Urbanization and humidity shape the intensity of influenza epidemics in U.S. cities

Abstract

Influenza epidemics vary in intensity from year to year, driven by climatic conditions and by viral antigenic evolution. However, important spatial variation remains unexplained. Here we show predictable differences in influenza incidence among cities, driven by population size and structure. Weekly incidence data from 603 cities in the United States reveal that epidemics in smaller cities are focused on shorter periods of the influenza season, whereas in larger cities, incidence is more diffuse. Base transmission potential estimated from city-level incidence data is positively correlated with population size and with spatiotemporal organization in population density, indicating a milder response to climate forcing in metropolises. This suggests that urban centers incubate critical chains of transmission outside of peak climatic conditions, altering the spatiotemporal geometry of herd immunity.

Fig. 1

Systematic differences among U.S. cities in the intensity of seasonal influenza epidemics. (A to C) Differences among cities in epidemic intensity are preserved across years, indicated by comparing the temporal dynamics of the cities with the highest and lowest average intensity. Points show means, vertical lines show interquartile ranges, and polygons enclose the central 95% of ILI incidence data that have been corrected for intercity variation in background incidence and reporting, by linear transformation of each city’s time series to have minimum 0 and a common total attack rate over the 6-year period. (D to F) Cities with higher mean intensity tend to be located in the east, have smaller population sizes, and have higher-amplitude seasonal fluctuations in specific humidity. In (F), the vertical axis is standard deviation (SD) and the labeled points are Atlanta (A) and Miami (M).

Fig. 2

Increasing base transmission potential can decrease epidemic intensity in a seasonally forced compartmental epidemic model. (A) Diagram of a susceptible-exposedinfected- removed-susceptible (SEIRS) model. The seasonally varying transmission rate β depends on specific humidity q and the base transmission potential of the population, κ. See materials and methods for details. (B) Diagram of transmission in two hypothetical populations. Points represent individual hosts and yellow lines show transmission events. In populations with higher base connectivity, chains of transmission are longer during the early influenza season, when climatic conditions are not yet ideal for wider spread. (C) Simulations of the model for two levels of base transmission (red and blue lines), which yield corresponding variation in epidemic intensity. (D) Incidence distributions in U.S. three-digit ZIP codes (e.g., Atlanta and Manhattan) show comparable variation in epidemic intensity, and also evidence of seasonal variation in transmission rates and reporting, which are included in the model during fitting (Fig. 3; materials and methods).

Fig. 3

Base transmission potential and specific humidity predict observed differences in the intensity of influenza epidemics across U.S. cities. (A and B) n-step ahead simulation performance of the fitted SEIRS model, 1 < n < 303 weeks, in two cities. (C) Observed versus forward simulated average epidemic intensity in all cities. (D) Observed and simulated incidence in all cities and years. (E) Larger cities have more organized spatial population distributions and mobility patterns. Gray points show expected population size in a randomly selected census block in each city; colored points show expected block-level population size experienced by a randomly selected individual in each city [Lloyd’s mean crowding $\text{m}*=\overline{m}+\frac{{\sigma }_{\overline{m}}^2}{\overline{m}}-1$, where $(\overline{m})$ represents mean population size in a census block, and ${\sigma }_m^2$ variance in population size across census blocks (31, 39)]. Mean crowding increases above mean block-level population size as spatial locations of individuals become more highly organized. (F) Population size and crowding estimated from census data predict base transmission potential estimated from ILI incidence data. Blue line shows fit for population size alone; yellow line, population size and crowding. Polygons enclose 1 SE around the fitted curves. Yellow points show the 20 cities with the most residential crowding. (G) Information-theoretic comparison of population size, climatic fluctuations, and fitted base transmission potential (i.e., base transmission potential predicted from population size and crowding rather than fitted to the incidence data) as predictors of observed epidemic intensity, via generalized linear models.