Mathematical analysis of an HIV infection model including quiescent cells and periodic antiviral therapy

作者：Kouche Mahieddine^*; Boulfoul Bilal; Ainseba Bedr'Eddine

来源：International Journal of Biomathematics, 2017, 10(5): 1750065.

DOI：10.1142/S1793524517500656

• HIV
• equilibria
• persistence
• stability
• semiflow

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 eta(-) of drug efficiency eta such that if eta>eta(-), the basic reproduction number R-0 < 1 and the infection is cleared and if eta<eta(-), the infectious equilibrium is globally asymptotically stable. When the drug efficiency function eta(t) 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.

• 出版日期2017-7