On the basic of a type of practical examples we set up a new queueing model with negative customers. By the use of “Supplemental Variables method” and “State transfer analysis”, we get the generating function wit...On the basic of a type of practical examples we set up a new queueing model with negative customers. By the use of “Supplemental Variables method” and “State transfer analysis”, we get the generating function with negative powers of queue length and the waiting time expressions.展开更多
In this paper, we have studied about the sensitivity analysis of the human immunodeficiency virus （HIV） protease inhibitor （PI） model and estimated the length of the delay. We have fabricated an HIV PI model accom...In this paper, we have studied about the sensitivity analysis of the human immunodeficiency virus （HIV） protease inhibitor （PI） model and estimated the length of the delay. We have fabricated an HIV PI model accompanied with humoral immunity. Stability analysis of the constructed model about its steady states has been deliberated. We have evaluated some numerical simulations for PI model with humoral immunity by using the existing patient data.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
基金This research is supported by the the Scientific Foundation of Jiangsu Province (BK97047) and the Foundation of Jiangsu Education bureau (00KJT11003)
文摘On the basic of a type of practical examples we set up a new queueing model with negative customers. By the use of “Supplemental Variables method” and “State transfer analysis”, we get the generating function with negative powers of queue length and the waiting time expressions.
文摘In this paper, we have studied about the sensitivity analysis of the human immunodeficiency virus （HIV） protease inhibitor （PI） model and estimated the length of the delay. We have fabricated an HIV PI model accompanied with humoral immunity. Stability analysis of the constructed model about its steady states has been deliberated. We have evaluated some numerical simulations for PI model with humoral immunity by using the existing patient data.
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.
