Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 5: Statistical physics in biological systems (joint session DY/BP)
DY 5.8: Vortrag
Montag, 25. Februar 2008, 16:15–16:30, MA 001
The effects of bidirectional host movements on infectious disease dynamics — •Vitaly Belik1, Benjamin Schwenker1, Theo Geisel1,2, and Dirk Brockmann1,3 — 1MPI for Dynamics and Self-Organization, Göttingen — 2Georg-August-University, Göttingen — 3Northwestern University, Evanston IL, USA
Reaction-Diffusion equations such of the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type are widely applied in the context of spatial dynamics of directly transmitted diseases. This ansatz assumes that host individuals perform random walks or diffuse in space. Although this approach may find applications for animal host systems, its validity must be questioned for human infectious diseases. Although humans visit various places, they subsequently return to their abode thus performing bidirection movements on starlike topologies. Ordinary reaction and diffusion models are therefore not adequate for description of human spatial disease dynamics. We propose a stochastic model in which individuals can travel between their home and distant locations. We establish a link between explicit travel behavior of individuals and effective coupling among populations. We derive and analyze corresponding mean-field equations for the epidemic spread, which are structurally different from FKPP equation, e.g. diffusion and reaction are no longer uncoupled. The dependence of the front speed of the epidemic wave on the travelling rate is bounded from above, contrary to the common reaction-diffusion case, where it can attain any value. Our analysis is supported by agent based simulation of the full stochastic model.