Epidemiological consequences of household-based antiviral prophylaxis for pandemic influenza

General behaviour of antivirals. Household basic reproduction number, R_*, and doubling time early in the pandemic, T_d, as a function of the mean delay to antiviral allocation for the SEEIIR model. The mean delay is taken as the time from the first infectious case to when antivirals take effect. This is composed of notification and further allocation delay. (a,c) SEEIIR with constant and exponential delay. (b,d) SEEIIR with notification (σ = 1). Dashed and solid lines are from the constant and exponential delay models, respectively, for three values of σ, where 1/σ is the average exposed period. (b) The coloured lines show the model results with notification for σ = 1. Black dashed and solid lines are constant and exponential delay models, respectively. The coloured curves end at minimum delay possible for a given value of the notification rate, r_n. (c,d) The doubling time, using the same colour scheme. Other parameters: k = 3, β_k = 2, α = 1, γ = 1, τ = 0.8 and ρ = 0.8. All rates are given in terms of days^–1. (a,c) Blue lines, σ = 50; green lines, σ = 1; red lines, σ = 0.5. (b,d) Blue lines, r_n = 10; green lines, r_n = 1; red lines, r_n = 0.2.

The reduction in transmission needed to reduce the household reproductive ratio, R_* < 1, for different household size distributions. (a–c) Three household size distributions for (a) UK 2001, (b) Indonesia 2003 and (c) Sudan 1990. The values of R_* for an uncontrolled epidemic are 2.3, 3.4 and 4.7 for the distributions (a–c), respectively. (d) The minimum value of the antiviral efficacy, τ, and the maximum mean delay to reduce R_* = 1 for the three distributions (a–c). The dashed lines are for the model assuming constant delay and solid lines are for the exponential delay (green, UK; blue, Indonesia; red, Sudan). Other parameters: β_k = 2, α = 1, γ = 1, σ = 1 and ρ = 0.8. All rates are given in terms of days^–1.

Pandemic influenza parameter estimates. (a(i–vii)) Kernel density plots for the within-household transmission rate, β_k, from 10 000 random samples from the posterior distributions given in [24]; (c) 2000 (randomly selected from the 10 000) random samples for the posterior distribution for the infectious and latent period parameters, γ and σ, estimated by fitting to the serial interval data (b); points are coloured according to their likelihood value as per the scale on the right. (d,e) The posteriors for the reduction in transmission, τ, (for both zanamivir (blue) and oseltamivir (green)) and the reduction in susceptibility, ρ.

Pandemic model results for the exponentially delayed model. (a,b) Kernel density plots for the household reproductive ratio, R_*, as a function of the mean delay to allocation for the two types of antivirals oseltamivir and zanamivir. Solid and dashed white curves in (a) and (b) mark the mean and the 95% credible intervals of these distributions, respectively. (c,d) The doubling time, T_d, as a function of the mean delay for oseltamivir and zanamivir, respectively. Black lines show the mean, and dashed red and blue lines show the 50% and 95% credible intervals, respectively.

Pandemic model results for the constant delay model. (a,b) Kernel density plots for the household reproductive ratio, R_*, as a function of the mean delay to allocation for the two types of antivirals oseltamivir and zanamivir. Solid and dashed white curves in (a) and (b) mark the mean and the 95% credible intervals of these distributions, respectively. (c,d) The doubling time, T_d, as a function of the mean delay for oseltamivir and zanamivir, respectively. Black lines show the mean, and dashed red and blue lines show the 50% and 95% credible intervals, respectively.