Delaying the international spread of pandemic influenza

Abstract

Background: The recent emergence of hypervirulent subtypes of avian influenza has underlined the potentially devastating effects of pandemic influenza. Were such a virus to acquire the ability to spread efficiently between humans, control would almost certainly be hampered by limited vaccine supplies unless global spread could be substantially delayed. Moreover, the large increases that have occurred in international air travel might be expected to lead to more rapid global dissemination than in previous pandemics.

Methods and findings: To evaluate the potential of local control measures and travel restrictions to impede global dissemination, we developed stochastic models of the international spread of influenza based on extensions of coupled epidemic transmission models. These models have been shown to be capable of accurately forecasting local and global spread of epidemic and pandemic influenza. We show that under most scenarios restrictions on air travel are likely to be of surprisingly little value in delaying epidemics, unless almost all travel ceases very soon after epidemics are detected.

Conclusions: Interventions to reduce local transmission of influenza are likely to be more effective at reducing the rate of global spread and less vulnerable to implementation delays than air travel restrictions. Nevertheless, under the most plausible scenarios, achievable delays are small compared with the time needed to accumulate substantial vaccine stocks.

Figure 1. Schematic Illustration of Model Structure

Figure 2. Model Fitting and Comparison by Sum of Squared Deviations

(A and B) SSQ/n values for ten runs with each combination of parameter values for two models: model 1 (black), in which transmissibility in the tropics is constant and taken as the north/south maximum; and model 2 (red), in which it is held at the north/south mean. n is the number of cities with observed peaks. The seasonal maximum R ₀ (R _0,max) is held constant at 3.0 in (A), and the seasonal minimum R ₀ (R _0,min) is held constant at 1.6 (the value giving the minimum SSQ/n for model 2) in (B). In both cases, the fraction of the population initially susceptible was fixed at 0.6. (C and D) SSQ/n values shown are the means of ten runs of the stochastic model for each combination of parameter values. Regions of parameter space supported by the data appear in green (darker green indicates better fit). A constant susceptible fraction of 0.6 is assumed in (C). R _0,min held constant at 1.2 in (D); broken lines indicate regions of the parameter space with constant effective reproduction numbers, R_max (where R_max = R_0,max× susceptible fraction).

Figure 3. Predicted and Observed Times of Influenza Activity and Epidemic Peaks in 1968/9

(A) Predicted combined incidence using baseline model assumptions (bold lines show mean incidence). (B) Observed and predicted times in individual cities. Peak times from individual simulation runs and mean peak times with 1968/9 data are shown as blue and white dots, respectively. Mean peak times that would have occurred with 2002 travel patterns are shown as yellow dots. Predictions are based on 100 simulation runs. Influenza activity was defined as at least one new symptomatic case per 100,000 people in a given week.

Figure 4. Time Course of a Pandemic with and without an Intervention to Suspend 99.9% of Air Travel from Affected Cities

Maps show the extent of epidemic spread and average impact on aviation network (taken from 100 simulation runs) 2, 5, 8, and 11 mo after the first cases on 1 June. The intervention is made after 100 cases in each city (or 1,000 cases for Hong Kong, the city of origin). Blue lines represent flights, with darker blues representing greater mean weekly passenger numbers (after accounting for interventions to suspend travel and averaging over all simulation runs). Flights are not shown when travel restrictions have been imposed by the given time in more than 95% of simulation runs. Area of circles is proportional to city population size, and shading indicates the probability of each city having experienced a major epidemic (greater than one case per 10,000 people per day) by the given time.

Figure 5. Impact of Interventions and Implementation Delays on Rate and Extent of Spread

Effect of reducing travel (A, C, E, and G) and transmission (B, D, F, and H) on the timing of major outbreaks (≥ 1 case per 10,000 per day) in 105 cities using contemporary transport and demographic data and baseline parameters. Transmission reductions are imposed in each city after one case in the given city (A and B); 100 cases (C and D); 1,000 cases (E and F); and 10,000 cases (G and H). Interventions in the originating city (Hong Kong) occur after 1,000 cases (A–F) or 10,000 cases (G and H). Lines and shaded regions show means of 100 simulation runs and ± standard deviation, respectively. In all cases, R _0,max = 3. and the proportion of the population initially susceptible is 0.6.

Figure 6. Impact of Interventions: Sensitivity to Disease Assumptions

Impact of interventions under different assumptions about how the probability of being infectious and the degree of infectiousness varies with time since infection (A–I) and with latitude (J–L). Interventions, key, and other details are as in Figure 4, except all interventions occur after 1,000 cases in Hong Kong, and 100 cases elsewhere. (A–C) Variable infectiousness (baseline daily progression and recovery probabilities, but degree of infectiousness declines sharply after day 1 since infection). Mean serial interval = 2.6 d; mean infectious period = 3.0 d; mean latent period = 1.9 d. (D–F) Reduced latent period (constant infectiousness): Mean serial interval = 3.8 d; mean infectious period = 3.4 d; mean latent period = 1.2 d. (G–I) Extended infectious period (constant infectiousness): Mean serial interval = 8.6 d; mean infectious period = 3.9 d; mean latent period = 5 d. (J–L) Baseline parameters (constant infectiousness), but transmission in the tropics set to the mean of that in the temperate region. (A, D, G, and J) Proportion of secondary transmission that occurs 0–20 d after infection. In all cases, no transmission occurs on day 0 and R _0,max = 3.