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 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.
Nonlinear System Group, INTEC-Facultad de Ingeniería Química (UNL-CONICET) , Santa Fe, Argentina . ; L'UNAM , IRCCyN, UMR-CNRS 6597, Nantes, France .
Pablo S
PS
Rivadeneira
L'UNAM , IRCCyN, UMR-CNRS 6597, Nantes, France .
Claude H
CH
Moog
Imperial College London, Department of Bioengineering , South Kensington Campus, United Kingdom .
Guy-Bart
GB
Stan
Infectious Diseases, University Hospital , Nantes, France . ; EA4271 Immunovirologie et polymorphisme génétique, Nantes University , Nantes, France .
Cecile
C
Brunet
Infectious Diseases, University Hospital , Nantes, France . ; EA4271 Immunovirologie et polymorphisme génétique, Nantes University , Nantes, France .
François
F
Raffi
Infectious Diseases, University Hospital , Nantes, France . ; EA4271 Immunovirologie et polymorphisme génétique, Nantes University , Nantes, France .
Virginie
V
Ferré
Nonlinear System Group, INTEC-Facultad de Ingeniería Química (UNL-CONICET) , Santa Fe, Argentina .
Vicente
V
Costanza
L'UNAM , IRCCyN, UMR-CNRS 6597, Nantes, France .
Marie J
MJ
Mhawej
Center of Applied Mathematics, School of Science and Technology, National University of San Martin , San Martín, Buenos Aires, Argentina .
Federico
F
Biafore
L'UNAM , IRCCyN, UMR-CNRS 6597, Nantes, France .
Djomangan A
DA
Ouattara
University of Liège , Department of Electrical Engineering and Computer Science, Montefiore Institute, Liège, Belgium .
Damien
D
Ernst
University of Liège , Department of Electrical Engineering and Computer Science, Montefiore Institute, Liège, Belgium .
Raphael
R
Fonteneau
Department of Electrical, Electronic and Computer Engineering, University of Pretoria , Pretoria, South Africa .
Xiaohua
X
Xia
AIDS; HIV; aid for diagnosis; apoptosis; dynamical systems; modeling; nonlinear control; pharmacodynamics; pharmacokinetics