Hopf Bifurcation for a Model of HIV Infection of CD4+ T Cells with Virus Released Delay

A viral model of HIV infection of C D 4 + T-cells with virus released period is formulated, and the effect of this released period on the stability of the equilibria is investigated. It is shown that the introduction of the viral released period can destabilize the system, and the period solution may arise. The direction and stability of the Hopf bifurcation are also discussed. Numerical simulations are presented to illustrate the results.

[1]  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.

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

[3]  Alan S. Perelson,et al.  Decay characteristics of HIV-1-infected compartments during combination therapy , 1997, Nature.

[4]  Y. Kuang Delay Differential Equations: With Applications in Population Dynamics , 2012 .

[5]  B. Weber Screening of HIV infection: role of molecular and immunological assays , 2006, Expert review of molecular diagnostics.

[6]  M A Nowak,et al.  Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Cuifang Lv,et al.  Stability analysis of delay differential equation models of HIV-1 therapy for fighting a virus with another virus , 2009 .

[8]  Junjie Wei,et al.  Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays , 2005 .

[9]  A. Perelson,et al.  Influence of delayed viral production on viral dynamics in HIV-1 infected patients. , 1998, Mathematical biosciences.

[10]  A S Perelson,et al.  Cyclic re-entry of germinal center B cells and the efficiency of affinity maturation. , 1993, Immunology today.

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

[12]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[13]  Wanbiao Ma,et al.  Asymptotic properties of a HIV-1 infection model with time delay , 2007 .

[14]  Xinyu Song,et al.  Analysis of stability and Hopf bifurcation for an HIV infection model with time delay , 2008, Appl. Math. Comput..

[15]  Xueyong Zhou,et al.  Delay induced stability switches in a viral dynamical model , 2011 .

[16]  Xinyu Song,et al.  A differential equation model of HIV infection of CD4+ T-cells with cure rate , 2008 .

[17]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.