Critical paths in a metapopulation model of H1N1: Efficiently delaying influenza spreading through flight cancellation

Abstract

Disease spreading through human travel networks has been a topic of great interest in recent years, as witnessed during outbreaks of influenza A (H1N1) or SARS pandemics. One way to stop spreading over the airline network are travel restrictions for major airports or network hubs based on the total number of passengers of an airport. Here, we test alternative strategies using edge removal, cancelling targeted flight connections rather than restricting traffic for network hubs, for controlling spreading over the airline network. We employ a SEIR metapopulation model that takes into account the population of cities, simulates infection within cities and across the network of the top 500 airports, and tests different flight cancellation methods for limiting the course of infection. The time required to spread an infection globally, as simulated by a stochastic global spreading model was used to rank the candidate control strategies. The model includes both local spreading dynamics at the level of populations and long-range connectivity obtained from real global airline travel data. Simulated spreading in this network showed that spreading infected 37% less individuals after cancelling a quarter of flight connections between cities, as selected by betweenness centrality. The alternative strategy of closing down whole airports causing the same number of cancelled connections only reduced infections by 18%. In conclusion, selecting highly ranked single connections between cities for cancellation was more effective, resulting in fewer individuals infected with influenza, compared to shutting down whole airports. It is also a more efficient strategy, affecting fewer passengers while producing the same reduction in infections.

(A) Spreading over the airline network with Mexico City as starting node (red)

Nodes in yellow are directly connected whereas nodes in green are airports not directly linked to the starting point. (B) Connectivity of the airline network showing four clusters. A dot in the adjacency matrix indicates the presence of a connection between two cities.

Influenza spreading for Mexico City as starting node

(A) Influenza spreading for Mexico City as starting node, measured by the number of infected individuals over time on the intact network (blue) and after removing 25% of edges by hub removal (red) or edge betweenness (green). (B) Maximum infected population following sequential edge elimination by betweenness centrality, Jaccard coefficient, difference and product of degrees and hub removal (see Methods).

Worldwide infections over time following edge removal as selected by edge betweenness centrality and Jaccard coefficient.

The two plots show results for two rewired versions of the original airline network: one preserving only the original degree distribution and another preserving both the degree distribution plus original communities. Full lines show the averaged results over 25 rewired versions of the airline network. Intact results are for the complete networks, while Jaccard and betweenness lines show the averaged results following the removal of 25% of edges as selected by each respective measure. Dotted lines show each corresponding standard deviation.