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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (4): 419-436.doi: https://doi.org/10.1007/s10483-011-1427-8

• Articles • 上一篇    下一篇

Modelling two different therapy strategies for drug T-20 on HIV-1 patients

宋保军1 娄洁2 文清芝3   

  1. 1. Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, USA;
    2. Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, P. R. China;
    3. Scientific Research Department, Pingxiang College, Pingxiang 337055, Jiangxi Province, P. R. China
  • 收稿日期:2011-09-27 修回日期:2011-01-17 出版日期:2011-03-29 发布日期:2011-04-01

Modelling two different therapy strategies for drug T-20 on HIV-1 patients

SONG Bao-Jun1, LOU Jie2, WEN Qing-Zhi3   

  1. 1. Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, USA;
    2. Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, P. R. China;
    3. Scientific Research Department, Pingxiang College, Pingxiang 337055, Jiangxi Province, P. R. China
  • Received:2011-09-27 Revised:2011-01-17 Online:2011-03-29 Published:2011-04-01

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摘要： A mathematical model describing the antiretroviral therapy of Enfuvirtide on HIV-1 patients is developed. The effect of Enfuvirtide (formerly called T-20) by impulsive differential equations is modeled by two different drug elimination kinetics, the first-order elimination kinetics and the Michaelis-Menten elimination kinetics. The model is a non-autonomous system of differential equations. For a time-dependent system, the disease-free equilibrium is mainly studied. Its stability, when the therapy is taken with perfect adherence, is obtained. To ensure the disease-free equilibrium remains stable, the analytical thresholds for dosage and dosing intervals are determined. The effects of supervised treatment interruption are also explored. It is shown that the supervised treatment interruption can be worse than no therapy at all.

Abstract: A mathematical model describing the antiretroviral therapy of Enfuvirtide on HIV-1 patients is developed. The effect of Enfuvirtide (formerly called T-20) by impulsive differential equations is modeled by two different drug elimination kinetics, the first-order elimination kinetics and the Michaelis-Menten elimination kinetics. The model is a non-autonomous system of differential equations. For a time-dependent system, the disease-free equilibrium is mainly studied. Its stability, when the therapy is taken with perfect adherence, is obtained. To ensure the disease-free equilibrium remains stable, the analytical thresholds for dosage and dosing intervals are determined. The effects of supervised treatment interruption are also explored. It is shown that the supervised treatment interruption can be worse than no therapy at all.

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