanto‐Valle,

Dey

et al. 2023

Biometrical J

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Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed‐effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed‐effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed‐effects state‐space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew‐t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG‐315) clinical trial data set.

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Dynamics of HIV infection of CD4+ T cells

Cited by 835 publications

References 49 publications

Optimizing within-host viral fitness: infected cell lifespan and virion production rate

Optimizing within-host viral fitness: infected cell lifespan and virion production rate

Optimal control of the chemotherapy of HIV

A Bayesian approach for mixed effects state‐space models under skewness and heavy tails

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