The stability and Hopf bifurcation for an HIV model with saturated infection rate and double delays

被引：8

作者：

Lv, Ying ^{[1
]}

Hu, Zhixing ^{[1
]}

Liao, Fucheng ^{[1
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2018年 / 11卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Double delays; Hopf bifurcation; locally asymptotical stability; globally asymptotical stability; GLOBAL STABILITY; DYNAMICS;

D O I：

10.1142/S1793524518500407

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

An HIV infection model with saturated infection rate and double delays is investigated. First, the existence of the infection-free equilibrium E-0, the immune-exhausted equilibrium E-1 and the infected equilibrium E-2 with immunity in different conditions is shown. By analyzing the characteristic equation, we study the locally asymptotical stability of the trivial equilibrium, and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold. Then with suitable Lyapunov function and LaSalle's invariance principle, the global stability of the three equilibriums is obtained. Finally, numerical simulations are presented to illustrate the main mathematical results.

引用

页数：43

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