Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza

doi:10.1126/science.1125237

Account Information

Guest Alerts | Access Rights | My Account | Sign In

Site Navigation

Article Views

VERSION HISTORY

312/5772/447 (most recent)
1125237v1

Article Tools

My Science

More Information

Related Jobs from ScienceCareers

Medicine

Originally published in Science Express on 30 March 2006
Science 21 April 2006:
Vol. 312. no. 5772, pp. 447 - 451
DOI: 10.1126/science.1125237

Prev | Table of Contents | Next

Reports

Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza

Cécile Viboud¹^*, Ottar N. Bjørnstad¹^,2^,3, David L. Smith¹, Lone Simonsen⁴, Mark A. Miller¹ and Bryan T. Grenfell¹^,3

¹ Fogarty International Center, National Institutes of Health, Bethesda, MD 20892, USA.
² Department of Entomology, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
³ Center for Infectious Disease Dynamics, Department of Biology, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
⁴ National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD 20818, USA.

Fig. 1. Weekly epidemic time series. (A) Death rates from pneumonia and influenza (P&I) in the United States (excluding Hawaii and Alaska) and each of the four administrative regions (Northeast, Midwest, South, and West). Deaths are shown per 100,000 population on a log10 scale. (B and C) Death rates in excess attributed to influenza in the United States (B) and by state as a color intensity plot (C). Rates are normalized to have zero mean and unit variance. (C) The 49 "states" are arranged by decreasing population sizes (from top = California to bottom = Wyoming). Vertical bands in red correspond to synchronized epidemics, which occur in the most populated states or during larger epidemics, suggesting that synchrony increases with population size and epidemic size. (See also fig. S1.) [View Larger Version of this Image (48K GIF file)]

Fig. 2. Patterns of influenza spread and geographical distance, population sizes, and circulating viruses. (A and B) Geographical distance. Synchrony in timing and seasonal amplitude of epidemics (y axis) is measured by pairwise correlation between states in weekly phases (A) and seasonal excess deaths attributed to influenza (B). Synchrony function (red curve) and 95% confidence bands (black curves) are presented along with the global countrywide synchrony (horizontal red line). See also fig. S3A. (C and D) Population sizes. Synchrony as a function of the product of population sizes for each pair of states (49 states, n = 1176 pairs). States are classified into four categories corresponding to the quartiles of the distribution of population sizes (from low to high, Q1 to Q4). Boxes represent the interquartile range of the synchrony distribution. (C) Pairwise correlation in weekly phases. (D) Pairwise correlation in weekly death rates. (E) Circulating virus. Epidemics associated with high mortality impact, generally dominated by A/H3N2 viruses, spread more quickly than mild ones. Spread is measured by the standard deviation (SD in weeks, y axis) of the difference in the timing of epidemic peaks between national and local P&I mortality time series. National mortality impact (x axis) is measured as seasonal P&I excess death rates per 100,000 population for the whole United States, 1972 to 2002 (30 seasons). Epidemics are classified according to the predominant viral subtype in the United States (green dots: A/H1N1 or B; red dots: A/H3N2). Gray line: linear fit, R² = 0.72, P < 0.0001. [View Larger Version of this Image (22K GIF file)]

Fig. 3. Influenza spread and workflows. (A) Gray dots represent the observed phase synchrony in influenza epidemics (y axis) plotted against the total number of individuals commuting between each (pair of) states (x axis, log10 scale). Superimposed is the best fit statistical model (spline, red curve) and 95% confidence intervals (CI, blue curve). (B) Relationship between total workflows (z axis), population sizes (y axis), and distance (x axis) as in the gravity framework. The spatial unit in (B) is the county. (See also fig. S4.) [View Larger Version of this Image (25K GIF file)]

Fig. 4. Simulated spread of influenza by a gravity model based on work movements, for epidemics originating in California or Wyoming. (A) Synchrony and geographical extent of epidemics increases with higher transmission. Transmission is manipulated through the reproduction ratio, R (x axis). Epidemics originating in California (filled symbols), a highly populated and connected state, are more synchronous and widespread than those originating in Wyoming, the least populated state (open symbols). Synchrony is measured by the inverse of the variance in dates of epidemic onsets (in weeks) in the 49 continental U.S. states (red triangles, right y axis). The probability of having a widespread epidemic, where infection has reached all 49 states, is represented by black circles (left y axis). Coupling between states follows a gravity model, fitted to work movement data (12). Results are based on 1000 simulations; 95% confidence intervals are ± 5% of indicated values. (B to D) Maps of simulated spread out of California or Wyoming for epidemic seasons [(B and C), intermediate R = 1.35] and pandemic seasons [(D), R = 1.89, as in the 1968 pandemic (6)]. The background in grayscale indicates county population sizes [from light gray (<1,000 inhabitants) to dark gray (>400,000)]. Filled black circles represent the location of initial cases. Arrows indicate the source of infection for individual states; arrows originate from, and point to, a state population center. Arrows are color coded, based on the date of epidemic onset in individual states, from black = early onset to green = late onset; see color bar. [View Larger Version of this Image (57K GIF file)]