Global stability of endemic equilibrium point of basic virus infection model with application to HBV infection

In this paper, the authors first show that if R0 ≤ 1, the infection free steady state is globally attractive by using approaches different from those given by Min, et al.(2008). Then the authors prove that if R0 > 1, the endemic steady state is also globally attractive. Finally, based on a patient’s clinical HBV DNA data of anti-HBV infection with drug lamivudine, the authors establish an ABVIM. The numerical simulations of the ABVIM are good in agreement with the clinical data.

[1]  M. Hirsch,et al.  4. Monotone Dynamical Systems , 2005 .

[2]  J. Larkin,et al.  New animal models of hepatitis B and C. , 2001, ILAR journal.

[3]  J. Schmidt,et al.  Effect of interferon alfa on the dynamics of hepatitis C virus turnover in vivo , 1996, Hepatology.

[4]  Stephen A. Gourley,et al.  Dynamics of a delay differential model of hepatitis B virus , 2007 .

[5]  Lequan Min,et al.  Mathematical Analysis of a Basic Virus Infection Model With Application to HBV Infection , 2008 .

[6]  Hal L. Smith,et al.  Virus Dynamics: A Global Analysis , 2003, SIAM J. Appl. Math..

[7]  Thomas Berg,et al.  Peginterferon Alfa-2a, lamivudine, and the combination for HBeAg-positive chronic hepatitis B. , 2005, The New England journal of medicine.

[8]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[9]  Stephen A. Gourley,et al.  Dynamics of a delay difierential model of hepatitis B virus , 2007 .

[10]  A. Perelson,et al.  HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time , 1996, Science.

[11]  Yang Kuang,et al.  Dynamics of a delay differential equation model of hepatitis B virus infection , 2008, Journal of biological dynamics.

[12]  James S. Muldowney,et al.  Compound matrices and ordinary differential equations , 1990 .

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

[14]  Alan S. Perelson,et al.  Hepatitis C Viral Dynamics in Vivo and the Antiviral Efficacy of Interferon-α Therapy , 1998 .

[15]  J. Stockman,et al.  Peginterferon Alfa-2a, Lamivudine, and the Combination for HBeAg-Positive Chronic Hepatitis B , 2007 .

[16]  M A Nowak,et al.  Viral dynamics in hepatitis B virus infection. , 1996, Proceedings of the National Academy of Sciences of the United States of America.