Rich dynamics in a delayed HTLV-I infection model: Stability switch, multiple stable cycles, and torus

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Pan, Xuejun¹  Chen, Yuming²  Shu, Hongying³ 

[1] Tongji Zhejiang Coll, Jiaxing 314051, Zhejiang, Peoples R China

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

[3] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710062, Shaanxi, Peoples R China

关键词: HTLV-I infection;    Stability switch;    Double Hopf bifurcation;    Multiple stable periodic solutions;    Quasi-periodic orbit;   

DOI  :  10.1016/j.jmaa.2019.07.051

来源: Elsevier

【 摘 要 】

In this paper, we investigate the impact of time delay in CTL immune response on a HTLV-I infection model. By defining basic reproduction number for viral infection R-0 and basic reproduction number for CTL response R-CTL, we characterize the model dynamics according to whether these two threshold values are greater than one. Especially, we obtain the global dynamics if R-0 <= 1 or R-CTL <= 1 < R-0, as well as infection persistent result when R-0 > 1. However, the model dynamics become much richer when R-CTL < 1. In this case, we use the time delay as a bifurcation parameter to obtain stability switch result on the positive equilibrium and global bifurcation diagrams for the model system. We also conduct higher-order normal form analysis and apply center manifold theory to classify the rich model dynamics near the double Hopf bifurcation points. Our analysis indicates that time delay in CTL immune response can induce not only Hopf bifurcation and double Hopf bifurcation, but also quasi-periodic orbits (torus) and coexistence of multiple stable periodic solutions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free