Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
838082 | Nonlinear Analysis: Real World Applications | 2011 | 16 Pages |
Abstract
An epidemic model is formulated by a reaction–diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Stefan Berres, Ricardo Ruiz-Baier,