Understanding the within-host dynamics of influenza A virus: from theory to clinical implications

Abstract

Mathematical models have provided important insights into acute viral dynamics within individual patients. In this paper, we study the simplest target cell-limited models to investigate the within-host dynamics of influenza A virus infection in humans. Despite the biological simplicity of the models, we show how these can be used to understand the severity of the infection and the key attributes of possible immunotherapy and antiviral drugs for the treatment of infection at different times post infection. Through an analytic approach, we derive and estimate simple summary biological quantities that can provide novel insights into the infection dynamics and the definition of clinical endpoints. We focus on nine quantities, including the area under the viral load curve, peak viral load, the time to peak viral load and the level of cell death due to infection. Using Markov chain Monte Carlo methods, we fitted the models to data collected from 12 untreated volunteers who participated in two clinical studies that tested the antiviral drugs oseltamivir and zanamivir. Based on the results, we also discuss various difficulties in deriving precise estimates of the parameters, even in the very simple models considered, when experimental data are limited to viral load measures and/or there is a limited number of viral load measurements post infection.

Keywords: acute viral infection; immune control; influenza A; viral kinetics; within-host modelling.

Figure 1.

A schematic diagram of the TIV model (2.1)–(2.4) of viral dynamics. (Online version in colour.)

Figure 2.

Summary of the infection-related quantities: the basic reproduction ratio, the initial viral growth rate, the generation time, the peak viral load, the time to peak viral load, the infection duration (time interval in which the viral load is above a threshold), the area under the viral load curve above a threshold and the fraction of dead cells. (Online version in colour.)

Figure 3.

TV model fit: the black line represents the median estimate of viral dynamics (in log₁₀ scale) and yellow lines are viral dynamic curves based on 10 000 samples from the posterior distribution of the parameters. Red squares are viral load data points. (a) Placebo-group patients from the oseltamivir trial (Roche dataset); (b) placebo-group patients from the zanamivir trial (GSK dataset).

Figure 4.

Estimated posterior medians of individual parameters and the corresponding 95% credible intervals for the 12 patients in the two datasets. The estimated values of the individual parameters are presented in the electronic supplementary material, table S5.

Figure 5.

Scatter plots illustrating the variability of the infection-related quantities between the 12 patients in the two datasets. Each colour represents a patient. Numerical solutions are represented by filled circles and analytical solutions by asterisks. The estimated values of the quantities are presented in table 4.