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This article is part of the supplement: Mathematical Modelling of Influenza

Open Access Research

Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture

Benjamin P Holder and Catherine AA Beauchemin*

Author Affiliations

Department of Physics, Ryerson University, Toronto, ON, M5B 2K3, Canada

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BMC Public Health 2011, 11(Suppl 1):S10  doi:10.1186/1471-2458-11-S1-S10

Published: 25 February 2011

Abstract

Background

For a typical influenza infection in vivo, viral titers over time are characterized by 1–2 days of exponential growth followed by an exponential decay. This simple dynamic can be reproduced by a broad range of mathematical models which makes model selection and the extraction of biologically-relevant infection parameters from experimental data difficult.

Results

We analyze in vitro experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of realistic models of infection. In particular, we demonstrate the viability of using a normal or lognormal distribution for the time a cell spends in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), while exposing the shortcomings of ordinary differential equation models which implicitly utilize exponential distributions and delay-differential equation models with fixed-length delays.

Conclusions

By fitting published viral titer data from challenge experiments in human volunteers, we show that alternative models can lead to different estimates of the key infection parameters.