An epidemic model is formulated by a reactionâeuro"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.