A Diffusion Approximation for an Epidemic Model

Influenza is one of the most common and severe diseases worldwide.
Devastating epidemics actuated by a new subtype of the influenza A
virus occur again and again with the most important example given
by the Spanish Flu in 1918/19 with more than 27 million deaths. For
the development of pandemic plans it is essential to understand the
character of the dissemination of the disease. We employ an
extended SIR model for a probabilistic analysis of the
spatio-temporal spread of influenza in Germany. The inhomogeneous
mixing of the population is taken into account by the introduction
of a network of subregions, connected according to Germany's
commuter and domestic air traffic. The infection dynamics is
described by a multivariate diffusion process, the discussion of
which is a major part of this report. We furthermore present
likelihood-based estimates of the model parameters.