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

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.

In-host Mathematical Modelling of COVID-19 in Humans

“…Ultimately, previous modelling efforts here and from others ( Gonçalves, Bertrand, Ke, Comets, de Lamballerie, Malvy, Pizzorno, Terrier, Calatrava, Mentré, Smith, Perelson, Guedj, 2020 , Goyal, Cardozo-Ojeda, Schiffer, 2020 , Pinky, Dobrovolny, 2020 ) to represent SARS-CoV-2 could be further extended with control theoretical approaches such as optimal control and model predictive control to schedule drug candidate as well as immune modulators. Control theory in cooperation with Pharmacokinetic (PK)/Pharmacodynamic (PD) modelling have served for optimizing therapies in HIV and influenza infection ( Chang, Astolfi, 2008 , Hernandez-Mejia, Alanis, Hernandez-Gonzalez, Findeisen, Hernandez-vargas, 2019 , Rivadeneira, Caicedo, Ferramosca, Gonzalez, 2017 , Rivadeneira, Moog, Stan, Brunet, Raffi, Ferré, Costanza, Mhawej, Biafore, Ouattara, Ernst, Fonteneau, Xia, 2014 ).…”

Oncolytic virus therapy benefits from control theory

“…In addition, the sliding mode reachability condition has been used to formulate dynamical conditions for the containment of HIV infection by the CD8+ T cell response and antiretroviral drugs [ 21 – 23 ]. Furthermore, antiretroviral treatments have been analysed as impulsive control strategies in which drug uptakes are impulses to force HIV loads to reach and remain at undetectable levels [ 18 , 24 , 25 ]. An impulsive control approach has also been used in the context of type-1 diabetes to regulate the injection of insulin [ 26 , 27 ].…”

Modeling CD4+ T cells and CTL response in HIV-1 infection with antiretroviral therapy

“…We simulate the evolution of CD4 + T cells, CTL cells, and virus populations to investigate numerically the effect of RTIs and PIs treatments. The initial conditions are taken T (0) = 850 cells mm 3 , T 1 (0) = 40 cells mm 3 ,T i (0) = 41 cells mm 3 , and V (0) = 3.76 virions mm 3 [26]. Next, we shall investigate the clearance effect of the virus to the dynamic of CD4 + T cells and free virus population.…”