Open AccessA delayed HIV-1 model with virus waning term
Author(s) -
Bing Li,
Yuming Chen,
Xuejuan Lu,
Shengqiang Liu
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016.13.135
Subject(s) - basic reproduction number , virus , clearance , viral load , population , ctl* , immune system , virology , viral replication , biology , term (time) , human immunodeficiency virus (hiv) , hopf bifurcation , steady state (chemistry) , viral infection , cd8 , immunology , control theory (sociology) , bifurcation , physics , medicine , computer science , control (management) , chemistry , environmental health , quantum mechanics , nonlinear system , urology , artificial intelligence
In this paper, we propose and analyze a delayed HIV-1 model with CTL immune response and virus waning. The two discrete delays stand for the time for infected cells to produce viruses after viral entry and for the time for CD8+ T cell immune response to emerge to control viral replication. We obtain the positiveness and boundedness of solutions and find the basic reproduction number R0. If R0 < 1, then the infection-free steady state is globally asymptotically stable and the infection is cleared from the T-cell population; whereas if R0 > 1, then the system is uniformly persistent and the viral concentration maintains at some constant level. The global dynamics when R0 > 1 is complicated. We establish the local stability of the infected steady state and show that Hopf bifurcation can occur. Both analytical and numerical results indicate that if, in the initial infection stage, the effect of delays on HIV-1 infection is ignored, then the risk of HIV-1 infection (if persists) will be underestimated. Moreover, the viral load differs from that without virus waning. These results highlight the important role of delays and virus waning on HIV-1 infection.