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具有一般发生率和免疫损伤的时滞HIV感染模型中的稳定性与霍普夫分岔

Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment.

作者信息

Li Fuxiang, Ma Wanbiao, Jiang Zhichao, Li Dan

机构信息

Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China.

Fundamental Science Department, North China Institute of Aerospace Engineering, Langfang, Hebei 065000, China.

出版信息

Comput Math Methods Med. 2015;2015:206205. doi: 10.1155/2015/206205. Epub 2015 Aug 4.

DOI:10.1155/2015/206205
PMID:26413141
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4539976/
Abstract

We investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction number R 0 and the immune response reproduction number R 1. By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.

摘要

我们研究了一个具有一般发生率和免疫损伤的延迟HIV感染模型的动力学行为。我们推导了两个阈值参数，即基本再生数(R_0)和免疫反应再生数(R_1)。通过使用Lyapunov泛函和LaSalle不变性原理，我们证明了无感染平衡点和无免疫感染平衡点的全局稳定性。此外，还研究了具有CTL反应的感染平衡点处Hopf分岔的存在性。通过理论分析和数值模拟，研究了免疫损伤率对具有CTL反应的感染平衡点稳定性的影响。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/366a5efc6d8a/CMMM2015-206205.007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/8595ac5e1071/CMMM2015-206205.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/fe6797c8f286/CMMM2015-206205.002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/5de2e335f9ad/CMMM2015-206205.003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/f9513955cb99/CMMM2015-206205.004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/fa1872c335bb/CMMM2015-206205.005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/f6e26219702c/CMMM2015-206205.006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/366a5efc6d8a/CMMM2015-206205.007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/8595ac5e1071/CMMM2015-206205.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/fe6797c8f286/CMMM2015-206205.002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/5de2e335f9ad/CMMM2015-206205.003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/f9513955cb99/CMMM2015-206205.004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/fa1872c335bb/CMMM2015-206205.005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/f6e26219702c/CMMM2015-206205.006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8524/4539976/366a5efc6d8a/CMMM2015-206205.007.jpg

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