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

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 infe...

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Vydané v:	BioResearch Open Access Ročník 3; číslo 5; s. 233 - 241
Hlavní autori:	Rivadeneira, PS, Moog, CH, Stan, GB, Brunet, C, Raffi, F, Ferré, V, Costanza, V, Mhawej, MJ, Biafore, F, Ouattara, DA, Ernst, D, Fonteneau, R, Xia, X
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Mary Ann Liebert Inc 01.10.2014 Mary Ann Liebert, Inc Mary Ann Liebert
Predmet:	[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering [SDV]Life Sciences [q-bio] aid for diagnosis AIDS apoptosis Automatic Control Engineering Computer Science dynamical systems Engineering, computing & technology HIV https://purl.org/becyt/ford/2 https://purl.org/becyt/ford/2.2 Human health sciences Human immunodeficiency virus Immunologie & maladie infectieuse Immunology & infectious disease Ingénierie, informatique & technologie Life Sciences Mini-Review modeling non linear control nonlinear control optimal control pharmacodynamics pharmacokinetics Sciences de la santé humaine Sciences informatiques side-effects dynamical systems modeling nonlinear control HIV pharmacodynamics pharmacokinetics AIDS apoptosis aid for diagnosis
ISSN:	2164-7860, 2164-7844, 2164-7860
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Abstract	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.
AbstractList	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. 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 pro-duced 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. 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.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.
Author	Stan, GB Raffi, F Ouattara, DA Fonteneau, R Brunet, C Xia, X Moog, CH Costanza, V Rivadeneira, PS Biafore, F Mhawej, MJ Ernst, D Ferré, V
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Copyright	(©) Copyright 2014, Mary Ann Liebert, Inc. Distributed under a Creative Commons Attribution 4.0 International License Copyright 2014, Mary Ann Liebert, Inc. 2014
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Snippet	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...
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SubjectTerms	[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering [SDV]Life Sciences [q-bio] aid for diagnosis AIDS apoptosis Automatic Control Engineering Computer Science dynamical systems Engineering, computing & technology HIV https://purl.org/becyt/ford/2 https://purl.org/becyt/ford/2.2 Human health sciences Human immunodeficiency virus Immunologie & maladie infectieuse Immunology & infectious disease Ingénierie, informatique & technologie Life Sciences Mini-Review modeling non linear control nonlinear control optimal control pharmacodynamics pharmacokinetics Sciences de la santé humaine Sciences informatiques side-effects
Title	Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review
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