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

摘要

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 E_2 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 E_2 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.