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

Amber Smith, Frederick R. Adler, Alan S. Perelson

Research output: Contribution to journalArticle

37 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)711-726
Number of pages16
JournalJournal of Mathematical Biology
Volume60
Issue number5
DOIs
StatePublished - Jan 1 2010
Externally publishedYes

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Virus Diseases
Viruses
Acute
Virus
Infection
Approximate Solution
viruses
Influenza
deterioration
Decay
influenza
infection
Human Influenza
Approximation
Growth
Model
dynamic models
Alternate
Antiviral Agents
microbial growth

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

An accurate two-phase approximate solution to an acute viral infection model. / Smith, Amber; Adler, Frederick R.; Perelson, Alan S.

In: Journal of Mathematical Biology, Vol. 60, No. 5, 01.01.2010, p. 711-726.

Research output: Contribution to journalArticle

Smith, Amber ; Adler, Frederick R. ; Perelson, Alan S. / An accurate two-phase approximate solution to an acute viral infection model. In: Journal of Mathematical Biology. 2010 ; Vol. 60, No. 5. pp. 711-726.
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