An accurate two-phase approximate solution to an acute viral infection model

During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate its accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the fall in virus concentration from its peak was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of model parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and in investigating host and virus heterogeneities.

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

[2]  Alan S. Perelson,et al.  Analysis of hepatitis B viral load decline under potent therapy: Complex decay profiles observed , 2001, Hepatology.

[3]  A. Perelson,et al.  Simulation and Prediction of the Adaptive Immune Response to Influenza A Virus Infection , 2009, Journal of Virology.

[4]  Alan S. Perelson,et al.  Dynamics of HIV Infection , 2003 .

[5]  F Y Aoki,et al.  Early administration of oral oseltamivir increases the benefits of influenza treatment. , 2003, The Journal of antimicrobial chemotherapy.

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

[7]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[8]  Andreas Handel,et al.  Neuraminidase Inhibitor Resistance in Influenza: Assessing the Danger of Its Generation and Spread , 2007, PLoS Comput. Biol..

[9]  M. Nowak,et al.  Virus dynamics: Mathematical principles of immunology and virology , 2001 .

[10]  L M Wahl,et al.  Viral dynamics of primary viremia and antiretroviral therapy in simian immunodeficiency virus infection , 1997, Journal of virology.

[11]  A S Perelson,et al.  Modeling plasma virus concentration during primary HIV infection. , 2000, Journal of theoretical biology.

[12]  A. Perelson,et al.  Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection , 1995, Nature.

[13]  A. Perelson,et al.  Kinetics of Influenza A Virus Infection in Humans , 2006, Journal of Virology.

[14]  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.

[15]  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.

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

[17]  A. Perelson Modelling viral and immune system dynamics , 2002, Nature Reviews Immunology.

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

[19]  A S Perelson,et al.  Effect of Drug Efficacy and the Eclipse Phase of the Viral Life Cycle on Estimates of HIV Viral Dynamic Parameters , 2001, Journal of acquired immune deficiency syndromes.