Global Dynamics of an In-host Viral Model with Intracellular Delay

The dynamics of a general in-host model with intracellular delay is studied. The model can describe in vivo infections of HIV-I, HCV, and HBV. It can also be considered as a model for HTLV-I infection. We derive the basic reproduction number R0 for the viral infection, and establish that the global dynamics are completely determined by the values of R0. If R0≤1, the infection-free equilibrium is globally asymptotically stable, and the virus are cleared. If R0>1, then the infection persists and the chronic-infection equilibrium is locally asymptotically stable. Furthermore, using the method of Lyapunov functional, we prove that the chronic-infection equilibrium is globally asymptotically stable when R0>1. Our results shows that for intercellular delays to generate sustained oscillations in in-host models it is necessary have a logistic mitosis term in target-cell compartments.

[1]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[2]  Alan S Perelson,et al.  Estimates of Intracellular Delay and Average Drug Efficacy from Viral Load Data of HIV-Infected Individuals under Antiretroviral Therapy , 2004, Antiviral therapy.

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

[4]  C. Connell McCluskey,et al.  Complete global stability for an SIR epidemic model with delay — Distributed or discrete , 2010 .

[5]  Henry C Tuckwell,et al.  On the behavior of solutions in viral dynamical models. , 2004, Bio Systems.

[6]  A. Perelson,et al.  Dynamics of HIV infection of CD4+ T cells. , 1993, Mathematical biosciences.

[7]  A. Korobeinikov.  Global properties of basic virus dynamics models , 2004, Bulletin of mathematical biology.

[8]  M A Nowak,et al.  Virus dynamics and drug therapy. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Denise Kirschner,et al.  Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression. , 2002, Mathematical biosciences.

[10]  M. Nowak,et al.  Population Dynamics of Immune Responses to Persistent Viruses , 1996, Science.

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

[12]  C. McCluskey,et al.  Global stability for an SEIR epidemiological model with varying infectivity and infinite delay. , 2009, Mathematical biosciences and engineering : MBE.

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

[14]  A. Perelson,et al.  A model of HIV-1 pathogenesis that includes an intracellular delay. , 2000, Mathematical biosciences.

[15]  Romulus Breban,et al.  Role of parametric resonance in virological failure during HIV treatment interruption therapy , 2006, The Lancet.

[16]  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.

[17]  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.

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

[19]  Michael Y. Li,et al.  Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells. , 2006, Mathematical biosciences.

[20]  Yan Wang,et al.  Oscillatory viral dynamics in a delayed HIV pathogenesis model. , 2009, Mathematical biosciences.

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

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

[23]  D. Ho,et al.  HIV-1 dynamics in vivo. , 1995, Journal of biological regulators and homeostatic agents.

[24]  Yongfeng Li,et al.  Global stability and periodic solution of a model for HTLV-I infection and ATL progression , 2006, Appl. Math. Comput..

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