Synchrony, waves, and spatial hierarchies in the spread of influenza.

Quantifying long-range dissemination of infectious diseases is a key issue in their dynamics and control. Here, we use influenza-related mortality data to analyze the between-state progression of interpandemic influenza in the United States over the past 30 years. Outbreaks show hierarchical spatial spread evidenced by higher pairwise synchrony between more populous states. Seasons with higher influenza mortality are associated with higher disease transmission and more rapid spread than are mild ones. The regional spread of infection correlates more closely with rates of movement of people to and from their workplaces (workflows) than with geographical distance. Workflows are described in turn by a gravity model, with a rapid decay of commuting up to around 100 km and a long tail of rare longer range flow. A simple epidemiological model, based on the gravity formulation, captures the observed increase of influenza spatial synchrony with transmissibility; high transmission allows influenza to spread rapidly beyond local spatial constraints.