Antiviral treatment for the control of pandemic influenza: some logistical constraints

Abstract

Disease control programmes for an influenza pandemic will rely initially on the deployment of antiviral drugs such as Tamiflu, until a vaccine becomes available. However, such control programmes may be severely hampered by logistical constraints such as a finite stockpile of drugs and a limit on the distribution rate. We study the effects of such constraints using a compartmental modelling approach. We find that the most aggressive possible antiviral programme minimizes the final epidemic size, even if this should lead to premature stockpile run-out. Moreover, if the basic reproductive number R(0) is not too high, such a policy can avoid run-out altogether. However, where run-out would occur, such benefits must be weighed against the possibility of a higher epidemic peak than if a more conservative policy were followed. Where there is a maximum number of treatment courses that can be dispensed per day, reflecting a manpower limit on antiviral distribution, our results suggest that such a constraint is unlikely to have a significant impact (i.e. increasing the final epidemic size by more than 10%), as long as drug courses sufficient to treat at least 6% of the population can be dispensed per day.

Figure 1

Summary of the basic model, where f=β(I_T+I_N). A proportion α of infected cases receive treatment (class I_T) and recover in 1/γ_T days. The remainder of infected cases (class I_N) recover in 1/γ_N days, where γ_T>γ_N.

Figure 2

Plots of AV usage U (or minimum required stockpile) versus coverage α, for different values of R₀.

Figure 3

Illustration of different run-out scenarios. (a) Stockpile of 10% and R₀=1.5. There are precisely two values of AV coverage, marked α₁ and α₂, such that U(α)=M. Run-out may be avoided by α<α₁ or by α>α₂. (b) Stockpile of 30% and R₀=2, 3. Here R₀ is sufficiently large for the antiviral usage U(α) to be monotonically increasing with respect to α. Run-out can be avoided only by a sufficiently low AV coverage.

Figure 4

Attack rate versus AV coverage α. For R₀=1.5 and a stockpile M=0.1.

Figure 5

Numerical plots of epidemic peak properties, where prevalence is I_T+I_N. The ‘kinks’ in both plots arise because, for sufficiently high α, the epidemic peak occurs after run-out. Parameters: γ_T=0.4, γ_N=0.25, M=0.2 and R₀=0.25. (a) Peak height and (b) peak timing.

Figure 6

Schematic illustration of the extended model, where $f={\beta }_{\text{CT}}{I}_{\text{CT}}+{\beta }_{\text{CN}}{I}_{\text{CN}}+{\beta }_{\text{N}}(L_2+L_2^{\prime }+I_{\text{AN}})$.

Figure 7

Numerical plots of epidemic peak properties for the extended model, measuring I_CT+I_CN. The ‘kinks’ arise because, for sufficiently high α, the peak occurs after run-out. (a) Peak height versus AV coverage. In the run-out range (α>0.32), peak height is an increasing function of α. (b) Peak timing in days versus AV coverage. Parameters: p=0.67, σ=σ′=1/1.2, δ=δ′=1/0.7, γ_T=0.4, γ_N=0.25, β_CT=0.3, β_CN=0.6, β_N=0.39, M=0.1 and R₀=2.5.

Figure 8

(a) Calculated attack rate versus distribution capacity C, for different values of α₀. (b) Prevalence versus time under a limited distribution capacity, α₀=0.6, for different values of C. Parameters: γ_N=0.25, γ_T=0.4 and R₀=2.

Figure 9

Minimum required distribution capacity C_fail, to ensure that attack rate is within 10% of the case of unlimited distribution capacity, versus R₀, for different values of γ_T. The ‘termination’ of each curve is where R₀ is sufficiently high that the percentage difference in attack rate between even the two most extreme cases, C=0 and C→∞, is less than 10%. γ_N=0.25.