Mathematical analysis of an HIV infection model including quiescent cells and periodic antiviral therapy
Mahiéddine Kouche, Bilal Boulfoul, Bedr’Eddine Ainseba
Source record
Source: Crossref
Published: May 9, 2017
DOI: 10.1142/s1793524517500656
Open original source ↗Source abstract
In this paper, we revisit the model by Guedj et al. [J. Guedj, R. Thibaut and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics 63 (2007) 198–206; J. Guedj, R. Thibaut and D. Commenges, Practical identifiability of HIV dynamics models, Bull. Math. Biol. 69 (2007) 2493–2513] which describes the effect of treatment with reverse transcriptase (RT) inhibitors and incorporates the class of quiescent cells. We prove that there is a threshold value [Formula: see text] of drug efficiency [Formula: see text] such that if [Formula: see text], the basic reproduction number [Formula: see text] and the infection is cleared and if [Formula: see text], the infectious equilibrium is globally asymptotically stable. When the drug efficiency function [Formula: see text] is periodic and of the bang–bang type we establish a threshold, in terms of spectral radius of some matrix, between the clearance and the persistence of the disease. As stated in related works [L. Rong, Z. Feng and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol. 69 (2007) 2027–2060; P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bull. Math. Biol. 71 (2009) 189–210.], we prove that the increase of the drug efficiency or the active duration of drug must clear the infection more quickly. We illustrate our results by some numerical simulations.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.