Stability and Hopf bifurcation in a HIV-1 infection model with delays and logistic growth

Qing Hu, Zhixing Hu and Fucheng Liao

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 128, issue C, 26-41

Abstract: In this paper, we consider the dynamical behavior of a HIV-1 infection model with logistic growth for target cells, time delay and two predominant infection modes, namely the classical cell-free infection and the direct cell-to-cell transfer. It is proved the existence of the positive equilibrium E2 in different conditions. By analyzing the characteristic equations and using stability theory of delay differential equations, we establish the local stability of the two boundary equilibria and the infected equilibrium of the model. The time delay does not affect the stability of the boundary equilibrium, but can change the stability of E2 and lead to the occurrence of Hopf bifurcations. The direction and stability of bifurcating periodic solutions is also studied. Finally, the numerical simulations are carried out to explain our theorems.

Keywords: HIV-1; Logistic growth; Delay; Local stability; Hopf bifurcation (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475416300325
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:128:y:2016:i:c:p:26-41

DOI: 10.1016/j.matcom.2016.04.003

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().