Environmental Engineering Reference
In-Depth Information
focussing on a specific predator-prey model. However, general PDEs, as given by
(
7.12
), have also been used to model bio-invasions (Shigesada and Kawasaki 1997),
epidemic spread (Brauer et al. 2008; Hilker 2005) and noise-induced pattern
formation and transitions between different spatiotemporal patterns (Sieber et al.
2007, 2010). Reaction-diffusion PDEs are also especially suitable for the modelling
of marine plankton dynamics, where small plankton particles are subject to turbu-
lent diffusion within the surrounding water column (Hilker et al. 2006; Malchow
et al. 2002, 2004, 2005). There is a rich literature for further reading on the use of
PDEs for modelling biological systems. A good overview has been provided in
Holmes et al. (1994) and Allen (2003) and a very nice and already classical
introduction to the role of diffusion processes in ecology has been given by Akira
Okubo (1980, 2001). Another recommended reading is the topic by Jim Murray
(2003), and a recent overview more focused on eco-epidemiology can be found in
Malchow et al. (2008).
