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

作　　者：Ying Lv Zhixing Hu Fucheng Liao 

机构地区：[1]School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, P. R. China

出　　处：《International Journal of Biomathematics》2018年第3期177-219,共43页生物数学学报（英文版）

基　　金：This work was supported by National Natural Science Foundation of China （61174209, 11471034）.

摘　　要：An HIV infection model with saturated infection rate and double delays is investigated. First, the existence of the infection-free equilibrium E0, the immune-exhausted equilibrium E1 and the infected equilibrium E2 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.

关 键 词：Double delays Hopf bifurcation locally asymptotical stability globally asymptotical stability. 

分 类 号：O153.3[理学—数学] S858.23[理学—基础数学]