Dynamics of Modern Epidemics

I will discuss the geographical spread of infectious diseases in a modern world in which humans travel on all scales. As an appetizer I will present a model for the geographical spread of the Severe Acute Respiratory Syndrome (SARS) on the entire civil aviation network and show that this network can be employed to identity endangered regions of future epidemics.

I will show that scale free dispersal is linked to a class of random walks known as Levy flights which leads to a description in terms of fractional reaction-dispersal equations which exhibit dynamics vastly different from ordinary reaction diffusion systems.