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. Commeng...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 7 of drug efficiency η such that if η 〉 7, the basic reproduction number R0 〈 1 and the infection is cleared and if η〈 η^-, the infectious equilibrium is globally asymptotically stable. When the drug efficiency function η（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.展开更多
文摘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 7 of drug efficiency η such that if η 〉 7, the basic reproduction number R0 〈 1 and the infection is cleared and if η〈 η^-, the infectious equilibrium is globally asymptotically stable. When the drug efficiency function η（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.
