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Journal of Mathematical Biology

, Volume 60, Issue 5, pp 711–726 | Cite as

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

  • Amber M. Smith
  • Frederick R. Adler
  • Alan S. Perelson
Article

Abstract

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.

Keywords

Acute virus infection Influenza Virus dynamics model Approximation of nonlinear differential equations 

Mathematics Subject Classification (2000)

92B05 37N25 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Amber M. Smith
    • 1
  • Frederick R. Adler
    • 2
  • Alan S. Perelson
    • 3
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Departments of Mathematics and BiologyUniversity of UtahSalt Lake CityUSA
  3. 3.Theoretical Biology and Biophysics Group, Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

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