Press Portal

The Hidden Geometry of Global Contagion

New mathematical theory for the global spread of epidemics

Scientists at Berlin’s Humboldt-Universität, ETH Zurich, Northwestern University and Robert Koch Institute develop a new mathematical theory for the global spread of epidemics. Insights cannot only facilitate finding an outbreak’s origin, but may significantly improve the forecast of global spreading pathways. The results of the study “The hidden geometry of complex, network-driven contagion phenomena” have recently been published in the journal Science.

When an unknown virus emerges at various locations in the world, scientists focus on answering the following questions: Where did the new disease originate? Where are new cases to be expected? When are they expected? And how many people will catch the disease? In order to contain the further spread – and potentially devastating consequences – rapid assessment is essential for the development of efficient mitigation strategies. Highly sophisticated computer simulations are an important tool for forecasting different scenarios: These simulations attempt to predict the likely epidemic time-course and spreading pattern. However, the computer simulations are very demanding in terms of computer time. They also require knowledge of disease-specific parameters that are typically not known for new, emergent infectious diseases.

Theoretical physicist Dirk Brockmann, Professor at Berlin’s Humboldt-Universität, and his fellow scientist Dirk Helbing, Professor at ETH Zurich, now propose a different approach for understanding global disease dynamics:  “Our theory is based on the intuitive notion that in our strongly connected world, conventional geographic distances are no longer the key variable but must be replaced with effective distances,” they explain. “From the perspective of Frankfurt, Germany, other metropolitan areas such as London, New York or Tokyo are effectively not more distant than geographically close German cities such as Bremen, Leipzig or Kiel,” says Brockmann, who developed the ideas for this research at the Northwestern Institute on Complex Systems. In their work, the researchers show that effective distances can be computed from the traffic intensities in the worldwide air-transportation network: “If the flux of passengers from A to B is large, the effective distance is small and vice versa. The only thing we had to do was to find the right mathematical formula for this,” Helbing explains.

With this type of mathematical foundation Brockmann and Helbing can now visualize the geographic spread of past diseases, such as SARS in 2003, or influenza H1N1 in 2009. Formerly complex dynamic patterns with no apparent structure thus turn into simple, concentric and regular wave patterns. These patterns can be easily captured mathematically. “With this new theory, we can reconstruct outbreak origins with higher confidence, compute epidemic spreading speed and forecast when an epidemic wave front is to arrive at any location worldwide. This may help to improve possible mitigation strategies,” Brockmann says.

“In the future, we hope that our approach can substantially improve existing, state-of-the-art models for disease spread,” Brockmann says. Helbing adds: “We believe that our theory will also help to better understand other important contagion phenomena, such as the spread of computer viruses, information and fads, or contagion phenomena in social networks.”


Dirk Brockmann and Dirk Helbing: The hidden geometry of complex, network-driven contagion phenomena. Science, 13 December (2013).

Further Information


Prof. Dr. Dirk Brockmann
Department of Biology
Humboldt-Universität zu Berlin

Phone: +49 30 2093-8383
Twitter: @DirkBrockman