时变环境下HIV病毒动力学模型的研究

项目名称： 时变环境下HIV病毒动力学模型的研究

项目编号： No.11301453

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 王霞

作者单位： 信阳师范学院

项目金额： 22万元

中文摘要： 时变环境在HIV的感染过程中占据着重要地位.本项目将时变系数、脉冲效应等生物学因素引入HIV病毒动力学模型，建立时变环境下HIV病毒动力学模型.主要研究内容包括:(1)考虑机体的免疫反应对艾滋病的发病机制和传播规律的影响，建立并研究免疫反应下的HIV时滞病毒动力学模型;(2)考虑HIV感染和治疗的时变性，以及抗逆转录药物的药效的可变性，建立具有时变系数的时滞HIV病毒模型，利用理论分析与数值模拟相结合的方法，研究相应的持久性与灭绝性、参数的敏感性;(3)考虑脉冲式HIV抗病毒治疗方案，建立具有脉冲给药的HIV病毒动力学模型，研究模型的稳定性，周期解等动力学行为.本项目旨在揭示时变环境下HIV病毒感染的发展过程，预测艾滋病的发展趋势，寻求预防和控制艾滋病的最优策略. 因此本项目的研究具有重要的理论意义和现实意义.

中文关键词： HIV 病毒动力学；时变环境；多靶细胞；脉冲效应；基本再生率

英文摘要： Time-varying environment plays an important role in the infection process of HIV. In this project, we will introduce the time-varying coefficient, pulse effect and other biological factors into the HIV virus dynamics model, and establish the HIV virus dynamics models in time-varying environments. The research contents mainly include: (1) In view of the influences of the body's immune response on the pathogenesis and propagation laws of AIDS, the delayed HIV virus dynamics model with the immune response will be established and studied; (2) Considering the time-varying of HIV infection and treatment, as well as the variability of drug action of anti-retroviral, the delayed HIV virus models with time-varying coefficient will be established. Using theoretical analysis and numerical simulation methods, the persistence, extinction and parameter sensitivity of the corresponding models will be studied; (3) Considering the plan of HIV antiviral treatment with impulsive drug, an HIV-1 virus dynamics model with impulsive drug will be established, and the dynamic behaviors such as the stability and the periodic solution of the model will be investigated. This project aims to reveal the development process of HIV infection under time-varying environment, predict the development trend of HIV/AIDS, and seek the optimal strat

英文关键词： HIV virus dynamics；Time-varing environment；Multiple target cells；Pulse effect；Basic reproduction ratio