Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 29: Statistical physics of complex networks

DY 29.2: Talk

Friday, March 27, 2009, 10:30–10:45, ZEU 255

The hierarchical system of PDE and a diffusive anomalous spread in media with multiscale connections — •Eugene Postnikov — Kursk State University, Kursk, Russia

Recently, there exists a large variety of real-world problems, which require mathematical methods for the modeling of diffusion in a strongly disordered complex environment. For example, description of human and animal mobility [González et al, 2008] as well as spread of information and diseases [Brockmann et al, 2006].

It has been shown [Naether, Postnikov, Sokolov, 2008] that realistic asymmetric Kendall waves of an SIR epidemic spread along a population with small mobility can be described with the PDE system, which contains the specific combination of infected individuals density and its Laplacian multiplied by the characteristic habitat size.

In the present contribution, the further development of this approach is presented. To model a spread in a hierarchical metapopulation, the unique “size coefficient” for diffusion term is replaced with the progressive set of values.

It has been shown that such an approach allows to reproduce the anomalous relaxation in the small world networks (with comparison with the direct simulation [Sokolov et al, 2000]) and some properties of anomalous human mobility patterns citied above.