# Dresden 2006 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 41: Dynamical Physics in Biological Systems

### DY 41.6: Vortrag

### Donnerstag, 30. März 2006, 11:15–11:30, SCH 251

**Dynamics of epidemic outbreaks in heterogeneous populations** — •Alejandro Morales Gallardo, Dirk Brockmann, Lars Hufnagel, and Theo Geisel — MPI for Dynamics and Self-Organization, Göttingen, Germany

The dynamics of epidemic outbreaks have been investigated in recent years within two alternative theoretical paradigms. Among the most successful models is the deterministic susceptible-infected-recovered (SIR) model which approximately describes the dynamics for a large number of individuals and in which homogeneous contact rates are assumed. The central parameter of the SIR model is the basic reproduction number, the average number of secondary infections caused by one infected individal. Recently, scale free network models have received much attention as they account for the high variability in the number of social contacts involved. These models predict an infinite basic reproduction number in some cases. We investigate the impact of heterogeneities of contact rates in a generic model for epidemic outbreaks. In constrast to common static network models we investigate a system in which both the time periods of being infectious and the time periods between transmissions are Poissonian processes. The heterogeneities are introduced by means of strongly variable contact rates which yield power laws in the number of overall contacts. In contrast to scale free network models we observe a finite basic reproduction number and, counterintuitively a smaller overall epidemic outbreak as compared to the homogeneous system. Our study thus reveals that heterogeneities in contact rates does not facilitate the spread to infectious disease but rather attenuates it.