Influenza A virus infection kinetics: quantitative data and models

Abstract

Influenza A virus is an important respiratory pathogen that poses a considerable threat to public health each year during seasonal epidemics and even more so when a pandemic strain emerges. Understanding the mechanisms involved in controlling an influenza infection within a host is important and could result in new and effective treatment strategies. Kinetic models of influenza viral growth and decay can summarize data and evaluate the biological parameters governing interactions between the virus and the host. Here we discuss recent viral kinetic models for influenza. We show how these models have been used to provide insight into influenza pathogenesis and treatment, and we highlight the challenges of viral kinetic analysis, including accurate model formulation, estimation of important parameters, and the collection of detailed data sets that measure multiple variables simultaneously. WIREs Syst Biol Med 2011 3 429-445 DOI: 10.1002/wsbm.129

Figure 1

Schematic diagram of the viral dynamics models. (a) Classic model of viral dynamics. Target cells (T) are supplied at constant rate s and die at rate d per day. These cells become infected at rate βV per day. Free virions are produced from infected cells (I) at a rate p and are removed at a rate c. Infected cells are lost at a rate δ. (b) Acute virus infection model modified from the classic model. Target cell regeneration and death are not included. Infected cells were split into two classes, I₁ and I₂, where virus production initially undergoes an eclipse phase (k).

Figure 1

Schematic diagram of the viral dynamics models. (a) Classic model of viral dynamics. Target cells (T) are supplied at constant rate s and die at rate d per day. These cells become infected at rate βV per day. Free virions are produced from infected cells (I) at a rate p and are removed at a rate c. Infected cells are lost at a rate δ. (b) Acute virus infection model modified from the classic model. Target cell regeneration and death are not included. Infected cells were split into two classes, I₁ and I₂, where virus production initially undergoes an eclipse phase (k).

Numerical solution of Eq. (2) using parameter values and viral titer data (boxes) from a human infected with influenza [2].

Comparison of the fit (circles) to viral titer data (boxes) from a human infected with influenza [2] and the approximate solution to Eq. (2)) [90]. The viral growth phase (red) lasts for t₁ days and the viral decay phase (blue) begins at t₂ days [90]. (Reprinted with permission from Ref. [90]. Copyright 2010 Springer Science+ Business Media.)

Log-linear fits [90] to viral titer data (boxes) from a human infected with influenza [2]. Titers during days 1-3 were considered part of the initial viral growth phase, and titers during days 4-7 as part of the viral decay phase [90]. (Reprinted with permission from Ref. [90]. Copyright 2010 Springer Science+Business Media.)

Numerical solution (virusblack, IFN-blue) of Eq. (2)-(3) using parameter values and viral titer data (boxes) from a human infected with influenza [2].

Simultaneously fitting Eq. 5 to viral loads (RNA copies/ml nasal secretion (NS)) and interferon concentrations in the nasal washes of a Welsh pony experimentally infected with influenza [82]. Reprinted from Saenz et al. [82]. Used with permission from the American Society of Microbiology.

Fits of the model in [65] to data (viral titers (not shown), CD8 T cells, IgG and IgM (not shown)) collected from experimentally infected mice [65]. Reprinted from Miao et al. [65]. Used with permission from the American Society of Microbiology.

Fits of the model in [65] to data (viral titers (not shown), CD8 T cells, IgG and IgM (not shown)) collected from experimentally infected mice [65]. Reprinted from Miao et al. [65]. Used with permission from the American Society of Microbiology.

Fits of Eq. (12) [39] to viral titer data from humans infected with influenza that were either given no treatment (blue) or antiviral treatment early (29 hours, red) or late (50 hours, green) [42]. Total virus (V_s + V_r) - solid lines, Resistant virus (V_r) - dashed lines. Reprinted from Handel et al. [39].