A Delayed HIV Infection Model with the Homeostatic Proliferation of CD4^(+)T Cells

作     者：Qiang-hui XU Ji-cai HUANG Yue-ping DONG Yasuhiro TAKEUCHI Qiang-hui XU;Ji-cai HUANG;Yue-ping DONG;Yasuhiro TAKEUCHI

作者机构：School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical SciencesCentral China Normal UniversityWuhan 430079China College of Science and EngineeringAoyama Gakuin UniversityKanagawa 252-5258Japan 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2022年第38卷第2期

页      面：441-462页

核心收录：

学科分类：1004[医学-公共卫生与预防医学(可授医学、理学学位)] 07[理学] 070104[理学-应用数学] 100401[医学-流行病与卫生统计学] 0701[理学-数学] 10[医学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11871235,11901225) the Natural Science Foundation of Hubei Province(2019CFB189) the Fundamental Research Funds for the Central Universities(Nos.CCNU19TS030,CCNU18XJ041) by the Japan Society for the Promotion of Science“Grand-in-Aid 20K03755”。 

主　　题：HIV infection and persistence T cell homeostatic proliferation delayed model dynamics analysis Hopf bifurcation 

摘      要：In this paper,we investigate a delayed HIV infection model that considers the homeostatic prolif-eration of CD4^(+)T cells.The existence and stability of uninfected equilibrium and infected equilibria(smaller and larger ones)are studied by analyzing the characteristic equation of the system.The intracellular delay does not affect the stability of uninfected equilibrium,but it can change the stability of larger positive equilibrium and Hopf bifurcation appears inducing stable limit cycles.Furthermore,direction and stability of Hopf bifur-cation are well investigated by using the central manifold theorem and the normal form theory.The numerical simulation results show that the stability region of larger positive equilibrium becomes smaller as the increase of time delay.Moreover,when the maximum homeostatic growth rate is very small,the larger positive equilibrium is always stable.On the contrary,when the rate of supply of T cells is very small,the larger positive equilibrium is always unstable.