Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Tuesday, 15.11.2005 16 c.t.

Dynamic of epidemic outbreaks and hierarchic synchronization in a network of cities with distributed size

by Bernd Blasius
from University of Potsdam

Contact person: Dirk Brockmann


Seminarraum Haus 2, 4. Stock (Bunsenstr.)


Recurrent epidemics of infectious childhood diseases such as measles are a major health problem and have been subject to extensive theoretical research. Here we develop a theory for the dynamics of epidemic outbreaks and their synchronization in a network of coupled cities with distributed sizes. Each city is described by a seasonally forced SEIR model. The model generates chaotic dynamics with annual and biennial dynamics in excellent agreement with long-term data sets. A new qualitative criterion based on the attractor topology is developed to distinguish between major outbreaks and epidemic fade-outs. This information is coded into a symbolic dynamics. We are able to deduce a one dimensional first return map of the chaotic SEIR equations, which upon iteration is able to generate the symbolic sequence of major outbreaks. The synchronization of epidemic outbreaks in a network of cities is defined as measure based on the symbolic dynamics. When applied to real data sets we find an excellent agreement between these spatio-temporal patterns and the results from the numerical simulation, when in the model the distribution of city sizes is taken into account. For this, we assume that the coupling strength between two interacting cities depends on the size ratio of the two cities. This, effectively gives rise to a hierarchical network topology, which translates to a hierarchic dynamics of the outbreaks.

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