Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 9: Statistical physics in biological systems

DY 9.6: Vortrag

Montag, 26. März 2007, 17:45–18:00, H3

The role of commuting in spread of infectious diseases — •Vitaly Belik and Dirk Brockmann — MPI für Dynamik und Selbstorganisation, Göttingen, FRG

Numerous spreading phenomena in population dynamic and ecological systems are successfully accounted for by the Fischer-Kolmogorov-Petrovsky-Piskunov (FKPP) equation. This equation can be derived on the assumption of diffusive dispersal of the reacting species. In epidemiological systems however, host individuals often perform commuting movements between their habitat and its surrounding. For instance, humans travel back and forth between their homes and their place of work day by day, and infectious diseases spread indirectly by a combination of transmission between and commuting of host individuals. Incorporating bidirectional transport of the host we develop a mean field discription for wave propagation that is structurally different from the ordinary FKPP equation, i.e. the diffusion and nonlinear logistic growth term do not decouple. We find that the velocity of the wave front is approximately proportional to the infection rate, unlike the square root dependence of the ordinary FKPP equation. For systems with high reaction rates, this implies a much faster spread of the infection as compared to common FKPP dynamics. On the other hand, the front shape exhibits a significantly smaller dependence on the infection rate. We conclude that spreading phenomena which are triggered by commuting movements of the host can spread much faster than those carried by diffusing agents, a result of particular importance for human infectious disease dynamics.