Abstract
BackgroundFor 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.ResultsWe 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.ConclusionsBy 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.
Highlights
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
The resulting viral production curve can be viewed as that of the average cell. This is in sharp contrast to “multiple-cycle” yield experiments (MOI ≪ 1), where only a few cells are initially infected, leading to successive cycles of infection; the resulting exponential growth of both infected cells and virus over time effectively masks the dynamics of a single cell
Virus infections of humans and animals are similar to this latter experiment in that they are likely initiated by the infection of a only a few cells [26,27], leading to the exponential consumption of a large target cell population
Summary
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. Mathematical models have improved our understanding of the course of the disease within human [4] and animal hosts [5] Because these models serve as a bridge between the microscopic scale (where virus interacts with cell) and the macroscopic scale (where the infection is manifested as a disease) they will inevitably be applied in the future to pressing public health questions such as the estimation of virulence and fitness for emerging strains, the spread of drug resistance and, more generally, the connections between viral genotypic information and clinical data. This allows a model to describe the phenomenon implementation of the time spent by a cell in each of the various stages of infection
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