Scaling in the global spreading patterns of pandemic Influenza A (H1N1) and the role of control: empirical statistics and modeling

Background: The pandemic of influenza A (H1N1) is a serious on-going global public crisis. Understanding its spreading dynamics is of fundamental importance for both public health and scientific researches. Recent studies have focused mainly on evaluation and prediction of on-going spreading, which strongly depends on detailed information about the structure of social contacts, human traveling patterns and biological activity of virus, etc. Methodology/Principal Findings: In this work we analyzed the distributions of confirmed cases of influenza A (H1N1) in different levels and find the Zipf’s law and Heaps’ law. Similar scaling properties were also observed for severe acute respiratory syndrome (SARS) and bird cases of H5N1. We also found a hierarchical spreading pattern from countries with larger population and GDP to countries with smaller ones. We proposed a model that considers generic control effects on both the local growth and transregional transmission, without the need of the above mentioned detailed information. We studied in detail the impact of control effects and heterogeneity on the spreading dynamics in the model and showed that they are responsible for the scaling and hierarchical spreading properties observed in empirical data. Conclusions/Significance: Our analysis and modeling showed that although strict control measures for interregional travelers could delay the outbreak in the regions without local cases, the focus should be turned to local prevention after the outbreak of local cases. Target control on a few regions with the largest number of active interregional travelers can efficiently prevent the spreading. This work provided not only a deeper understanding of the generic mechanisms underlying the spread of infectious diseases, but also some practical guidelines for decision makers to adopt suitable control strategies.