 
Summary: CHAPTER 11
Dynamics of modern epidemics
Dirk Brockmann, Lars Hufnagel, and Theo Geisel
11.1 Summary
The application of mathematical modelling to the
spread of epidemics has a long history and was
initiated by Daniel Bernoulli's work on the effect of
cowpox inoculation on the spread of smallpox in
1760 (Bernoulli 1760). While most studies con
centrate on the temporal development of diseases
and epidemics, their geographical spread is less
well understood. The key question and difficulty is
how to include spatial heterogeneities and to
quantify the dispersal of individuals (Keeling et al.
2001; Smith et al. 2002; Keeling et al. 2003; Lipsitch
et al. 2003). In a well established class of models
spatial dispersal is accounted for by ordinary
diffusion (Murray 1993). This approach admits a
description in terms of reactiondiffusion equa
tions which generically exhibit epidemic wave
