Communicated by G. Balakrish Nair, International Centre for Diarrhoeal Disease Research Bangladesh, Dhaka, Bangladesh, February 16, 2006 (received for review January 10, 2006)
Two simulated pandemic influenza outbreaks with R 0 = 1.9, initiated by the daily entry of a small number of infected individuals through 14 major international airports in the continental U.S. (beginning on day 0). The tract-level prevalence of symptomatic cases at any point in time is indicated on a logarithmic color scale, from 0.03% (green) to 3% (red) of the population. No mitigation strategies are used in the baseline simulation (Left), resulting in a 43.5% attack rate. (Right) A 60% TAP intervention begins at day 31, or 7 days after the pandemic alert. At day 99, the nationwide supply of 20 million antiviral courses is exhausted, leading to a nationwide pandemic.
Epidemic curves (note the logarithmic scale) demonstrating the effectiveness of several different mitigation strategies, as compared to the baseline scenario without any intervention, for different values of R 0. See Table 2 for details of each intervention. In the case of vaccination, results shown here are for a uniform coverage of the entire population with a single-dose regimen.
Characteristics of simulated pandemic influenza in the U.S. in the absence of interventions
| Basic reproductive number, R 0 | 1.6 | 1.9 | 2.1 | 2.4 |
| Rate of spread: 1,000th ill person* | 14 | 13 | 12 | 11 |
| 10,000th ill person* | 29 | 24 | 22 | 19 |
| 100,000th ill person* | 48 | 37 | 34 | 29 |
| 1,000,000th ill person* | 70 | 52 | 46 | 39 |
| Peak of epidemic* | 117 | 85 | 75 | 64 |
| Daily number of new cases at peak activity | 2.3 M | 4.5 M | 6.0 M | 7.9 M |
| Number of days with >100,000 new cases | 86 | 68 | 60 | 52 |
| Cumulative number of ill persons | 92 M | 122 M | 136 M | 151 M |
M, million.
↵*Days after initial introduction.
Simulated mean number of ill people (cumulative incidence per 100) and for TAP, the number of antiviral courses required for various interventions and R 0
| Intervention | R0 = 1.6 | R0 = 1.9 | R0 = 2.1 | R0 = 2.4 |
|---|---|---|---|---|
| Baseline (no intervention) | 32.6 | 43.5 | 48.5 | 53.7 |
| Unlimited TAP (no. of courses)* | 0.06 (2.8 M) | 4.3 (182 M) | 12.2 (418 M) | 19.3 (530 M) |
| Dynamic vaccination (one-dose regimen) † , ‡ | 0.7 | 17.7 | 30.1 | 41.1 |
| Dynamic child-first vaccination † , ‡ | 0.04 | 2.8 | 16.3 | 35.3 |
| Dynamic vaccination (two-dose regimen) ‡ , § | 3.2 | 33.8 | 41.1 | 48.5 |
| Dynamic child-first vaccination ‡ , § | 0.9 | 25.1 | 37.2 | 47.3 |
| School closure ¶ | 1.0 | 29.3 | 37.9 | 46.4 |
| Local social distancing ¶ | 25.1 | 39.2 | 44.6 | 50.3 |
| Travel restrictions during entire simulation ‖ | 32.8 | 44.0 | 48.9 | 54.1 |
| Local social distancing and travel restictions ¶ , ‖ | 19.6 | 39.3 | 44.7 | 50.5 |
| TAP,* school closure,** and social distancing** | 0.02 (0.6 M) | 0.07 (1.6 M) | 0.14 (3.3 M) | 2.8 †† (20 M) |
| Dynamic vaccination, † , ‡ social distancing,¶ travel restrictions,¶‖ and school closure** | 0.04 | 0.2 | 0.6 | 4.5 |
| TAP,* dynamic vaccination, † , ‡ social distancing, ¶ travel restrictions,¶‖ and school closure** | 0.02 (0.3 M) | 0.03 (0.7 M) | 0.06 (1.4 M) | 0.1 (3.0 M) |
| Dynamic child-first vaccination, † , ‡ social distancing, ¶ s travel restrictions, ¶ , ‖ and school closure** | 0.02 | 0.2 | 0.9 | 7.7 |
M, million.
↵*60% TAP, 7 days after pandemic alert, antiviral supply of 20 M courses unless stated.
↵ †10 million doses of a low-efficacy vaccine (single-dose regimen) per week.
↵ ‡Intervention continues for 25 weeks, beginning such that the first individuals treated develop an immune response on the date of the first U.S. introduction.
↵ §10 million doses of a high-efficacy vaccine (two-dose regimen) per week.
↵ ¶Intervention starting 7 days after pandemic alert.
↵ ‖Reduction in long-distance travel, to 10% of normal frequency.
↵**Intervention starting 14 days after pandemic alert.
↵ ††Exhausted the available supply of 20 M antiviral courses.
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Germann et al. 10.1073/pnas.0601266103. |
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Fig. 3. (a) Example of the calculation of the daily probability that a susceptible individual (blue) will become infected, due to infectious people (red) in various contact groups. For clarity, only the four household members and infectious contacts are shown; in general, each person may potentially come into contact with as many as 4,000 persons each day (2,000 each at their daytime and nighttime community locations). (b) Modeled natural history of influenza. Newly infected people pass through an incubation stage lasting from 1 to 3 days, slightly longer than the latent period during which they are completely noninfectious. Following the incubation period, we assume that 67% of infected people develop clinical symptoms, while 33% are asymptomatic and only half as infectious (the same as during the last day of the incubation period). Antiviral treatment is assumed to reduce both the likelihood of developing symptoms if infected and the infectious period by 1 day. Antivirals and vaccines can both reduce the infectiousness and susceptibility of infected and uninfected people, respectively.
Fig. 4. Illness attack rate for the different age groups as a function of transmission probability for the model community. For transmission probabilities 0.1, 0.12, 0.15, 0.17, and 0.2, the total illness attack rates are 23%, 34%, 44.5%, 49%, and 54%, respectively. The values are given for an ensemble of 500 isolated communities, each with 12 initial randomly infected persons. There is a one-to-one correspondence between transmission probabilities and R0 values; the transmission probabilities used in the present study are indicated by arrows, together with the corresponding R0 values as calculated by the slope of the cumulative number of cases (see Table 7).
Fig. 5. (a) Distribution of census tract populations. (b) Distribution of the distance between tract centers in the U.S. tract-to-tract worker flow data. Travel distances 100 miles or less are assumed to be daily commutes between home and work, while longer distances are neglected.
Fig. 6. The basic reproductive number (R0) for pandemic influenza, calculated by introducing one random infected person into a fully susceptible population in which no other person is able to transmit infection. This is repeated for 128,000 stochastic realizations, and the number of secondary cases is counted for each realization. The frequency distribution is shown here, which produces the overall average, R0 = 1.77 for a transmission probability Ptrans = 0.12. As seen in Table 7, the estimated R0 is increased by 5–8% by taking into account an attack rate weighted index case or estimating R0 by the slope of the cumulative number of cases, respectively.
Fig. 7. (Upper) The reproductive number R as a function of time for different transmission probabilities for simulations of the whole nation seeded at the beginning with 8 infected persons per 10,000 daily international passengers at the 14 major hubs. The full lines are values based on the local slope, whereas the open circles are based on slope averages starting at day 30. The initial reproductive number is enhanced due to the fact that school-age children, who have a higher reproductive number, are hit earliest (see Table 7 and bottom panel). (Lower) The age-specific cumulative attack rate normalized by the overall cumulative attack rate during the course of an epidemic in an ensemble of 500 isolated communities initially seeded with 12 random index cases. The transmission probability is 0.12, corresponding to R0 = 1.6. It can be seen that school-age children become ill first, which boosts the overall R0 for »20 days, since the reproductive number for this age group is larger than for all other age groups (see Table 7).
Fig. 8. (a) Effect of seeding rate (number of infecteds per 10,000 daily international passengers at 14 major international airports) and of a static seeding on only day 0 versus a continual seeding every day of the 180-day simulation, on the resulting epidemic curves (for R0 = 1.9). In all simulations, the cumulative attack rate is 43.53%, with the seeding rate only affecting the timing of the epidemic peak. (b) Epidemic curves for various one-time introductions of infecteds on day 0, either of 76 infected people at 14 major airports (the same static seeding simulation shown in the top panel) or of 40 infected people either on the East Coast (New York County) or on the West Coast (Los Angeles County), for pandemic influenza with R0 = 1.9. Also shown for the Los Angeles seeding are three different travel reductions, to either 10% or 1% of the normal long-range travel frequency during the entire 180-day simulation, or to 1% only after the pandemic alert threshold of 10,000 cumulative ill is reached on day 38.
Fig. 9. Spatiotemporal spread of a national epidemic (for R0 = 1.9), starting with 40 infectious people on day 0 in either New York County (left column) or Los Angeles County (right column). Snapshots are shown at day 60, 80, 100, and 120 (from top to bottom), and the corresponding nationally averaged epidemic curves are in Fig. 8.
Fig. 10. (a) Effect of delays in vaccine production and distribution on the cumulative attack rates, 180 days after the initial introduction of pandemic influenza (with R0 = 1.6) into the U.S. A production rate of 10 million doses per week is assumed, ending when a total of 250 million doses have been distributed. A single dose per person is assumed to confer a low efficacy response, and two doses a higher efficacy; for this production rate and limit the vaccination of twice as many people with a lower efficacy is preferred. (b) Effect of delays in implementing a 60% TAP intervention on the resulting cumulative attack rate and number of antiviral courses consumed, 180 days after the initial introduction of pandemic influenza (with R0 = 1.9) into the U.S. Shown is a comparison of a standing TAP policy (in place on day 0) with postalert interventions beginning 1, 4, 7, 10, and 14 days after the pandemic alert threshold 10,000 cumulative ill is reached on day 24. (Solid curves are quadratic polynomial fits to the data points.)
Fig. 11. Epidemic curves for R0 = 1.9 and 2.4, for the baseline scenario without any intervention and with long-distance travel reduced to 10% and 1% of the usual frequency throughout the entire simulation.
Movie 1. Baseline scenario, without any intervention.
Movie 2. Baseline (top) compared to a 60% TAP intervention initiated 7 days after pandemic threshold is reached and continuing until the national supply of 20 million antiviral courses is exhausted. Frames from this movie are shown in Fig. 1.
Movie 3. Baseline (top) compared to a dynamic production and distribution of 10 million doses of a low-efficacy vaccine (single-dose regimen) per week for 25 weeks, beginning such that the first persons treated develop an immune response on the date of the first U.S. introduction.
Movie 4. Baseline (top) compared to a 90% reduction in long-range travel, beginning 1 day after the pandemic threshold is reached and continuing throughout the remainder of the simulation.
