一类具有脉冲免疫治疗的HIV-1感染模型的动力学分析

王小娥; 蔺小林; 李建全

doi:10.21656/1000-0887.390334

一类具有脉冲免疫治疗的HIV-1感染模型的动力学分析

doi: 10.21656/1000-0887.390334

陕西科技大学文理学院, 西安 710021

基金项目: 国家自然科学基金(11371031;11371369)

详细信息

作者简介:
王小娥(1993—)，女，硕士生(E-mail: 1255013427@qq.com);李建全(1965—)，男，博士(通讯作者. E-mail: jianq_li@263.net).

中图分类号: O29
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- 被引次数: 0
出版历程
- 收稿日期: 2018-11-29
- 修回日期: 2019-05-06
- 刊出日期: 2019-07-01

Dynamic Analysis of a Class of HIV-1 Infection Models With Pulsed Immunotherapy

School of Arts and Sciences, Shaanxi University of Science and Technology,Xi’an 710021, P.R.China

Funds: The National Natural Science Foundation of China(11371031;11371369)

摘要

摘要: 该文基于一类HIV-1感染免疫治疗模型，研究了一类具有脉冲免疫治疗的HIV-1感染模型.借助脉冲微分方程理论，研究了脉冲免疫治疗模型解的非负性和一致有界性.利用Floquet乘子理论和微分方程的比较定理，推导出脉冲免疫模型无感染周期解局部和全局渐近稳定以及HIV-1一致持续的阈值条件.通过数值模拟，比较了3种不同治疗方案的治疗效果，验证了脉冲免疫治疗的有效性.数值模拟结果表明，当药物输入量足够大或服药间隔适当短时，从理论上可以有效控制甚至根除病毒.
- HIV-1感染模型 /
- 周期解 /
- 一致持续 /
- 免疫治疗
Abstract: Based on a class of HIV-1 infection immunotherapy models, an HIV-1 infection model with pulsed immunotherapy was addressed. The non-negativity and uniform boundedness of the solutions to the pulsed immunotherapy model were studied with the pulsed differential equation theory. According to the Floquet multiplier theory and the comparison theorem for differential equations, the threshold conditions for the local and global asymptotic stability of the infection-free periodic solution as well as uniform persistence of HIV-1 were obtained. Through numerical simulation, the therapeutic effects of 3 different treatment regimens were compared, and the effectiveness of the pulsed immunotherapy was verified. The numerical results show that, the virus can be effectively controlled or eliminated theoretically when the drug input is large enough or the dosing interval is short properly.
- HIV-1 infection model /
- infection-free periodic solution /
- uniform persistence /
- immunotherapy

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参考文献(24)

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