Properties of stability and Hopf bifurcation for a HIV infection model with time delay

In this paper, we consider the classical mathematical model with saturation response of the infection rate and time delay. By stability analysis we obtain sufficient conditions for the global stability of the infection-free steady state and the permanence of the infected steady state. Numerical simulations are carried out to explain the mathematical conclusions.

[1]  Youde Tao,et al.  LYAPUNOV FUNCTION AND GLOBAL PROPERTIES OF VIRUS DYNAMICS WITH CTL IMMUNE RESPONSE , 2008 .

[2]  Judy Tam,et al.  Delay effect in a model for virus replication. , 1999, IMA journal of mathematics applied in medicine and biology.

[3]  S. Ruan,et al.  A delay-differential equation model of HIV infection of CD4(+) T-cells. , 2000, Mathematical biosciences.

[4]  Xinyu Song,et al.  A DELAY-DIFFERENTIAL EQUATION MODEL OF HIV INFECTION OF CD4 + T-CELLS , 2005 .

[5]  G. Webb,et al.  A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay , 2003, Journal of mathematical biology.

[6]  A S Perelson,et al.  Target cell limited and immune control models of HIV infection: a comparison. , 1998, Journal of theoretical biology.

[7]  Martin A. Nowak,et al.  Viral dynamics in human immunodeficiency virus type 1 infection , 1995, Nature.

[8]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[9]  Yang Kuang,et al.  Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters , 2002, SIAM J. Math. Anal..

[10]  A S Perelson,et al.  Dynamics of HIV-1 and CD4+ lymphocytes in vivo. , 1997, AIDS.

[11]  Patrick W Nelson,et al.  Mathematical analysis of delay differential equation models of HIV-1 infection. , 2002, Mathematical biosciences.

[12]  A. Neumann,et al.  Global stability and periodic solution of the viral dynamics , 2007 .

[13]  Jack K. Hale,et al.  Persistence in infinite-dimensional systems , 1989 .