DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE

doi:10.1007/s10473-021-0322-y

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 991-1016.doi: 10.1007/s10473-021-0322-y

DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE

杨俊仙¹, 王雷宏²

1. School of Science, Anhui Agricultural University, Hefei 230036, China;
2. School of Forestry and Landscape Architecture, Anhui Agricultural University, Hefei 230036, China

收稿日期:2020-03-05 修回日期:2020-09-17 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Junxian YANG, Leihong WANG E-mail:yangjunxian1976@126.com
作者简介:Leihong WANG,E-mail:wangleihong208010@126.com
基金资助:
The work was supported by NSF of China (11201002) and Natural Science Foundation of Universities in Anhui Province (KJ2017A815).

DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE

Junxian YANG¹, Leihong WANG²

1. School of Science, Anhui Agricultural University, Hefei 230036, China;
2. School of Forestry and Landscape Architecture, Anhui Agricultural University, Hefei 230036, China

Received:2020-03-05 Revised:2020-09-17 Online:2021-06-25 Published:2021-06-07
Contact: Junxian YANG, Leihong WANG E-mail:yangjunxian1976@126.com
About author:Leihong WANG,E-mail:wangleihong208010@126.com
Supported by:
The work was supported by NSF of China (11201002) and Natural Science Foundation of Universities in Anhui Province (KJ2017A815).

摘要/Abstract

摘要： In this paper, dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated. The model involves the concentrations of uninfected cells, infected cells, free virus, CTL response cells, and antibody antibody response cells. There are three delays in the model: the intracellular delay, virus replication delay and the antibody delay. The basic reproductive number of viral infection, the antibody immune reproductive number, the CTL immune reproductive number, the CTL immune competitive reproductive number and the antibody immune competitive reproductive number are derived. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions for the stability of each equilibrium is established. The results show that the intracellular delay and virus replication delay do not impact upon the stability of each equilibrium, but when the antibody delay is positive, Hopf bifurcation at the antibody response and the interior equilibrium will exist by using the antibody delay as a bifurcation parameter. Numerical simulations are carried out to justify the analytical results.

关键词: Beddington-DeAngelis incidence, CTL immune response, antibody immune response, delay

Abstract: In this paper, dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated. The model involves the concentrations of uninfected cells, infected cells, free virus, CTL response cells, and antibody antibody response cells. There are three delays in the model: the intracellular delay, virus replication delay and the antibody delay. The basic reproductive number of viral infection, the antibody immune reproductive number, the CTL immune reproductive number, the CTL immune competitive reproductive number and the antibody immune competitive reproductive number are derived. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions for the stability of each equilibrium is established. The results show that the intracellular delay and virus replication delay do not impact upon the stability of each equilibrium, but when the antibody delay is positive, Hopf bifurcation at the antibody response and the interior equilibrium will exist by using the antibody delay as a bifurcation parameter. Numerical simulations are carried out to justify the analytical results.

Key words: Beddington-DeAngelis incidence, CTL immune response, antibody immune response, delay

中图分类号:

34C05

杨俊仙, 王雷宏. DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE[J]. 数学物理学报(英文版), 2021, 41(3): 991-1016.

Junxian YANG, Leihong WANG. DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE[J]. Acta mathematica scientia,Series B, 2021, 41(3): 991-1016.

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DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE

DYNAMICS ANALYSIS OF A DELAYED HIV INFECTION MODEL WITH CTL IMMUNE RESPONSE AND ANTIBODY IMMUNE RESPONSE

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