Infection of human immunodeficiency virus （HIV） is determined through the decay of healthy CD44- T-cells in a well-mixed compartment, such as a bloodstream. A mathe- matical model is considered to illustrate the eff...Infection of human immunodeficiency virus （HIV） is determined through the decay of healthy CD44- T-cells in a well-mixed compartment, such as a bloodstream. A mathe- matical model is considered to illustrate the effects of combined drug therapy, i.e. reverse transcription plus protease inhibitor, on viral growth and T-cell population dynamics. This model is used to explain the existence and stability of infected and uninfected steady states in HIV growth. An analytical technique, called variational iteration method （VIM）, is used to solve the mathematical model. This method is modified to obtain the rapidly convergent successive approximations of the exact solution. These approximations are obtained without any restrictions or the transformations that may change the physical behavior of the problem. Numerical simulations are computed and exhibited to illustrate the effects of proposed drug therapy on the growth or decay of infection.展开更多
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Infection of human immunodeficiency virus （HIV） is determined through the decay of healthy CD44- T-cells in a well-mixed compartment, such as a bloodstream. A mathe- matical model is considered to illustrate the effects of combined drug therapy, i.e. reverse transcription plus protease inhibitor, on viral growth and T-cell population dynamics. This model is used to explain the existence and stability of infected and uninfected steady states in HIV growth. An analytical technique, called variational iteration method （VIM）, is used to solve the mathematical model. This method is modified to obtain the rapidly convergent successive approximations of the exact solution. These approximations are obtained without any restrictions or the transformations that may change the physical behavior of the problem. Numerical simulations are computed and exhibited to illustrate the effects of proposed drug therapy on the growth or decay of infection.
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.
