Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Clinical Research Study

Rivadeneira, Pablo S.; Moog, Claude H.; Stan, Guy‐Bart; Costanza, Vicente; Brunet, C.; Raffi, François; Ferré, Virginie; Mhawej, Marie-José; Biafore, Federico L.; Ouattara, Djomangan Adama; Ernst, Damien; Fonteneau, Raphaël; Xia, Xiaohua

doi:10.1089/aid.2013.0286

Cited by 7 publications

(31 citation statements)

References 3 publications

(4 reference statements)

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“…This patient was very young and his immunological system proved after 6 months its ability to recover from its critical status. 8,29 t 200 lay within the range 3 months< t 200 <6 months (predicted from Equation 4 and can be found in table 1 in reference 29). …”

Section: Discussionmentioning

confidence: 78%

“…The numerical results of the identification of the parameters s | A =0 and A | s =6 for each patient in the EDV05 trial and the analysis of the remaining parameters of the dynamical model can be found in previous articles. 4,8,29 …”

Section: Resultsmentioning

confidence: 99%

“…In Rivadeneira et al, 29 the last column of table 1 displays the theoretical time t 200 necessary to recover a CD4 level above 200 CD4/mm 3 . This theoretical time t 200 was computed from Equation 4 using the parameter identification method based only on the samples from the first 3 weeks after initiation of the therapy.…”

Section: Discussionmentioning

confidence: 99%

“…1). The measurements were done at the same time using the Roche Taqman 48 ™ test, with a detectable threshold of 50 copies/mL (CD4 T cells and virus load values for the 16 patients are given in table 2 of Prud'homme et al 29 ).…”

Section: Methodsmentioning

confidence: 99%

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Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

Rivadeneira

Moog

Stan

et al. 2014

BioResearch Open Access

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This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.

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Section: Discussionmentioning

confidence: 78%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

Rivadeneira

Moog

Stan

et al. 2014

BioResearch Open Access

Self Cite

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“…The earliest mathematical models were based on the interaction between the CD4 + T-cells and the HIV virions. These basic non-linear models were developed and used in the analysis of HIV dynamics and consequently, in estimating fundamental parameters that brought in new concepts of the disease processes and its progression [11]. With the aim of providing the most fundamental information on controlling the viral progression, most of these basic models include atleast three state variables, which include: the susceptible CD4 + T-cells, free HIV virions and the already infected CD4 + T-cells.…”

Section: Virus (Hiv) That Leads To Acquired Immunodeficiency Syndromementioning

confidence: 99%

Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells

Ngina¹,

Mbogo²,

Luboobi³

2017

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There have been many mathematical models aimed at analysing the in-vivo dynamics of HIV. However, in most cases the attention has been on the interaction between the HIV virions and the CD4 + T-cells. This paper brings in the intervention of the CD8 + T-cells in seeking, destroying, and killing the in- In addition, we show that the solutions are biologically meaningful. Both the endemic and virions-free equilibria are determined and their stability investigated. In addition, the basic reproductive number is derived by the next generation matrix method. We prove that the virions-free equilibrium state is locally asymptotically stable if and only if 0 1 R < and unstable otherwise. The results show that at acute infection the CD8 + T-cells play a paramount role in reducing HIV viral replication. We also observe that the model exhibits backward and trans-critical bifurcation for some set of parameters for 0 1 R < . This is a clear indication that having 0 1 R < is not sufficient condition for virions depletion.

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HIV Vertical Transmission DTSM Simulation Models: Global and National Perspective

Basavarajaiah

Murthy

2019

HIV Transmission

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Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Clinical Research Study

Cited by 7 publications

References 3 publications

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells

HIV Vertical Transmission DTSM Simulation Models: Global and National Perspective

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