The Mechanisms for Within-Host Influenza Virus Control Affect Model-Based Assessment and Prediction of Antiviral Treatment

Abstract

Models of within-host influenza viral dynamics have contributed to an improved understanding of viral dynamics and antiviral effects over the past decade. Existing models can be classified into two broad types based on the mechanism of viral control: models utilising target cell depletion to limit the progress of infection and models which rely on timely activation of innate and adaptive immune responses to control the infection. In this paper, we compare how two exemplar models based on these different mechanisms behave and investigate how the mechanistic difference affects the assessment and prediction of antiviral treatment. We find that the assumed mechanism for viral control strongly influences the predicted outcomes of treatment. Furthermore, we observe that for the target cell-limited model the assumed drug efficacy strongly influences the predicted treatment outcomes. The area under the viral load curve is identified as the most reliable predictor of drug efficacy, and is robust to model selection. Moreover, with support from previous clinical studies, we suggest that the target cell-limited model is more suitable for modelling in vitro assays or infection in some immunocompromised/immunosuppressed patients while the immune response model is preferred for predicting the infection/antiviral effect in immunocompetent animals/patients.

Keywords: drug efficacy; immune response; model selection; neuraminidase inhibitor; target cell depletion.

Figure 1

Schematic illustration of the typical solutions to the target cell-limited models (A) and models incorporating both innate and adaptive immune responses (B). For the target cell-limited models, severe depletion of target cells stops viral growth leading to viral clearance (the approximate turning point is indicated by a filled triangle). In contrast, for the models with both innate and adaptive immune responses, timely activation of the innate immune response stops viral growth and later activation of the adaptive immune response is responsible for viral clearance (the approximate times of activation are indicated by filled triangles). p.i.: post-infection.

Figure 2

Schematic diagram showing the definitions of three important quantities characterising the viral load profile. Peak viral load indicates the maximum of the viral load curve. Duration of infection is the period of time from the start of infection to the time when the viral load reaches the limit of detection. The area under the viral load curve within the first N days p.i. (${\mathrm{AUC}}_{\mathrm{N}}$; calculated by integrating the viral load over the relevant period) is a measure of the cumulative viral load over a certain period of infection.

Figure 3

Results showing the contributions of various processes to the establishment of the viral load profile. (A) For the TIV model, three processes are involved: production of free virus ($p_{V}I$), unspecified virus clearance (${\delta }_{V}V$) and binding to target cells ($\beta VT$). The terms appear on the righthand side of Equation (3); (B) For the IR model, four processes are involved: production of free virus ($p_{V}I$), unspecified virus clearance (${\delta }_{V}V$), binding to target cells ($\beta VT$) and virus neutralisation by antibodies (${\kappa }_S{A}_{S}V+{\kappa }_L{A}_{L}V$). The terms appear on the righthand side of Equation (4). The processes leading to an increase in viral load are labelled by (+) and shown by solid curves, while the processes reducing the viral load are labelled by (−) and shown by dotted curves.

Figure 4

Dependence of viral load profile on drug efficacy for the TIV model. The time course of plasma oseltamivir carboxylate (OC) concentration is shown in (B). For $E{C}_{50}$ (half maximal effective concentration) varying from 10 ng/mL to 300 ng/mL, corresponding viral load solutions are shown in (A) with different colours. The solution with no drug applied is shown by the dashed black curve. ${\mathrm{EID}}_{50}/\mathrm{mL}$ : 50% egg infective dose.

Figure 5

Dependence of infection-related quantities on drug efficacy for the TIV model. As drug efficacy $E{C}_{50}$ varies from 10 ng/mL to 800 ng/mL, infection-related quantities, under the curve (AUC) (A,B), peak viral load (C) and duration of infection (D), are shown in different panels. ${\mathrm{AUC}}_8$, ${\mathrm{AUC}}_4$ and peak viral load are normalised to their corresponding quantities in the no-drug control. Insets show sub-parts of the plots. For duration of infection longer than 30 days, we truncate the duration at 30 days in panel D. The duration of infection without antiviral treatment is indicated by the dotted red line in panel D.

Figure 6

Dependence of viral load profile on drug efficacy for the IR model. The time course of plasma oseltamivir carboxylate (OC) concentration is shown in (B). For $E{C}_{50}$ varying from 10 ng/mL to 300 ng/mL, corresponding viral load solutions are shown in (A) with different colours. The solution with no drug applied is shown by the dashed black curve.

Figure 7

Dependence of infection-related quantities on drug efficacy for the IR model. As drug efficacy $E{C}_{50}$ varies from 10 ng/mL to 800 ng/mL, infection-related quantities, AUC (A,B), peak viral load (C) and duration of infection (D), are shown in different panels. ${\mathrm{AUC}}_8$, ${\mathrm{AUC}}_4$ and peak viral load are normalised to their corresponding quantities in the no-drug control. The duration of infection without antiviral treatment is indicated by the dotted red line in panel D.

Figure 8

Comparison of model behaviours of the TIV model (A,C) and the IR model (B,D) for a highly effective drug ($E{C}_{50}=20$ ng/mL) and varied drug administration time. The time when drug is first taken is varied from 12 h p.i. to 96 h p.i. and the corresponding viral load solutions are shown in different colours. ${\mathrm{AUC}}_8$ is normalised to its corresponding quantity in the no-drug control. The solutions with no treatment are shown by dashed black curves.

Figure 9

Comparison of model behaviours of the TIV model (A,C) and the IR model (B,D) for a less effective drug ($E{C}_{50}=200$ ng/mL) and varied drug administration time. The time when drug is first taken is varied from 12 h p.i. to 96 h p.i. and the corresponding viral load solutions are shown in different colours. ${\mathrm{AUC}}_8$ is normalised to its corresponding quantity in the no-drug control. The solutions with no treatment are shown by dashed black curves.