The in vivo efficacy of neuraminidase inhibitors cannot be determined from the decay rates of influenza viral titers observed in treated patients

Abstract

Antiviral therapy is a first line of defence against new influenza strains. Current pandemic preparations involve stock- piling oseltamivir, an oral neuraminidase inhibitor (NAI), so rapidly determining the effectiveness of NAIs against new viral strains is vital for deciding how to use the stockpile. Previous studies have shown that it is possible to extract the drug efficacy of antivirals from the viral decay rate of chronic infections. In the present work, we use a nonlinear mathematical model representing the course of an influenza infection to explore the possibility of extracting NAI drug efficacy using only the observed viral titer decay rates seen in patients. We first show that the effect of a time-varying antiviral concentration can be accurately approximated by a constant efficacy. We derive a relationship relating the true treatment dose and time elapsed between doses to the constant drug dose required to approximate the time- varying dose. Unfortunately, even with the simplification of a constant drug efficacy, we show that the viral decay rate depends not just on drug efficacy, but also on several viral infection parameters, such as infection and production rate, so that it is not possible to extract drug efficacy from viral decay rate alone.

Figure 1. Comparing the effect of a constant vs time-varying antiviral concentration.

Viral titers and drug concentrations for infections treated with a time-varying drug concentration, D(t) from Eq. 4 (black lines), and the best fit assuming a constant drug concentration (red lines). The dashed line shows the untreated infection.

Figure 2. Evaluating the accuracy of assuming a constant drug concentration.

The goodness-of-fit (SSR) between viral titers resulting from PK modelling of the time-varying drug concentration and a fit of these titers using a constant drug concentration, D_cst, administered at fixed time, t_on, when (Left) D_cst and t_on are fitted; or (Right) t_on = t_admin and D_cst is computed using Eq. (1).

Figure 3. Relationship between parameters of the PK model and those of the constant drug concentration approximation.

Relationships between D_cst and τ (upper left), t_on and τ (upper right), D_cst and D_admin (bottom left), and t_on and D_admin (bottom right). Solid lines indicate actual values determined from fitting; dotted lines indicate our approximations using the constant drug concentration predicted by Eq. 1 and a constant value for t_on.

Figure 4. Viral titers and drug concentrations for infections treated with time-varying drug D(t) from Eq. 4 (black lines), and the viral titers and drug concentrations for infections treated with a constant drug concentration approximation from Eq. 1 and t_on = t_admin.

The dashed line shows the untreated infection.

Figure 5. Percent error in decay rate when using a constant drug concentration determined by Eq. (1) and applied at a fixed t_on = t_admin to approximate viral titers produced with a time-dependent drug concentration.

Figure 6. Ratio of viral titer to infectious cells.

The ratio of viral titer to infectious cells over the course of an influenza infection.

Figure 7. Effect of infection parameters on viral titer decay.

Oseltamivir treatment is applied at various times post infection and at different efficacies. Top graph shows the effect of different treatments on the base viral infection parameters. The effect of varying the base infection parameters is also explored by either decreasing (bottom row) or increasing (upper row) viral production rate (p) (first column), infection rate (β) (second column), viral clearance rate (c) (third column), eclipse duration (τ_E) (fourth column), infectious lifespan (τ_I) (last column) by 10-fold (except τ_E, see text) compared to the base parameters.

Figure 8. Effect of treatment delay on viral titer decay.

Oseltamivir treatment is applied at various times post infection and at different efficacies. The effect of varying the base infection parameters is also explored by either decreasing (bottom row) or increasing (top row) viral production rate (p) (first column), infection rate (β) (second column), viral clearance rate (c) (third column), eclipse duration (τ_E) (fourth column), infectious lifespan (τ_I) (last column) by 10-fold (except τ_E, see text) compared to the base parameters.